Some human biases in conditional reasoning

Tracking down coding mistakes is a common developer activity (for which training is rarely provided).

Debugging code involves reasoning about differences between the actual and expected output produced by particular program input. The goal is to figure out the coding mistake, or at least narrow down the portion of code likely to contain the mistake.

Interest in human reasoning dates back to at least ancient Greece, e.g., Aristotle and his syllogisms. The study of the psychology of reasoning is very recent; the field was essentially kick-started in 1966 by the surprising results of the Wason selection task.

Debugging involves a form of deductive reasoning known as conditional reasoning. The simplest form of conditional reasoning involves an input that can take one of two states, along with an output that can take one of two states. Using coding notation, this might be written as:

    if (p) then q       if (p) then !q
    if (!p) then q      if (!p) then !q

The notation used by the researchers who run these studies is a 2×2 contingency table (or conditional matrix):

          OUTPUT
          1    0
   
      1   A    B
INPUT
      0   C    D

where: A, B, C, and D are the number of occurrences of each case; in code notation, p is the input and q the output.

The fertilizer-plant problem is an example of the kind of scenario subjects answer questions about in studies. Subjects are told that a horticultural laboratory is testing the effectiveness of 31 fertilizers on the flowering of plants; they are told the number of plants that flowered when given fertilizer (A), the number that did not flower when given fertilizer (B), the number that flowered when not given fertilizer (C), and the number that did not flower when not given any fertilizer (D). They are then asked to evaluate the effectiveness of the fertilizer on plant flowering. After the experiment, subjects are asked about any strategies they used to make judgments.

Needless to say, subjects do not make use of the available information in a way that researchers consider to be optimal, e.g., Allan’s Delta p index Delta p=P(A vert C)-P(B vert D)=A/{A+B}-C/{C+D} (sorry about the double, vert, rather than single, vertical lines).

What do we know after 40+ years of active research into this basic form of conditional reasoning?

The results consistently find, for this and other problems, that the information A is given more weight than B, which is given by weight than C, which is given more weight than D.

That information provided by A and B is given more weight than C and D is an example of a positive test strategy, a well-known human characteristic.

Various models have been proposed to ‘explain’ the relative ordering of information weighting: w(A)>w(B) > w(C) > w(D)” title=”w(A)>w(B) > w(C) > w(D)”/><a href=, e.g., that subjects have a bias towards sufficiency information compared to necessary information.

Subjects do not always analyse separate contingency tables in isolation. The term blocking is given to the situation where the predictive strength of one input is influenced by the predictive strength of another input (this process is sometimes known as the cue competition effect). Debugging is an evolutionary process, often involving multiple test inputs. I’m sure readers will be familiar with the situation where the output behavior from one input motivates a misinterpretation of the behaviour produced by a different input.

The use of logical inference is a commonly used approach to the debugging process (my suggestions that a statistical approach may at times be more effective tend to attract odd looks). Early studies of contingency reasoning were dominated by statistical models, with inferential models appearing later.

Debugging also involves causal reasoning, i.e., searching for the coding mistake that is causing the current output to be different from that expected. False beliefs about causal relationships can be a huge waste of developer time, and research on the illusion of causality investigates, among other things, how human interpretation of the information contained in contingency tables can be ‘de-biased’.

The apparently simple problem of human conditional reasoning over two variables, each having two states, has proven to be a surprisingly difficult to model. It is tempting to think that the performance of professional software developers would be closer to the ideal, compared to the typical experimental subject (e.g., psychology undergraduates or Mturk workers), but I’m not sure whether I would put money on it.

A study of deceit when reporting information in a known context

A variety of conflicting factors intrude when attempting to form an impartial estimate of the resources needed to perform a task. The customer/manager, asking for the estimate wants to hear a low value, creating business/social pressure to underestimate; overestimating increases the likelihood of completing the task within budget.

A study by Oey, Schachner and Vul investigated the strategic reasoning for deception/lying in a two-person game.

A game involved a Sender and Receiver, with the two players alternating between the roles. The game started with both subjects seeing a picture of a box containing red and blue marbles (the percentage of red marbles was either 20%, 50%, or 80%). Ten marbles were randomly selected from this ‘box’, and shown to the Sender. The Sender was asked to report to the Receiver the number of red marbles appearing in the random selection, K_{report} (there was an incentive to report higher/lower, and punishment for being caught being inaccurate). The Receiver could accept or reject the number of red balls reported by the Sender. In the actual experiment, unknown to the human subjects, one of every game’s subject pair was always played by a computer. Every subject played 100 games.

In the inflate condition: If the Receiver accepted the report, the Sender gained K_{report} points, and the Receiver gained 10-K_{report} points.

If the Receiver rejected the report, then:

  • if the Sender’s report was accurate (i.e.,K_{report} == K_{actual}), the Sender gained K_{report} points, and the Receiver gained 10-K_{report}-5 points (i.e., a -5 point penalty),
  • if the Sender’s report was not accurate, the Receiver gained 5 points, and the Sender lost 5 points.

In the deflate condition: The points awarded to the Sender was based on the number of blue balls in the sample, and the points awarded to the Received was based on the number of red balls in the sample (i.e., the Sender had in incentive to report fewer red balls).

The plot below shows the mean rate of deceit (i.e., the fraction of a subject’s reports where K_{actual} < K_{report}, averaged over all 116 subject’s mean) for a given number of red marbles actually seen by the Sender; vertical lines show one standard deviation, calculated over the mean of all subjects (code+data):

Mean rate of deceit for each number of red marbles seen, with bars showing standard deviation.

Subjects have some idea of the percentage of red/blue balls, and are aware that their opponent has a similar idea.

The wide variation in the fraction of reports where a subject reported a value greater than the number of marbles seen, is likely caused by variation in subject level of risk aversion. Some subjects may have decided to reduce effort by always accurately reporting, while others may have tried to see how much they could get away with.

The wide variation is particularly noticeable in the case of a box containing 80% red. If a Sender’s random selection contains few reds, then the Sender can feel confident reporting to have seen more.

The general pattern shows subjects being more willing to increase the reported number when they are supplied with few.

There is a distinct change of behavior when half of the sample contains more than five red marbles. In this situation, subjects may be happy to have been dealt a good hand, and are less inclined to risk losing 5-points for less gain.

Estimating involves considering more factors than the actual resources likely to be needed to implement the task; the use of round numbers is one example. This study is one of few experimental investigations of numeric related deception. The use of students having unknown motivation is far from ideal, but they are better than nothing.

When estimating in a team context, there is an opportunity to learn about the expectations of others and the consequences of over/under estimating. An issue for another study 🙂

Clustering source code within functions

The question of how best to cluster source code into functions is a perennial debate that has been ongoing since functions were first created.

Beginner programmers are told that clustering code into functions is good, for a variety of reasons (none of the claims are backed up by experimental evidence). Structuring code based on clustering the implementation of a single feature is a common recommendation; this rationale can be applied at both the function/method and file/class level.

The idea of an optimal function length (measured in statements) continues to appeal to developers/researchers, but lacks supporting evidence (despite a cottage industry of research papers). The observation that most reported fault appear in short functions is a consequence of most of a program’s code appearing in short functions.

I have had to deal with code that has not been clustered into functions. When microcomputers took off, some businessmen taught themselves to code, wrote software for their line of work and started selling it. If the software was a success, more functionality was needed, and the businessman (never encountered a woman doing this) struggled to keep on top of things. A common theme was a few thousand lines of unstructured code in one function in a single file

Adding structural bureaucracy (e.g., functions and multiple files) reduced the effort needed to maintain and enhance the code.

The problem with ‘born flat’ source is that the code for unrelated functionality is often intermixed, and global variables are freely used to communicate state. I have seen the same problems in structured function code, but instances are nowhere near as pervasive.

When implementing the same program, do different developers create functions implementing essentially the same functionality?

I am aware of two datasets relating to this question: 1) when implementing the same small specification (average length program 46.3 lines), a surprising number of variants (6,301) are created, 2) an experiment that asked developers to reintroduce functions into ‘flattened’ code.

The experiment (Alexey Braver’s MSc thesis) took an existing Python program, ‘flattened’ it by inlining functions (parameters were replaced by the corresponding call arguments), and asked subjects to “… partition it into functions in order to achieve what you consider to be a good design.”

The 23 rows in the plot below show the start/end (green/brown delimited by blue lines) of each function created by the 23 subjects; red shows code not within a function, and right axis is percentage of each subjects’ code contained in functions. Blue line shows original (currently plotted incorrectly; patched original code+data):

3n+1 programs containing various lines of code.

There are many possible reasons for the high level of agreement between subjects, including: 1) the particular example chosen, 2) the code was already well-structured, 3) subjects were explicitly asked to create functions, 4) the iterative process of discovering code that needs to be written did not occur, 5) no incentive to leave existing working code as-is.

Given that most source has a short and lonely existence, is too much time being spent bike-shedding function contents?

Given how often lower level design time happens at code implementation time, perhaps discussion of function contents ought to be viewed as more about thinking how things fit together and interact, than about each function in isolation.

Analyzing each function in isolation can create perverse incentives.

Shopper estimates of the total value of items in their basket

Agile development processes break down the work that needs to be done into a collection of tasks (which may be called stories or some other name). A task, whose implementation time may be measured in hours or a few days, is itself composed of a collection of subtasks (which may in turn be composed of subsubtasks, and so on down).

When asked to estimate the time needed to implement a task, a developer may settle on a value by adding up estimates of the effort needed to implement the subtasks thought to be involved. If this process is performed in the mind of the developer (i.e., not by writing down a list of subtask estimates), the accuracy of the result may be affected by the characteristics of cognitive arithmetic.

Humans have two cognitive systems for processing quantities, the approximate number system (which has been found to be present in the brain of many creatures), and language. Researchers studying the approximate number system often ask subjects to estimate the number of dots in an image; I recently discovered studies of number processing that used language.

In a study by Benjamin Scheibehenne, 966 shoppers at the checkout counter in a grocery shop were asked to estimate the total value of the items in their shopping basket; a subset of 421 subjects were also asked to estimate the number of items in their basket (this subset were also asked if they used a shopping list). The actual price and number of items was obtained after checkout.

There are broad similarities between shopping basket estimation and estimating task implementation time, e.g., approximate idea of number of items and their cost. Does an analysis of the shopping data suggest ideas for patterns that might be present in software task estimate data?

The left plot below shows shopper estimated total item value against actual, with fitted regression line (red) and estimate==actual (grey); the right plot shows shopper estimated number of items in their basket against actual, with fitted regression line (red) and estimate==actual (grey) (code+data):

Left: Shopper estimated total value against actual, with fitted regression line; right: shopper estimated number of items against actual, with fitted regression line.

The model fitted to estimated total item value is: totalActual=1.4totalEstimate^{0.93}, which differs from software task estimates/actuals in always underestimating over the range measured; the exponent value, 0.93, is at the upper range of those seen for software task estimates.

The model fitted to estimated number of items in the basket is: itemsActual=1.8itemsEstimate^{0.75}. This pattern, of underestimating small values and overestimating large values is seen in software task estimation, but the exponent of 0.75 is much smaller.

Including the estimated number of items in the shopping basket, Nguess, in a model for total value produces a slightly better fitting model: totalActual=1.4totalEstimate^{0.92}e^{0.003itemsEstimate}, which explains 83% of the variance in the data (use of a shopping list had a relatively small impact).

The accuracy of a software task implementation estimate based on estimating its subtasks dependent on identifying all the subtasks, or having a good enough idea of the number of subtasks. The shopping basket study found a pattern of inaccuracies in estimates of the number of recently collected items, which has been seen before. However, adding Nguess to the Shopping model only reduced the unexplained variance by a few percent.

Would the impact of adding an estimate of the number of subtasks to models of software task estimates also only be a few percent? A question to add to the already long list of unknowns.

Like task estimates, round numbers were often given as estimate values; see code+data.

The same study also included a laboratory experiment, where subjects saw a sequence of 24 numbers, presented one at a time for 0.5 seconds each. At the end of the sequence, subjects were asked to type in their best estimate of the sum of the numbers seen (other studies asked subjects to type in the mean). Each subject saw 75 sequences, with feedback on the mean accuracy of their responses given after every 10 sequences. The numbers were described as the prices of items in a shopping basket. The values were drawn from a distribution that was either uniform, positively skewed, negatively skewed, unimodal, or bimodal. The sequential order of values was either increasing, decreasing, U-shaped, or inversely U-shaped.

Fitting a regression model to the lab data finds that the distribution used had very little impact on performance, and the sequence order had a small impact; see code+data.

Impact of number of files on number of review comments

Code review is often discussed from the perspective of changes to a single file. In practice, code review often involves multiple files (or at least pull-based reviews do), which begs the question: Do people invest less effort reviewing files appearing later?

TLDR: The number of review comments decreases for successive files in the pull request; by around 16% per file.

The paper First Come First Served: The Impact of File Position on Code Review extracted and analysed 219,476 pull requests from 138 Java projects on Github. They also ran an experiment which asked subjects to review two files, each containing a seeded coding mistake. The paper is relatively short and omits a lot of details; I’m guessing this is due to the page limit of a conference paper.

The plot below shows the number of pull requests containing a given number of files. The colored lines indicate the total number of code review comments associated with a given pull request, with the red dots showing the 69% of pull requests that did not receive any review comments (code+data):

Number of pull requests containing a given number of files, for all pull requests, and those receiving at least 1, 2, 5, and 10 comments.

Many factors could influence the number of comments associated with a pull request; for instance, the number of people commenting, the amount of changed code, whether the code is a test case, and the number of files already reviewed (all items which happen to be present in the available data).

One factor for which information is not present in the data is social loafing, where people exert less effort when they are part of a larger group; or at least I did not find a way of easily estimating this factor.

The best model I could fit to all pull requests containing less than 10 files, and having a total of at least one comment, explained 36% of the variance present, which is not great, but something to talk about. There was a 16% decline in comments for successive files reviewed, test cases had 50% fewer comments, and there was some percentage increase with lines added; number of comments increased by a factor of 2.4 per additional commenter (is this due to importance of the file being reviewed, with importance being a metric not present in the data).

The model does not include information available in the data, such as file contents (e.g., Java, C++, configuration file, etc), and there may be correlated effects I have not taken into account. Consequently, I view the model as a rough guide.

Is the impact of file order on number of comments a side effect of some unrelated process? One way of showing a causal connection is to run an experiment.

The experiment run by the authors involved two files, each containing one seeded coding mistake. The 102 subjects were asked to review the two files, with file order randomly selected. The experiment looks well-structured and thought through (many are not), but the analysis of the results is confused.

The good news is that the seeded coding mistake in the first file was much more likely to be detected than the mistake in the second file, and years of Java programming experience also had an impact (appearing first had the same impact as three years of Java experience). The bad news is that the model (a random effect model using a logistic equation) explains almost none of the variance in the data, i.e., these effects are tiny compared to whatever other factors are involved; see code+data.

What other factors might be involved?

Most experiments show a learning effect, in that subject performance improves as they perform more tasks. Having subjects review many pairs of files would enable this effect to be taken into account. Also, reviewing multiple pairs would reduce the impact of random goings-on during the review process.

The identity of the seeded mistake did not have a significant impact on the model.

Review comments are an important issue which is amenable to practical experimental investigation. I hope that the researchers run more experiments on this issue.

Estimating quantities from several hundred to several thousand

How much influence do anchoring and financial incentives have on estimation accuracy?

Anchoring is a cognitive bias which occurs when a decision is influenced by irrelevant information. For instance, a study by John Horton asked 196 subjects to estimate the number of dots in a displayed image, but before providing their estimate subjects had to specify whether they thought the number of dots was higher/lower than a number also displayed on-screen (this was randomly generated for each subject).

How many dots do you estimate appear in the plot below?

Image containing 500 dots.

Estimates are often round numbers, and 46% of dot estimates had the form of a round number. The plot below shows the anchor value seen by each subject and their corresponding estimate of the number of dots (the image always contained five hundred dots, like the one above), with round number estimates in same color rows (e.g., 250, 300, 500, 600; code+data):

Anchor value seen by a subject and corresponding estimate of number of dots.

How much influence does the anchor value have on the estimated number of dots?

One way of measuring the anchor’s influence is to model the estimate based on the anchor value. The fitted regression equation Estimate=54*Anchor^{0.33} explains 11% of the variance in the data. If the higher/lower choice is included the model, 44% of the variance is explained; higher equation is: Estimate=169+1.1*Anchor and lower equation is: Estimate=169+0.36*Anchor (a multiplicative model has a similar goodness of fit), i.e., the anchor has three-times the impact when it is thought to be an underestimate.

How much would estimation accuracy improve if subjects’ were given the option of being rewarded for more accurate answers, and no anchor is present?

A second experiment offered subjects the choice of either an unconditional payment of $2.50 or a payment of $5.00 if their answer was in the top 50% of estimates made (labelled as the risk condition).

The 196 subjects saw up to seven images (65 only saw one), with the number of dots varying from 310 to 8,200. The plot below shows actual number of dots against estimated dots, for all subjects; blue/green line shows Estimate == Actual, and red line shows the fitted regression model Estimate approx Actual^{0.9} (code+data):

Actual and estimated number of dots in image seen by subjects.

The variance in the estimated number of dots is very high and increases with increasing actual dot count, however, this behavior is consistent with the increasing variance seen for images containing under 100 dots.

Estimates were not more accurate in those cases where subjects chose the risk payment option. This is not surprising, performance improvements require feedback, and subjects were not given any feedback on the accuracy of their estimates.

Of the 86 subjects estimating dots in three or more images, 44% always estimated low and 16% always high. Subjects always estimating low/high also occurs in software task estimates.

Estimation patterns previously discussed on this blog have involved estimated values below 100. This post has investigated patterns in estimates ranging from several hundred to several thousand. Patterns seen include extensive use of round numbers and increasing estimate variance with increasing actual value; all seen in previous posts.

Most percentages are more than half

Most developers think …

Most editors …

Most programs …

Linguistically most is a quantifier (it’s a proportional quantifier); a word-phrase used to convey information about the number of something, e.g., all, any, lots of, more than half, most, some.

Studies of most have often compared and contrasted it with the phrase more than half; findings include: most has an upper bound (i.e., not all), and more than half has a lower bound (but no upper bound).

A corpus analysis of most (432,830 occurrences) and more than half (4,857 occurrences) found noticeable usage differences. Perhaps the study’s most interesting finding, from a software engineering perspective, was that most tended to be applied to vague and uncountable domains (i.e., there was no expectation that the population of items could be counted), while uses of more than half almost always had a ‘survey results’ interpretation (e.g., supporting data cited as collaboration for 80% of occurrences; uses of most cited data for 19% of occurrences).

Readers will be familiar with software related claims containing the most qualifier, which are actually opinions that are not grounded in substantive numeric data.

When most is used in a numeric based context, what percentage (of a population) is considered to be most (of the population)?

When deciding how to describe a proportion, a writer has the choice of using more than half, most, or another qualifier. Corpus based studies find that the distribution of most has a higher average percentage value than more than half (both are left skewed, with most peaking around 80-85%).

When asked to decide whether a phrase using a qualifier is true/false, with respect to background information (e.g., Given that 55% of the birlers are enciad, is it true that: Most of the birlers are enciad?), do people treat most and more than half as being equivalent?

A study by Denić and Szymanik addressed this question. Subjects (200 took part, with results from 30 were excluded for various reasons) saw a statement involving a made-up object and verb, such as: “55% of the birlers are enciad.” They then saw a sentence containing either most or more than half, that was either upward-entailing (e.g., “More than half of the birlers are enciad.”), or downward-entailing (e.g., “It is not the case that more than half of the birlers are enciad.”); most/more than half and upward/downward entailing creates four possible kinds of sentence. Subjects were asked to respond true/false.

The percentage appearing in the first sentence of the two seen by subjects varied, e.g., “44% of the tiklets are hullaw.”, “12% of the puggles are entand.”, “68% of the plipers are sesare.” The percentage boundary where each subjects’ true/false answer switched was calculated (i.e., the mean of the percentages present in the questions’ each side of true/false boundary; often these values were 46% and 52%, whose average is 49; this is an artefact of the question wording).

The plot below shows the number of subjects whose true/false boundary occurred at a given percentage (code+data):

Number of subjects whose true/false boundary occurred at a given percentage.

When asked, the majority of subjects had a 50% boundary for most/more than half+upward/downward. A downward entailment causes some subjects to lower their 50% boundary.

So now we know (subject to replication). Most people are likely to agree that 50% is the boundary for most/more than half, but some people think that the boundary percentage is higher for most.

When asked to write a sentence, percentages above 50% attract more mosts than more than halfs.

Most is preferred when discussing vague and uncountable domains; more than half is used when data is involved.

Study of developers for the cost of a phase I clinical drug trial

For many years now, I have been telling people that software researchers need to be more ambitious and apply for multi-million pound/dollar grants to run experiments in software engineering. After all, NASA spends a billion or so sending a probe to take some snaps of a planet and astronomers lobby for $100million funding for a new telescope.

What kind of experimental study might be run for a few million pounds (e.g., the cost of a Phase I clinical drug trial)?

Let’s say that each experiment involves a team of professional developers implementing a software system; call this a Project. We want the Project to be long enough to be realistic, say a week.

Different people exhibit different performance characteristics, and the experimental technique used to handle this is to have multiple teams independently implement the same software system. How many teams are needed? Fifteen ought to be enough, but more is better.

Different software systems contain different components that make implementation easier/harder for those involved. To remove single system bias, a variety of software systems need to be used as Projects. Fifteen distinct Projects would be great, but perhaps we can get away with five.

How many developers are on a team? Agile task estimation data shows that most teams are small, i.e., mostly single person, with two and three people teams making up almost all the rest.

If we have five teams of one person, five of two people, and five of three people, then there are 15 teams and 30 people.

How many people will be needed over all Projects?

15 teams (30 people) each implementing one Project
 5 Projects, which will require 5*30=150 people (5*15=75 teams)

How many person days are likely to be needed?

If a 3-person team takes a week (5 days), a 2-person team will take perhaps 7-8 days. A 1-person team might take 9-10 days.

The 15 teams will consume 5*3*5+5*2*7+5*1*9=190 person days
The  5 Projects will consume              5*190=950 person days

How much is this likely to cost?

The current average daily rate for a contractor in the UK is around £500, giving an expected cost of 190*500=£475,000 to hire the experimental subjects. Venue hire is around £40K (we want members of each team to be co-located).

The above analysis involves subjects implementing one Project. If, say, each subject implements two, three or four Projects, one after the other, the cost is around £2million, i.e., the cost of a Phase I clinical drug trial.

What might we learn from having subjects implement multiple Projects?

Team performance depends on the knowledge and skill of its members, and their ability to work together. Data from these experiments would be the first of their kind, and would provide realistic guidance on performance factors such as: impact of team size; impact of practice; impact of prior experience working together; impact of existing Project experience. The multiple implementations of the same Project created provide a foundation for measuring expected reliability and theories of N-version programming.

A team of 1 developer will take longer to implement a Project than a team of 2, who will take longer than a team of 3.

If 20 working days is taken as the ballpark period over which a group of subjects are hired (i.e., a month), there are six team size sequences that one subject could work (A to F below); where individual elapsed time is close to 20 days (team size 1 is 10 days elapsed, team size 2 is 7.5 days, team size 3 is 5 days).

Team size    A      B      C      D      E      F
    1      twice   once   once  
    2                     once  thrice  once
    3             twice                twice   four

The cost of hiring subjects+venue+equipment+support for such a study is likely to be at least £1,900,000.

If the cost of beta testing, venue hire and research assistants (needed during experimental runs) is included, the cost is close to £2.75 million.

Might it be cheaper and simpler to hire, say, 20-30 staff from a medium size development company? I chose a medium-sized company because we would be able to exert some influence over developer selection and keeping the same developers involved. The profit from 20-30 people for a month is not enough to create much influence within a large company, and a small company would not want to dedicate a large percentage of its staff for a solid month.

Beta testing is needed to validate both the specifications for each Project and that it is possible to schedule individuals to work in a sequence of teams over a month (individual variations in performance create a scheduling nightmare).

Estimation experiments: specification wording is mostly irrelevant

Existing software effort estimation datasets provide information about estimates made within particular development environments and with particular aims. Experiments provide a mechanism for obtaining information about estimates made under conditions of the experimenters choice, at least in theory.

Writing the code is sometimes the least time-consuming part of implementing a requirement. At hackathons, my default estimate for almost any non-trivial requirement is a couple of hours, because my implementation strategy is to find the relevant library or package and write some glue code around it. In a heavily bureaucratic organization, the coding time might be a rounding error in the time taken up by meeting, documentation and testing; so a couple of months would be considered normal.

If we concentrate on the time taken to implement the requirements in code, then estimation time and implementation time will depend on prior experience. I know that I can implement a lexer for a programming language in half-a-day, because I have done it so many times before; other people take a lot longer because they have not had the amount of practice I have had on this one task. I’m sure there are lots of tasks that would take me many days, but there is somebody who can implement them in half-a-day (because they have had lots of practice).

Given the possibility of a large variation in actual implementation times, large variations in estimates should not be surprising. Does the possibility of large variability in subject responses mean that estimation experiments have little value?

I think that estimation experiments can provide interesting information, as long as we drop the pretence that the answers given by subjects have any causal connection to the wording that appears in the task specifications they are asked to estimate.

If we assume that none of the subjects is sufficiently expert in any of the experimental tasks specified to realistically give a plausible answer, then answers must be driven by non-specification issues, e.g., the answer the client wants to hear, a value that is defensible, a round number.

A study by Lucas Gren and Richard Berntsson Svensson asked subjects to estimate the total implementation time of a list of tasks. I usually ignore software engineering experiments that use student subjects (this study eventually included professional developers), but treating the experiment as one involving social processes, rather than technical software know-how, makes subject software experience a lot less relevant.

Assume, dear reader, that you took part in this experiment, saw a list of requirements that sounded plausible, and were then asked to estimate implementation time in weeks. What estimate would you give? I would have thrown my hands up in frustration and might have answered 0.1 weeks (i.e., a few hours). I expected the most common answer to be 4 weeks (the number of weeks in a month), but it turned out to be 5 (a very ‘attractive’ round number), for student subjects (code+data).

The professional subjects appeared to be from large organizations, who I assume are used to implementations including plenty of bureaucratic stuff, as well as coding. The task specification did not include enough detailed information to create an accurate estimate, so subjects either assumed their own work environment or played along with the fresh-faced, keen experimenter (sorry Lucas). The professionals showed greater agreement in that the range of value given was not as wide as students, but it had a more uniform distribution (with maximums, rather than peaks, at 4 and 7); see below. I suspect that answers at the high end were from managers and designers with minimal coding experience.

What did the experimenters choose weeks as the unit of estimation? Perhaps they thought this expressed a reasonable implementation time (it probably is if it’s not possible to use somebody else’s library/package). I think that they could have chosen day units and gotten essentially the same results (at least for student subjects). If they had chosen hours as the estimation unit, the spread of answers would have been wider, and I’m not sure whether to bet on 7 (hours in a working day) or 10 being the most common choice.

Fitting a regression model to the student data shows estimates increasing by 0.4 weeks per year of degree progression. I was initially baffled by this, and then I realized that more experienced students expect to be given tougher problems to solve, i.e., this increase is based on self-image (code+data).

The stated hypothesis investigated by the study involved none of the above. Rather, the intent was to measure the impact of obsolete requirements on estimates. Subjects were randomly divided into three groups, with each seeing and estimating one specification. One specification contained four tasks (A), one contained five tasks (B), and one contained the same tasks as (A) plus an additional task followed by the sentence: “Please note that R5 should NOT be implemented” (C).

A regression model shows that for students and professions the estimate for (A) is about 1-2 weeks lower than (B), while (A) estimates are 3-5 weeks lower than (C) estimated.

What are subjects to make of an experimental situation where the specification includes a task that they are explicitly told to ignore?

How would you react? My first thought was that the ignore R5 sentence was itself ignored, either accidentally or on purpose. But my main thought is that Relevance theory is a complicated subject, and we are a very long way away from applying it to estimation experiments containing supposedly redundant information.

The plot below shows the number of subjects making a given estimate, in days; exp0to2 were student subjects (dashed line joins estimate that include a half-hour value, solid line whole hour), exp3 MSc students, and exp4 professional developers (code+data):

Number of subjects making a given estimate.

I hope that the authors of this study run more experiments, ideally working on the assumption that there is no connection between specification and estimate (apart from trivial examples).

Where are we with models of human learning?

Learning is an integral part of writing software. What have psychologists figured out about the characteristics of human learning?

A study of memory, published in 1885, kicked off the start of modern psychology research. At the start of the 1900s, learning research was still closely tied to the study of the characteristics of what we now call working memory, e.g., measuring the time taken for subjects to correctly recall sequences of digits, nonsense syllables, words and prose. By the 1930s, learning was a distinct subject in its own right.

What is now known as the power law of learning was first proposed in 1926. Wikipedia is right to use the phrase power law of practice, since it is some measure of practice that appears in the power law of learning equation: T=a+b*P^{-c}, where: T is the time taken to do the task,P is some measure of practice (such as the number of times the subject has performed the task), and a, b, and c are constants fitted to the data.

For the next 70 years some form of power law did a good job of fitting the learning data produced by researchers. Then in 1997 a paper pointed out that researchers were fitting aggregate data (i.e., one equation fitted to all subject data), and that an exponential equation was a better fit to individual subject response times: T=a+b*e^{-cP}. The power law appeared to be the result of aggregating the exponential response performance of multiple subjects; oops.

What is the situation today, 25 years later? Do the subsystems of our brains produce a power law or exponential improvement in performance, with practice?

The problem with answering this question is that both equations can fit the available data quite well, with one being a technically better fit than the other for different datasets. The big difference between the two equations is in their tails, however, it is costly and time-consuming to obtain enough data to distinguish between them in this region.

When discussing learning in my evidence-based software engineering book, I saw no compelling reason to run counter to the widely cited power law, but I did tell readers about the exponential fit issue.

Studies of learnings have tended to use simple tasks; subjects are usually only available for a short time, and many task repetitions are needed to model the impact of learning. Simple tasks tend to be dominated by one primary activity, which means that subjects can focus their learning on this one activity.

Complicated tasks involve many activities, each potentially providing distinct learning opportunities. Which activities will a subject focus on improving, will the performance on one activity improve faster than others, will the approach chosen for one activity limit the performance on a second activity?

For a complicated task, the change in performance with amount of practice could be a lot more complicated than a single power law/exponential equation, e.g., there may be multiple equations with each associated with one or more activities.

In the previous paragraph, I was careful to say “could be a lot more complicated”. This is because the few datasets of organizational learning show a power law performance improvement, e.g., from 1936 we have the most cited study Factors Affecting the Cost of Airplanes, and the less well known but more interesting Liberty shipbuilding from the 1940s.

If the performance of something involving multiple people performing many distinct activities follows a power law improvement with practice, then the performance of an individual carrying out a complicated task might follow a simple equation; perhaps the combined form of many distinct simple learning activities is a simple equation.

Researchers are now proposing more complicated models of learning, along with fitting them to existing learning datasets.

Which equation should software developers use to model the learning process?

I continue to use a power law. The mathematics tend to be straight-forward, and it often gives an answer that is good enough (because the data fitted contains lots of variance). If it turned out that an exponential would be easier to work with, I would be happy to switch. Unless there is a lot of data in the tail, the difference between power law/exponent is usually not worth worrying about.

There are situations where I have failed to successfully add a learning (power law) component to a model. Was this because there was no learning present, or was the learning not well-fitted by a power law? I don’t know, and I cannot think of an alternative equation that might work, for these cases.

How large an impact does social conformity have on estimates?

People experience social pressure to conform to group norms. How big an impact might social pressure have on a developer’s estimate of the effort needed to implement some functionality?

If a manager suggests that the effort likely to be required is large/small, I would expect a developer to respond accordingly (even if the manager is thought to be incompetent; people like to keep their boss happy). Of course, customer opinions are also likely to have an impact, but what about fellow team members, or even the receptionist. Until somebody runs the experiments, we are going to have to do with non-software related tasks.

A study by Molleman, Kurversa, and van den Bos asked subjects (102 workers on Mechanical Turk) to estimate the number of animals in an image (which contained between 50 and 100 ants, flamingos, bees, cranes or crickets). Subjects were given 30 seconds to respond, and after typing their answer they were told that “another participant had estimated X“, and given 45 seconds to give a second estimate. The ‘social pressure’ estimate, X, was chosen to be around 15-25% larger/smaller than the estimate given (values from a previous experiment were randomly selected).

The plot below shows the number of second estimates where there was a given percentage change between the first and second estimates, red line is a loess fit; the formula used is {secondEstimate-firstEstimate}/{SocialEstimate-firstEstimate} (code+data):

Number of second estimates having a given change in the first estimate towards social estimate.

Around 25% of second estimates were unchanged, and 2% were changed to equal the social estimate. In two cases the second estimate was less than the first, and in eleven cases it was larger than the social estimate. Both the mean and median for shift towards the social estimate were just over 30% of the difference between the first estimate and the social estimate.

As with previous estimating studies, a few round numbers were often chosen. I was interested in finding out what impact the use of a round number value for the first estimate, or the social estimate, might have on the change in estimated value. The best regression model I could find showed that if the first estimate was exactly divisible by 5 (or 10), then the second estimate was likely to be around 5% larger. In fact divisible-by-5 was the only variable that had any predictive power.

My initial hypothesis was that the act of choosing a round numbers is an expression of uncertainty, and that this uncertainty increases the impact of the social estimate (when making the second estimate). An analysis of later experiments suggested that this pattern was illusionary (see below).

Modelling estimate values, rather than their differences, the equation: secondEstimate approx firstEstimate^{0.6}*SocialEstimate^{0.3} explains nearly all the variance present in the data.

Two weeks after the first experiment, all 102 subjects were asked to repeat the experiment (they each saw the same images, in the same order, and social estimates as in the first study); 69 subjects participated. Nine months after the first experiment, subjects were asked to repeat the experiment again; 47 subjects participated, again with each subject seeing the same images in the same order, and social estimates. Thirty-five subjects participated in all three experiments.

To what extent were subjects consistently influenced by the social estimate, across three identical sessions? The Pearson correlation coefficient between both the first/second experiment, and the first/third experiment, was around 0.6.

The impact of round numbers was completely different, i.e., no impact on the second, and a -7% impact on the third (i.e., a reduced change). So much for my initial hypothesis.

The exponents in the above equation did not change much for the data from the second and third reruns of the experiment.

The variability in the social estimates used in these experiments, involving image contents, differs from software estimates in that they were only 12-25% different from the first estimate. Software estimates often differ by significantly larger amounts (in fact, a 12% difference would probably be taken as agreement).

With some teams, people meet to thrash out a team estimate. Data is sometimes available on the final estimate, but data on the starting values is very hard to come by. Pointers to experiments where social estimates are significantly different (i.e., greater than 50%) from the ones given by subjects welcome.

The Approximate Number System and software estimating

The ability to perform simple numeric operations can improve the fitness of a creature (e.g., being able to select which branch contains the most fruit), increasing the likelihood of it having offspring. Studies have found that a wide variety of creatures have a brain subsystem known as the Approximate Number System (ANS).

A study by Mechner rewarded rats with food, if they pressed a lever N times (with N taking one of the values 4, 8, 12 or 16), followed by pressing a second lever. The plot below shows the number of lever presses made before pressing the second lever, for a given required N; it suggests that the subject rat is making use of an approximate number system (code+data):

Daily article counts for blog.

Humans have a second system for representing numbers, which is capable of exact representation, it is language. The Number Sense by Stanislas Dehaene was on my list of Christmas books for 2011.

One method used to study the interface between the two language systems, available to humans, involves subjects estimating the number of dots in a briefly presented image. While reading about one such study, I noticed that some of the plots showed patterns similar to the patterns seen in plots of software estimate/actual data. I emailed the lead author, Véronique Izard, who kindly sent me a copy of the experimental data.

The patterns I was hoping to see are those invariably seen in software effort estimation data, e.g., a power law relationship between actual/estimate, consistent over/under estimation by individuals, and frequent use of round numbers.

Psychologists reading this post may be under the impression that estimating the time taken to implement some functionality, in software, is a relatively accurate process. In practice, for short tasks (i.e., under a day or two) the time needed to form a more accurate estimate makes a good-enough estimate a cost-effective option.

This Izard and Dehaene study involved two experiments. In the first experiment, an image containing between 1 and 100 dots was flashed on the screen for 100ms, and subjects then had to type the estimated number of dots. Each of the six subjects participated in five sessions of 600 trials, with each session lasting about one hour; every number of dots between 1 and 100 was seen 30 times by each subject (for one subject the data contains 1,783 responses, other subjects gave 3,000 responses). Subjects were free to type any value as their estimate.

These kinds of studies have consistently found that subject accuracy is very poor (hardly surprising, given that subjects are not provided with any feedback to help calibrate their estimates). But since researchers are interested in patterns that might be present in the errors, very low accuracy is not an issue.

The plot below shows stimulus (number of dots shown) against subject response, with green line showing Response==Stimulus, and red line a fitted regression model having the form Response=1.7*Stimulus^{0.7} (which explains just over 70% of the variance; code+data):

Response given for given number of stimulus dots, with fitted regression model.

Just like software estimates, there is a good fit to a power law, and the only difference in accuracy performance is that software estimates tend not to be so skewed towards underestimating (i.e., there are a lot more low accuracy overestimates).

Adding subjectID to the model gives: Response=1.8*Stimulus^{0.7}*SubjectID, with SubjectID varying between 0.65 and 1.57; more than a factor of two difference between subjects (this model explains just under 90% of the variance). This is a smaller range than the software estimation data, but with only six subjects there was less chance of a wider variation (code+data).

The software estimation data finds shows that accuracy does not improve with practice. The experimental subjects were not given any feedback, and would not be expected to improve, but does the strain of answering so many questions cause them to get worse? Adding trial number to the model suggests a 12% increase in underestimation, over 600 trials. However, adding an interaction with SubjectID shows that the performance of two subjects remains unchanged, while two subjects experience a 23% increase in underestimation.

The plot below shows the number of times each response was given, combining all subjects, with commonly given responses in red (code+data):

Number of occurrences of response values, over all subjects.

The commonly occurring values that appear in software estimation data are structured as fractions of units of time, e.g., 0.5 hours, or 1 hour or 1 day (appearing in the data as 7 hours). The only structure available to experimental subjects was subdivisions of powers of 10 (i.e., 10 and 100).

Analysing the responses by subject shows that each subject had their own set of preferred round numbers.

To summarize: The results from an experiment investigating the interface between the two human number systems contains three patterns seen in software estimation data, i.e., power law relationship between actual and estimate, individual differences in over/underestimating, and extensive use of round numbers.

Izard’s second experiment limited response values to prespecified values (i.e., one to 10 and multiples of 10), and gave a calibration example after each block of 46 trials. The calibration example improved performance, and the use of round numbers as prespecified response values had the effect of removing spikes from the response counts (which were relatively smooth; code+data)).

We now have circumstantial evidence that software developers are using the Approximate Number System when making software estimates. We will have to wait for brain images from a developer in an MRI scanner, while estimating a software task, to obtain more concrete proof that the ANS is involved in the process. That is, are the areas of the brain thought to be involved in the ANS (e.g., the intraparietal sulcus) active during software estimation?

Readability: a scientific approach

Readability, as applied to software development today, is a meaningless marketing term. Readability is promoted as a desirable attribute, and is commonly claimed for favored programming languages, particular styles of programming, or ways of laying out source code.

Whenever somebody I’m talking to, or listening to in a talk, makes a readability claim, I ask what they mean by readability, and how they measured it. The speaker invariably fumbles around for something to say, with some dodging and weaving before admitting that they have not measured readability. There have been a few studies that asked students to rate the readability of source code (no guidance was given about what readability might be).

If somebody wanted to investigate readability from a scientific perspective, how might they go about it?

The best way to make immediate progress is to build on what is already known. There has been over a century of research on eye movement during reading, and two model of eye movement now dominate, i.e., the E-Z Reader model and SWIFT model. Using eye-tracking to study developers is slowly starting to be adopted by researchers.

Our eyes don’t smoothly scan the world in front of us, rather they jump from point to point (these jumps are known as a saccade), remaining fixed long enough to acquire information and calculate where to jump next. The image below is an example from an eye tracking study, where subjects were asking to read a sentence (see figure 770.11). Each red dot appears below the center of each saccade, and the numbers show the fixation time (in milliseconds) for that point (code):

Saccade points in a sentence, and fixation times.

Models of reading are judged by the accuracy of their predictions of saccade landing points (within a given line of text), and fixation time between saccades. Simulators implementing the E-Z Reader and SWIFT models have found that these models have comparable performance, and the robustness of these models are compared by looking at the predictions they make about saccade behavior when reading what might be called unconventional material, e.g., mirrored or scarmbeld text.

What is the connection between the saccades made by readers and their understanding of what they are reading?

Studies have found that fixation duration increases with text difficulty (it is also affected by decreases with word frequency and word predictability).

It has been said that attention is the window through which we perceive the world, and our attention directs what we look at.

A recent study of the SWIFT model found that its predictions of saccade behavior, when reading mirrored or inverted text, agreed well with subject behavior.

I wonder what behavior SWIFT would predict for developers reading a line of code where the identifiers were written in camelCase or using underscores (sometimes known as snake_case)?

If the SWIFT predictions agreed with developer saccade behavior, a raft of further ‘readability’ tests spring to mind. If the SWIFT predictions did not agree with developer behavior, how might the model be updated to support the reading of lines of code?

Until recently, the few researchers using eye tracking to investigate software engineering behavior seemed to be having fun playing with their new toys. Things are starting to settle down, with some researchers starting to pay attention to existing models of reading.

What do I predict will be discovered?

Lots of studies have found that given enough practice, people can become proficient at handling some apparently incomprehensible text layouts. I predict that given enough practice, developers can become equally proficient at most of the code layout schemes that have been proposed.

The important question concerning text layout, is: which one enables an acceptable performance from a wide variety of developers who have had little exposure to it? I suspect the answer will be the one that is closest to the layout they have had the most experience,i.e., prose text.

Readability: a scientific approach

Readability, as applied to software development today, is a meaningless marketing term. Readability is promoted as a desirable attribute, and is commonly claimed for favored programming languages, particular styles of programming, or ways of laying out source code.

Whenever somebody I’m talking to, or listening to in a talk, makes a readability claim, I ask what they mean by readability, and how they measured it. The speaker invariably fumbles around for something to say, with some dodging and weaving before admitting that they have not measured readability. There have been a few studies that asked students to rate the readability of source code (no guidance was given about what readability might be).

If somebody wanted to investigate readability from a scientific perspective, how might they go about it?

The best way to make immediate progress is to build on what is already known. There has been over a century of research on eye movement during reading, and two model of eye movement now dominate, i.e., the E-Z Reader model and SWIFT model. Using eye-tracking to study developers is slowly starting to be adopted by researchers.

Our eyes don’t smoothly scan the world in front of us, rather they jump from point to point (these jumps are known as a saccade), remaining fixed long enough to acquire information and calculate where to jump next. The image below is an example from an eye tracking study, where subjects were asking to read a sentence (see figure 770.11). Each red dot appears below the center of each saccade, and the numbers show the fixation time (in milliseconds) for that point (code):

Saccade points in a sentence, and fixation times.

Models of reading are judged by the accuracy of their predictions of saccade landing points (within a given line of text), and fixation time between saccades. Simulators implementing the E-Z Reader and SWIFT models have found that these models have comparable performance, and the robustness of these models are compared by looking at the predictions they make about saccade behavior when reading what might be called unconventional material, e.g., mirrored or scarmbeld text.

What is the connection between the saccades made by readers and their understanding of what they are reading?

Studies have found that fixation duration increases with text difficulty (it is also affected by decreases with word frequency and word predictability).

It has been said that attention is the window through which we perceive the world, and our attention directs what we look at.

A recent study of the SWIFT model found that its predictions of saccade behavior, when reading mirrored or inverted text, agreed well with subject behavior.

I wonder what behavior SWIFT would predict for developers reading a line of code where the identifiers were written in camelCase or using underscores (sometimes known as snake_case)?

If the SWIFT predictions agreed with developer saccade behavior, a raft of further ‘readability’ tests spring to mind. If the SWIFT predictions did not agree with developer behavior, how might the model be updated to support the reading of lines of code?

Until recently, the few researchers using eye tracking to investigate software engineering behavior seemed to be having fun playing with their new toys. Things are starting to settle down, with some researchers starting to pay attention to existing models of reading.

What do I predict will be discovered?

Lots of studies have found that given enough practice, people can become proficient at handling some apparently incomprehensible text layouts. I predict that given enough practice, developers can become equally proficient at most of the code layout schemes that have been proposed.

The important question concerning text layout, is: which one enables an acceptable performance from a wide variety of developers who have had little exposure to it? I suspect the answer will be the one that is closest to the layout they have had the most experience,i.e., prose text.

Cognitive bias or not paying enough attention?

Assume you are responsible for two teams who independently work on projects, say Team A and Team B. The teams have different work completion rates, with Team A completing work at the rate of 70 widgets per week, while Team B completes 30 widgets per week. Both teams always work on projects that require the completion of the same number of widgets.

You have the resources to send just one of the teams on a course. It is predicted that sending Team A on the course would improve their performance to 110 widgets per week, while attending the course would improve the performance of Team B to 40 widgets per week.

Senior management have decreed that time to market is the metric by which project managers are judged.

You want to impress senior management by significantly improving time to market for your projects; which team do you send on the course (i.e., the one that is likely to experience the largest reduction in time to market)?

This question is a restatement of a one involving cars travelling at different speeds, that has grown into a niche research area. Studies have found that a large percentage of subjects give the wrong answer, and they are said to have a time-saving bias, or time-loss bias.

The inability to correctly process “inverse variables” has been given as the reason people tend to give the wrong answer. The term “inverse variables” comes from the formula for calculating completion time, where the velocity appears as the denominator. Another way of looking at this problem is that when going slowly, there is more scope for improvement, compared to when going much faster.

A speed increase from 30 to 40 is only 10, or a 33% improvement; while an increase from 70 to 110 is an increase of 40, or 57%. Based on these numbers, Team A should be sent on the course.

However, we are interested in time to market. Let’s assume that both teams have to complete a project requiring 100 widgets. Before attending the course, Team A completes 100 widgets in 100/70=1.4 weeks, and Team B completes 100 widgets in 100/30=3.3 weeks. After attending the course, Team A would complete 100 widgets in 100/110=0.91 weeks, and Team B would complete 100 widgets in 100/40=2.5 weeks. Time to market for Team A has been reduced by (1.4-0.9)=0.5 weeks, while the reduction for Team B is (3.3-2.5)=0.8 weeks. So sending Team B on the course makes you look better, on the time to market metric.

If somebody ran an experiment with project managers, would the subjects tend to incorrectly process “inverse variables”. Well, somebody has done the experiment, and yes, many subjects exhibited the time-saving bias (the experimental scenario described in the appendix is a lot easier to understand than the one in the main body of the paper, which is a mess; Magne Jørgensen continues to be the only person doing interesting experiments in software estimation).

It has become common practice that, when a large percentage of subjects in a psychology experiment respond in ways that are inconsistent with a mathematical approach, the behavior is labelled as being a bias. I think the use of this terminology makes the behavior sound more interesting than it actually is; what’s wrong with saying that people make mistakes. Perhaps labelling experimental responses as being a bias makes it easier to get papers published.

Whether people are biased, or don’t pay enough attention, when solving non-trivial equations, what might be done about it?

This is not about whether any particular metric is a useful one, rather it is about calculating the right answer for whatever metric happens to be chosen.

Would an awareness campaign highlighting the problems people have with “inverse variables” be worthwhile? I don’t think so. Many people have problems with equations, and I don’t see why this case is more worthy of being highlighted than any other.

Am I missing something?

Psychology researchers are interested in figuring out the functioning of the brain/mind, so they are looking for patterns in the responses subjects give. Once someone has published a few papers on a research topic, they become invested in it. If they continue to get funding, the papers keep on coming. Sometimes a niche topic acquires a major following, and the work contributes to a major change of thinking about the mind, e.g., the Wason selection task helped increase the evidence that culture has an impact on cognitive behavior.

I think that software engineering researchers need to carefully evaluate the likely importance of behaviors that psychology researchers have labelled as a bias.

Cognitive bias or not paying enough attention?

Assume you are responsible for two teams who independently work on projects, say Team A and Team B. The teams have different work completion rates, with Team A completing work at the rate of 70 widgets per week, while Team B completes 30 widgets per week. Both teams always work on projects that require the completion of the same number of widgets.

You have the resources to send just one of the teams on a course. It is predicted that sending Team A on the course would improve their performance to 110 widgets per week, while attending the course would improve the performance of Team B to 40 widgets per week.

Senior management have decreed that time to market is the metric by which project managers are judged.

You want to impress senior management by significantly improving time to market for your projects; which team do you send on the course (i.e., the one that is likely to experience the largest reduction in time to market)?

This question is a restatement of a one involving cars travelling at different speeds, that has grown into a niche research area. Studies have found that a large percentage of subjects give the wrong answer, and they are said to have a time-saving bias, or time-loss bias.

The inability to correctly process “inverse variables” has been given as the reason people tend to give the wrong answer. The term “inverse variables” comes from the formula for calculating completion time, where the velocity appears as the denominator. Another way of looking at this problem is that when going slowly, there is more scope for improvement, compared to when going much faster.

A speed increase from 30 to 40 is only 10, or a 33% improvement; while an increase from 70 to 110 is an increase of 40, or 57%. Based on these numbers, Team A should be sent on the course.

However, we are interested in time to market. Let’s assume that both teams have to complete a project requiring 100 widgets. Before attending the course, Team A completes 100 widgets in 100/70=1.4 weeks, and Team B completes 100 widgets in 100/30=3.3 weeks. After attending the course, Team A would complete 100 widgets in 100/110=0.91 weeks, and Team B would complete 100 widgets in 100/40=2.5 weeks. Time to market for Team A has been reduced by (1.4-0.9)=0.5 weeks, while the reduction for Team B is (3.3-2.5)=0.8 weeks. So sending Team B on the course makes you look better, on the time to market metric.

If somebody ran an experiment with project managers, would the subjects tend to incorrectly process “inverse variables”. Well, somebody has done the experiment, and yes, many subjects exhibited the time-saving bias (the experimental scenario described in the appendix is a lot easier to understand than the one in the main body of the paper, which is a mess; Magne Jørgensen continues to be the only person doing interesting experiments in software estimation).

It has become common practice that, when a large percentage of subjects in a psychology experiment respond in ways that are inconsistent with a mathematical approach, the behavior is labelled as being a bias. I think the use of this terminology makes the behavior sound more interesting than it actually is; what’s wrong with saying that people make mistakes. Perhaps labelling experimental responses as being a bias makes it easier to get papers published.

Whether people are biased, or don’t pay enough attention, when solving non-trivial equations, what might be done about it?

This is not about whether any particular metric is a useful one, rather it is about calculating the right answer for whatever metric happens to be chosen.

Would an awareness campaign highlighting the problems people have with “inverse variables” be worthwhile? I don’t think so. Many people have problems with equations, and I don’t see why this case is more worthy of being highlighted than any other.

Am I missing something?

Psychology researchers are interested in figuring out the functioning of the brain/mind, so they are looking for patterns in the responses subjects give. Once someone has published a few papers on a research topic, they become invested in it. If they continue to get funding, the papers keep on coming. Sometimes a niche topic acquires a major following, and the work contributes to a major change of thinking about the mind, e.g., the Wason selection task helped increase the evidence that culture has an impact on cognitive behavior.

I think that software engineering researchers need to carefully evaluate the likely importance of behaviors that psychology researchers have labelled as a bias.

Impact of native language on variable naming

When creating a variable name, to what extent are developers influenced by their native human language?

There is lots of evidence that variable names are either English words, abbreviations of English words, or some combination of these two. Source code containing a large percentage of identifiers using words from other languages does exist, but it requires effort to find; there is a widely expressed view that source should be English based (based on my experience of talking to non-native English speakers, and even the odd paper discussing the issue, e.g., Language matters).

Given that variable names can prove information that reduces the effort needed to understand code, and that most code is only ever read by the person who wrote it, developers should make the most of their expertise in using their native language.

To what extent do non-native English-speaking developers make use of their non-English native language?

I have found it very difficult to even have a discussion around this question. When I broach the subject with non-native English speakers, the response is often along the lines of “our develo0pers speak good English.” I am careful to set the scene by telling them of my interest in naming, and that I think there are benefits for developers to make use of their native language. The use of non-English languages in software development is not yet a subject that is open for discussion.

I knew that sooner or later somebody would run an experiment…

How Developers Choose Names is another interesting experiment involving Dror Feitelson (the paper rather confusingly refers to it as a survey, a post on an earlier experiment).

What makes this experiment interesting is that bilingual subjects (English and Hebrew) were used, and the questions were in English or Hebrew. The 230 subjects (some professional, some student) were given a short description and asked to provide an appropriate variable/function/data-structure name; English was used for 26 of the question, and Hebrew for the other 21 questions, and subjects answered a random subset.

What patterns of Hebrew usage are present in the variable names?

Out of 2017 answers, 14 contained Hebrew characters, i.e., not enough for statistical analysis. This does not mean that all the other variable names were only derived from English words, in some cases Hebrew words appeared via transcription using the 26 English letters. For instance, using “pinuk” for the Hebrew word that means “benefit” in English. Some variables were created from a mixture of Hebrew and English words, e.g., deservedPinuks and pinuksUsed.

Analysing this data requires someone who is fluent in Hebrew and English. I am not a fluent, or even non-fluent, Hebrew speaker. My role in this debate is encouraging others, and at last I have some interesting data to show people.

The paper spends time showing how for personal preferences result in a wide selection of names being chosen by different people for the same quantity. I cannot think of any software engineering papers that have addressed this issue for variable names, but there is lots of evidence from other fields; also see figure 7.33.

Those interested in searching source code for the impact of native-language might like to look at the names of variables appearing as operands of the bitwise and logical operators. Some English words occur much more frequently in the names of these variable, compared to variables that are operands of arithmetic operators, e.g., flag, status, and signal. I predict that non-native English-speaking developers will make use of corresponding non-English words.

Estimate variability for the same task

If 100 people estimate the time needed to implement a feature, in software, what is the expected variability in the estimates?

Studies of multiple implementations of the same specification suggest that standard deviation of the mean number of lines across implementations is 25% of the mean (based on data from 10 sets of multiple implementations, of various sizes).

The plot below shows lines of code against the number of programs (implementing the 3n+1 problem) containing that many lines (red line is a Normal distribution fitted by eye, code and data):

3n+1 programs containing various lines of code.

Might any variability in the estimates for task implementation be the result of individuals estimating their own performance (which is variable)?

To the extent that an estimate is based on a person’s implementation experience, a developer’s past performance will have some impact on their estimate. However, studies have found a great deal of variability between individual estimates and their corresponding performance.

One study asked 14 companies to bid on implementing a system (four were eventually chosen to implement it; see figure 5.2 in my book). The estimated elapsed time varied by a factor of ten. Until the last week this was the only study of this question for which the data was available (and may have been the only such study).

A study by Alhamed and Storer investigated crowd-sourcing of effort estimates, structured by use of planning poker. The crowd were workers on Amazon’s Mechanical Turk, and the tasks estimated came from the issue trackers of JBoss, Apache and Spring Integration (using issues that had been annotated with an estimate and actual time, along with what was considered sufficient detail to make an estimate). An initial set of 419 issues were whittled down to 30, which were made available, one at a time, as a Mechanical Turk task (i.e., only one issue was available to be estimated at any time).

Worker estimates were given using a time-based category (i.e., the values 1, 4, 8, 20, 40, 80), with each value representing a unit of actual time (i.e., one hour, half-day, day, half-week, week and two weeks, respectively).

Analysis of the results from a pilot study were used to build a model that detected estimates considered to be low quality, e.g., providing a poor justification for the estimate. These were excluded from any subsequent iterations.

Of the 506 estimates made, 321 passed the quality check.

Planning poker is an iterative process, with those making estimates in later rounds seeing estimates made in earlier rounds. So estimates made in later rounds are expected to have some correlation with earlier estimates.

Of the 321 quality check passing estimates, 153 were made in the first-round. Most of the 30 issues have 5 first-round estimates each, one has 4 and two have 6.

Workers have to pick one of five possible value as their estimate, with these values being roughly linear on a logarithmic scale, i.e., it is not possible to select an estimate from many possible large values, small values, or intermediate values. Unless most workers pick the same value, the standard deviation is likely to be large. Taking the logarithm of the estimate maps it to a linear scale, and the plot below shows the mean and standard deviation of the log of the estimates for each issue made during the first-round (code+data):

Mean against standard deviation for log of estimates of each issue.

The wide spread in the standard deviations across a spread of mean values may be due to small sample size, or it may be real. The only way to find out is to rerun with larger sample sizes per issue.

Now it has been done once, this study needs to be run lots of times to measure the factors involved in the variability of developer estimates. What would be the impact of asking workers to make hourly estimates (they would not be anchored by experimenter specified values), or shifting the numeric values used for the categories (which probably have an anchoring effect)? Asking for an estimate to fix an issue in a large software system introduces the unknown of all kinds of dependencies, would estimates provided by workers who are already familiar with a project be consistently shifted up/down (compared to estimates made by those not familiar with the project)? The problem of unknown dependencies could be reduced by giving workers self-contained problems to estimate, e.g., the 3n+1 problem.

The crowdsourcing idea is interesting, but I don’t think it will scale, and I don’t see many companies making task specifications publicly available.

To mimic actual usage, research on planning poker (which appears to have non-trivial usage) needs to ensure that the people making the estimates are involved during all iterations. What is needed is a dataset of lots of planning poker estimates. Please let me know if you know of one.

Software engineering experiments: sell the idea, not the results

A new paper investigates “… the feasibility of stealthily introducing vulnerabilities in OSS via hypocrite commits (i.e., seemingly beneficial commits that in fact introduce other critical issues).” Their chosen Open source project was the Linux kernel, and they submitted three patches to the kernel review process.

This interesting idea blew up in their faces, when the kernel developers deduced that they were being experimented on (they obviously don’t have a friend on the inside). The authors have come out dodging and weaving.

What can be learned by reading the paper?

Firstly, three ‘hypocrite commits’ is not enough submissions to do any meaningful statistical analysis. I suspect it’s a convenience sample, a common occurrence in software engineering research. The authors sell three as a proof-of-concept.

How many of the submitted patches passed the kernel review process?

The paper does not say. The first eight pages provide an introduction to the Open source development model, the threat model for introducing vulnerabilities, and the characteristics of vulnerabilities that have been introduced (presumably by accident). This is followed by 2.5 pages of background and setup of the experiment (labelled as a proof-of-concept).

The paper then switches (section VII) to discussing a different, but related, topic: the lifetime of (unintended) vulnerabilities in patches that had been accepted (which I think should have been the topic of the paper. This interesting discussion is 1.5 pages; also see The life and death of statically detected vulnerabilities: An empirical study, covered in figure 6.9 in my book.

The last two pages discuss mitigation, related work, and conclusion (“…a proof-of-concept to safely demonstrate the practicality of hypocrite commits, and measured and quantified the risks.”; three submissions is not hard to measure and quantify, but the results are not to be found in the paper).

Having the paper provide the results (i.e., all three commits spotted, and a very negative response by those being experimented on) would have increased the chances of negative reviewer comments.

Over the past few years I have started noticing this kind of structure in software engineering papers, i.e., extended discussion of an interesting idea, setup of experiment, and cursory or no discussion of results. Many researchers are willing to spend lots of time discussing their ideas, but are unwilling to invest much time in the practicalities of testing them. Some reviewers (who decide whether a paper is accepted to publication) don’t see anything wrong with this approach, e.g., they accept these kinds of papers.

Software engineering research remains a culture of interesting ideas, with evidence being an optional add-on.

The impact of believability on reasoning performance

What are the processes involved in reasoning? While philosophers have been thinking about this question for several thousand years, psychologists have been running human reasoning experiments for less than a hundred years (things took off in the late 1960s with the Wason selection task).

Reasoning is a crucial ability for software developers, and I thought that there would be lots to learn from the cognitive psychologists research into reasoning. After buying all the books, and reading lots of papers, I realised that the subject was mostly convoluted rabbit holes individually constructed by tiny groups of researchers. The field of decision-making is where those psychologists interested in reasoning, and a connection to reality, hang-out.

Is there anything that can be learned from research into human reasoning (other than that different people appear to use different techniques, and some problems are more likely to involve particular techniques)?

A consistent result from experiments involving syllogistic reasoning is that subjects are more likely to agree that a conclusion they find believable follows from the premise (and are more likely to disagree with a conclusion they find unbelievable). The following is perhaps the most famous syllogism (the first two lines are known as the premise, and the last line is the conclusion):

    All men are mortal.
    Socrates is a man.
    Therefore, Socrates is mortal. 

Would anybody other than a classically trained scholar consider that a form of logic invented by Aristotle provides a reasonable basis for evaluating reasoning performance?

Given the importance of reasoning ability in software development, there ought to be some selection pressure on those who regularly write software, e.g., software developers ought to give a higher percentage of correct answers to reasoning problems than the general population. If the selection pressure for reasoning ability is not that great, at least software developers have had a lot more experience solving this kind of problem, and practice should improve performance.

The subjects in most psychology experiments are psychology undergraduates studying in the department of the researcher running the experiment, i.e., not the general population. Psychology is a numerate discipline, or at least the components I have read up on have a numeric orientation, and I have met a fair few psychology researchers who are decent programmers. Psychology undergraduates must have an above general-population performance on syllogism problems, but better than professional developers? I don’t think so, but then I may be biased.

A study by Winiger, Singmann, and Kellen asked subjects to specify whether the conclusion of a syllogism was valid/invalid/don’t know. The syllogisms used were some combination of valid/invalid and believable/unbelievable; examples below:

        Believable                  Unbelievable
Valid
        No oaks are jubs.           No trees are punds.
        Some trees are jubs.        Some Oaks are punds.
        Therefore, some trees       Therefore, some oaks
                   are not oaks.               are not trees.
Invalid
        No tree are brops.          No oaks are foins.
        Some oaks are brops.        Some trees are foins.
        Therefore, some trees       Therefore, some oaks
                   are not oaks.               are not trees.

The experiment was run using an online crowdsource site, and 354 data sets were obtained.

The plot below shows the impact of conclusion believability (red)/unbelievability (blue/green) on subject performance, when deciding whether a syllogism was valid (left) or invalid (right), (code+data):

Benchmark runtime at various array sizes, for each algorithm using a 32-bit datatype.

The believability of the conclusion biases the responses away/towards the correct answer (the error bars are tiny, and have not been plotted). Building a regression model puts numbers to the difference, and information on the kind of premise can also be included in the model.

Do professional developers exhibit such a large response bias (I would expect their average performance to be better)?

People tend to write fewer negative tests, than positive tests. Is this behavior related to the believability that certain negative events can occur?

Believability is an underappreciated coding issue.

Hopefully people will start doing experiments to investigate this issue :-)

Performance impact of comments on tasks taking a few minutes

How cost-effective is an investment in commenting code?

Answering this question requires knowing the time needed to write the comment and the time they save for later readers of the code.

A recent study investigated the impact of comments in small programming tasks on developer performance, and Sebastian Nielebock, the first author, kindly sent me a copy of the data.

How might the performance impact of comments be measured?

The obvious answer is to ask subjects to solve a coding problem, with half the subjects working with code containing comments and the other half the same code without the comments. This study used three kinds of commenting: No comments, Implementation comments and Documentation comments; the source was in Java.

Were the comments in the experiment useful, in the sense of providing information that was likely to save readers some time? A preliminary run was used to check that the comments provided some benefit.

The experiment was designed to be short enough that most subjects could complete it in less than an hour (average time to complete all tasks was 31 minutes). My own experience with running experiments is that it is possible to get professional developers to donate an hour of their time.

What is a realistic and experimentally useful amount of work to ask developers to in an hour?

The authors asked subjects to complete 9-tasks; three each of applying the code (i.e., use the code’s API), fix a bug in the code, and extend the code. Would a longer version of one of each, rather than a shorter three of each been better? I think the only way to find out is to try it both ways (I hope the authors plan to do another version).

What were the results (code+data)?

Regular readers will know, from other posts discussing experiments, that the biggest factor is likely to be subject (professional developers+students) differences, and this is true here.

Based on a fitted regression model, Documentation comments slowed performance on a task by 30 seconds, compared to No comments and Implementation comments (which both had the same performance impact). Given that average task completion time was 205 seconds, this is a 15% slowdown for Documentation comments.

This study set out to measure the performance impact of comments on small programming tasks. The answer, at least for tasks designed to take a few minutes, is that No comments, or if comments are required, then write Implementation comments.

This experiment measured the performance impact of comments on developers who did not write the code containing them. These developers have to first read and understand the comments (which takes time). However, the evidence suggests that code is mostly modified by the developer who wrote it (just reading the code does not leave a record that can be analysed). In this case, the reading a comment (that the developer previously wrote) can trigger existing memories, i.e., it has a greater information content for the original author.

Will comments have a bigger impact when read by the person who wrote them (and the code), or on tasks taking more than a few minutes? I await the results of more experiments…

Payback time-frame for research in software engineering

What are the major questions in software engineering that researchers should be trying to answer?

A high level question whose answer is likely to involve life, the universe, and everything is: What is the most cost-effective way to build software systems?

Viewing software engineering research as an attempt to find the answer to a big question mirrors physicists quest for a Grand Unified Theory of how the Universe works.

Physicists have the luxury of studying the Universe at their own convenience, the Universe does not need their input to do a better job.

Software engineering is not like physics. Once a software system has been built, the resources have been invested, and there is no reason to recreate it using a more cost-effective approach (the zero cost of software duplication means that manufacturing cost is the cost of the first version).

Designing and researching new ways of building software systems may be great fun, but the time and money needed to run the realistic experiments needed to evaluate their effectiveness is such that they are unlikely to be run. Searching for more cost-effective software development techniques by paying to run the realistic experiments needed to evaluate them, and waiting for the results to become available, is going to be expensive and time-consuming. A theory is proposed, experiments are run, results are analysed; rinse and repeat until a good-enough cost-effective technique is found. One iteration will take many years, and this iterative process is likely to take many decades.

Very many software systems are being built and maintained, and each of these is an experiment. Data from these ‘experiments’ provides a cost-effective approach to improving existing software engineering practices by studying the existing practices to figure out how they work (or don’t work).

Given the volume of ongoing software development, most of the payback from any research investment is likely to occur in the near future, not decades from now; the evidence shows that source code has a short and lonely existence. Investing for a payback that might occur 30-years from now makes no sense; researchers I talk to often use this time-frame when I ask them about the benefits of their research, i.e., just before they are about to retire. Investing in software engineering research only makes economic sense when it is focused on questions that are expected to start providing payback in, say, 3-5 years.

Who is going to base their research on existing industry practices?

Researching existing practices often involves dealing with people issues, and many researchers in computing departments are not that interested in the people side of software engineering, or rather they are more interested in the computer side.

Algorithm oriented is how I would describe researchers who claim to be studying software engineering. I am frequently told about the potential for huge benefits from the discovery of more efficient algorithms. For many applications, algorithms are now commodities, i.e., they are good enough. Those with a career commitment to studying algorithms have a blinkered view of the likely benefits of their work (most of those I have seen are doing studying incremental improvements, and are very unlikely to make a major break through).

The number of researchers studying what professional developers do, with an aim to improving it, is very small (I am excluding the growing number of fake researchers doing surveys). While I hope there will be a significant growth in numbers, I’m not holding my breadth (at least in the short term; as for the long term, Planck’s experience with quantum mechanics was: “Science advances one funeral at a time”).

How should involved if-statement conditionals be structured?

Which of the following two if-statements do you think will be processed by readers in less time, and with fewer errors, when given the value of x, and asked to specify the output?

// First - sequence of subexpressions
if (x > 0 && x < 10 || x > 20 && x < 30)
   print("a");
else
   print "b");

// Second - nested ifs
if (x > 0 && x < 10)
   print("c");
else if (x > 20 && x < 30)
   print("d");
else
   print("e");

Ok, the behavior is not identical, in that the else if-arm produces different output than the preceding if-arm.

The paper Syntax, Predicates, Idioms — What Really Affects Code Complexity? analyses the results of an experiment that asked this question, including more deeply nested if-statements, the use of negation, and some for-statement questions (this post only considers the number of conditions/depth of nesting components). A total of 1,583 questions were answered by 220 professional developers, with 415 incorrect answers.

Based on the coefficients of regression models fitted to the results, subjects processed the nested form both faster and with fewer incorrect answers (code+data). As expected performance got slower, and more incorrect answers given, as the number of intervals in the if-condition increased (up to four in this experiment).

I think short-term memory is involved in this difference in performance; or at least I can concoct a theory that involves a capacity limited memory. Comprehending an expression (such as the conditional in an if-statement) requires maintaining information about the various components of the expression in working memory. When the first subexpression of x > 0 && x < 10 || x > 20 && x < 30 is false, and the subexpression after the || is processed, there is no now forget-what-went-before point like there is for the nested if-statements. I think that the single expression form is consuming more working memory than the nested form.

Does the result of this experiment (assuming it is replicated) mean that developers should be recommended to write sequences of conditions (e.g., the first if-statement example) about as:

if (x > 0 && x < 10)
   print("a");
else if (x > 20 && x < 30)
   print("a");
else
   print("b");

Duplicating code is not good, because both arms have to be kept in sync; ok, a function could be created, but this is extra effort. As other factors are taken into account, the costs of the nested form start to build up, is the benefit really worth the cost?

Answering this question is likely to need a lot of work, and it would be a more efficient use of resources to address questions about more commonly occurring conditions first.

A commonly occurring use is testing a single range; some of the ways of writing the range test include:

if (x > 0 && x < 10) ...

if (0 < x && x < 10) ...

if (10 > x && x > 0) ...

if (x > 0 && 10 > x) ...

Does one way of testing the range require less effort for readers to comprehend, and be more likely to be interpreted correctly?

There have been some experiments showing that people are more likely to give correct answers to questions involving information expressed as linear syllogisms, if the extremes are at the start/end of the sequence, such as in the following:

     A is better than B
     B is better than C

and not the following (which got the lowest percentage of correct answers):

     B is better than C
     B is worse than A

Your author ran an experiment to find out whether developers were more likely to give correct answers for particular forms of range tests in if-conditions.

Out of a total of 844 answers, 40 were answered incorrectly (roughly one per subject; it was a paper and pencil experiment, so no timings). It's good to see that the subjects were so competent, but with so few mistakes made the error bars are very wide, i.e., too few mistakes were made to be able to say that one representation was less mistake-prone than another.

I hope this post has got other researchers interested in understanding developer performance, when processing if-statements, and that they will be running more experiments help shed light on the processes involved.

An experiment involving matching regular expressions

Recommendations for/against particular programming constructs have one thing in common: there is no evidence backing up any of the recommendations. Running experiments to measure the impact of particular language features on developer performance is not something that researchers do (there have been a handful of experiments looking at the impact of strong typing on developer performance; the effect measured was tiny).

In February I discovered two groups researching regular expressions. In the first post on duplicate regexs, I promised to say something about the second group. This post discusses an experiment comparing developer comprehension of various regular expressions; the paper is: Exploring Regular Expression Comprehension.

The experiment involved 180 workers on Mechanical Turk (to be accepted, workers had to correctly answer four or five questions about regular expressions). Workers/subjects performed two different tasks, matching and composition.

  • In the matching task workers saw a regex and a list of five strings, and had to specify whether the regex matched (or not) each string (there was also an unsure response).
  • In the composition task workers saw a regular expression, and had to create a string matched by this regex. Each worker saw 10 different regexs, which were randomly drawn from a set of 60 regexs (which had been created to be representative of various regex characteristics). I have not analysed this data yet.

What were the results?

For the matching task: given each of the pairs of regexs below, which one (of each pair) would you say workers were most likely to get correct?

         R1                  R2
1.     tri[a-f]3         tri[abcdef]3
2.     no[w-z]5          no[wxyz]5
3.     no[w-z]5          no(w|x|y|z)5
4.     [ˆ0-9]            [\D]

The percentages correct for (1) were essentially the same, at 94.0 and 93.2 respectively. The percentages for (2) were 93.3 and 87.2, which is odd given that the regex is essentially the same as (1). Is this amount of variability in subject response to be expected? Is the difference caused by letters being much less common in text, so people have had less practice using them (sounds a bit far-fetched, but its all I could think of). The percentages for (3) are virtually identical, at 93.3 and 93.7.

The percentages for (4) were 58 and 73.3, which surprised me. But then I have been using regexs since before \D support was generally available. The MTurk generation have it easy not having to use the ‘hard stuff’ 😉

See Table III in the paper for more results.

This matching data might be analysed using Item Response theory, which can take into account differences in question difficulty and worker/subject ability. The plot below looks complicated, but only because there are so many lines. Each numbered colored line is a different regex, worker ability is on the x-axis (greater ability on the right), and the y-axis is the probability of giving a correct answer (code+data; thanks to Peipei Wang for fixing the bugs in my code):

Probability of giving a correct answer, by subject ability, for 60 regex matching questions

Yes, for question 51 the probability of a correct answer decreases with worker ability. Heads are being scratched about this.

There might be some patterns buried in amongst all those lines, e.g., particular kinds of patterns require a given level of ability to handle, or correct response to some patterns varying over the whole range of abilities. These are research questions, and this is a blog article: answers in the comments :-)

This is the first experiment of its kind, so it is bound to throw up more questions than answers. Are more incorrect responses given for longer regexs, particularly if they cannot be completely held in short-term memory? It is convenient for the author to use a short-hand for a range of characters (e.g., a-f), and I was expecting a difference in performance when all the letters were enumerated (e.g., abcdef); I had theories for either one being less error-prone (I obviously need to get out more).

How useful are automatically generated compiler tests?

Over the last decade, testing compilers using automatically generated source code has been a popular research topic (for those working in the compiler field; Csmith kicked off this interest). Compilers are large complicated programs, and they will always contain mistakes that lead to faults being experienced. Previous posts of mine have raised two issues on the use of automatically generated tests: a financial issue (i.e., fixing reported faults costs money {most of the work on gcc and llvm is done by people working for large companies}, and is intended to benefit users not researchers seeking bragging rights for their latest paper), and applicability issue (i.e., human written code has particular characteristics and unless automatically generated code has very similar characteristics the mistakes it finds are unlikely to commonly occur in practice).

My claim that mistakes in compilers found by automatically generated code are unlikely to be the kind of mistakes that often lead to a fault in the compilation of human written code is based on the observations (I don’t have any experimental evidence): the characteristics of automatically generated source is very different from human written code (I know this from measurements of lots of code), and this difference results in parts of the compiler that are infrequently executed by human written code being more frequently executed (increasing the likelihood of a mistake being uncovered; an observation based on my years working on compilers).

An interesting new paper, Compiler Fuzzing: How Much Does It Matter?, investigated the extent to which fault experiences produced by automatically generated source are representative of fault experiences produced by human written code. The first author of the paper, Michaël Marcozzi, gave a talk about this work at the Papers We Love workshop last Sunday (videos available).

The question was attacked head on. The researchers instrumented the code in the LLVM compiler that was modified to fix 45 reported faults (27 from four fuzzing tools, 10 from human written code, and 8 from a formal verifier); the following is an example of instrumented code:

warn ("Fixing patch reached");
if (Not.isPowerOf2()) {
   if (!(C-> getValue().isPowerOf2()  // Check needed to fix fault
         && Not != C->getValue())) {
      warn("Fault possibly triggered");
   } else { /* CODE TRANSFORMATION */ } } // Original, unfixed code

The instrumented compiler was used to build 309 Debian packages (around 10 million lines of C/C++). The output from the builds were (possibly miscompiled) built versions of the packages, and log files (from which information could be extracted on the number of times the fixing patches were reached, and the number of cases where the check needed to fix the fault was triggered).

Each built package was then checked using its respective test suite; a package built from miscompiled code may successfully pass its test suite.

A bitwise compare was run on the program executables generated by the unfixed and fixed compilers.

The following (taken from Marcozzi’s slides) shows the percentage of packages where the fixing patch was reached during the build, the percentages of packages where code added to fix a fault was triggered, the percentage where a different binary was generated, and the percentages of packages where a failure was detected when running each package’s tests (0.01% is one failure):

Percentage of packages where patched code was reached during builds, and packages with failing tests.

The takeaway from the above figure is that many packages are affected by the coding mistakes that have been fixed, but that most package test suites are not affected by the miscompilations.

To find out whether there is a difference, in terms of impact on Debian packages, between faults reported in human and automatically generated code, we need to compare number of occurrences of “Fault possibly triggered”. The table below shows the break-down by the detector of the coding mistake (i.e., Human and each of the automated tools used), and the number of fixed faults they contributed to the analysis.

Human, Csmith and EMI each contributed 10-faults to the analysis. The fixes for the 10-fault reports in human generated code were triggered 593 times when building the 309 Debian packages, while each of the 10 Csmith and EMI fixes were triggered 1,043 and 948 times respectively; a lot more than the Human triggers :-O. There are also a lot more bitwise compare differences for the non-Human fault-fixes.

Detector  Faults   Reached    Triggered   Bitwise-diff   Tests failed
Human       10      1,990         593         56              1
Csmith      10      2,482       1,043        318              0
EMI         10      2,424         948        151              1
Orange       5        293          35          8              0
yarpgen      2        608         257          0              0
Alive        8      1,059         327        172              0

Is the difference due to a few packages being very different from the rest?

The table below breaks things down by each of the 10-reported faults from the three Detectors.

Ok, two Human fault-fix locations are never reached when compiling the Debian packages (which is a bit odd), but when the locations are reached they are just not triggering the fault conditions as often as the automatic cases.

Detector   Reached    Triggered
Human
              300       278
              301         0
              305         0
                0         0
                0         0
              133        44
              286       231
              229         0
              259        40
               77         0
Csmith
              306         2
              301       118
              297       291
              284         1
              143         6
              291       286
              125       125
              245         3
              285        16
              205       205
EMI      
              130         0
              307       221
              302       195
              281        32
              175         5
              122         0
              300       295
              297       215
              306       191
              287        10

It looks like I am not only wrong, but that fault experiences from automatically generated source are more (not less) likely to occur in human written code (than fault experiences produced by human written code).

This is odd. At best I would expect fault experiences from human and automatically generated code to have the same characteristics.

Ideas and suggestions welcome.

Three books discuss three small data sets

During the early years of a new field, experimental data relating to important topics can be very thin on the ground. Ever since the first computer was built, there has been a lot of data on the characteristics of the hardware. Data on the characteristics of software, and the people who write it has been (and often continues to be) very thin on the ground.

Books are sometimes written by the researchers who produce the first data associated with an important topic, even if the data set is tiny; being first often generates enough interest for a book length treatment to be considered worthwhile.

As a field progresses lots more data becomes available, and the discussion in subsequent books can be based on findings from more experiments and lots more data

Software engineering is a field where a few ‘first’ data books have been published, followed by silence, or rather lots of arm waving and little new data. The fall of Rome has been followed by a 40-year dark-age, from which we are slowly emerging.

Three of these ‘first’ data books are:

  • “Man-Computer Problem Solving” by Harold Sackman, published in 1970, relating to experimental data from 1966. The experiments investigated the impact of two different approaches to developing software, on programmer performance (i.e., batch processing vs. on-line development; code+data). The first paper on this work appeared in an obscure journal in 1967, and was followed in the same issue by a critique pointing out the wide margin of uncertainty in the measurements (the critique agreed that running such experiments was a laudable goal).

    Failing to deal with experimental uncertainty is nothing compared to what happened next. A 1968 paper in a widely read journal, the Communications of the ACM, contained the following table (extracted from a higher quality scan of a 1966 report by the same authors, and available online).

    Developer performance ratios.

    The tale of 1:28 ratio of programmer performance, found in an experiment by Grant/Sackman, took off (the technical detail that a lot of the difference was down to the techniques subjects’ used, and not the people themselves, got lost). The Grant/Sackman ‘finding’ used to be frequently quoted in some circles (or at least it did when I moved in them, I don’t know often it is cited today). In 1999, Lutz Prechelt wrote an expose on the sorry tale.

    Sackman’s book is very readable, and contains lots of details and data not present in the papers, including survey data and a discussion of the intrinsic uncertainties associated with the experiment; it also contains the table above.

  • “Software Engineering Economics” by Barry W. Boehm, published in 1981. I wrote about the poor analysis of the data contained in this book a few years ago.

    The rest of this book contains plenty of interesting material, and even sounds modern (because books moving the topic forward have not been written).

  • “Program Evolution: Process of Software Change” edited by M. M. Lehman and L. A. Belady, published in 1985, relating to experimental data from 1977 and before. Lehman and Belady managed to obtain data relating to 19 releases of an IBM software product (yes, 19, not nineteen-thousand); the data was primarily the date and number of modules contained in each release, plus less specific information about number of statements. This data was sliced and diced every which way, and the book contains many papers with the same data appearing in the same plot with different captions (had the book not been a collection of papers it would have been considerably shorter).

    With a lot less data than Isaac Newton had available to formulate his three laws, Lehman and Belady came up with five, six, seven… “laws of software evolution” (which themselves evolved with the publication of successive papers).

    The availability of Open source repositories means there is now a lot more software system evolution data available. Lehman’s laws have not stood the test of more data, although people still cite them every now and again.

How much is a 1-hour investment today worth a year from now?

Today, I am thinking of investing 1-hour of effort adding more comments to my code; how much time must this investment save me X-months from now, for today’s 1-hour investment to be worthwhile?

Obviously, I must save at least 1-hour. But, the purpose of making an investment is to receive a greater amount at a later time; ‘paying’ 1-hour to get back 1-hour is a poor investment (unless I have nothing else to do today, and I’m likely to be busy in the coming months).

The usual economic’s based answer is based on compound interest, the technique your bank uses to calculate how much you owe them (or perhaps they owe you), i.e., the expected future value grows exponentially at some interest rate.

Psychologists were surprised to find that people don’t estimate future value the way economists do. Hyperbolic discounting provides a good match to the data from experiments that asked subjects to value future payoffs. The form of the equation used by economists is: e^{-kD}, while hyperbolic discounting has the form 1/{1+kD}, where: k is a constant, and D the period of time.

The simple economic approach does not explicitly include the risk that one of the parties involved may cease to exist. Including risk is non-trivial, banks handle the risk that you might disappear by asking for collateral, or adding something to the interest rate charged.

The fact that humans, and some other animals, have been found to use hyperbolic discounting suggests that evolution has found this approach, to discounting time, increases the likelihood of genes being passed on to the next generation. A bird in the hand is worth two in the bush.

How do software developers discount investment in software engineering projects?

The paper Temporal Discounting in Technical Debt: How do Software Practitioners Discount the Future? describes a study that specifies a decision that has to be made and two options, as follows:

“You are managing an N-years project. You are ahead of schedule in the current iteration. You have to decide between two options on how to spend our upcoming week. Fill in the blank to indicate the least amount of time that would make you prefer Option 2 over Option 1.

  • Option 1: Implement a feature that is in the project backlog, scheduled for the next iteration. (five person days of effort).
  • Option 2: Integrate a new library (five person days effort) that adds no new functionality but has a 60% chance of saving you person days of effort over the duration of the project (with a 40% chance that the library will not result in those savings).

Subjects are then asked six questions, each having the following form (for various time frames):

“For a project time frame of 1 year, what is the smallest number of days that would make you prefer Option 2? ___”

The experiment is run twice, using professional developers from two companies, C1 and C2 (23 and 10 subjects, respectively), and the data is available for download :-)

The following plot shows normalised values given by some of the subjects from company C1, for the various time periods used (y-axis shows PresentValue/FutureValue). On a log scale, values estimated using the economists exponential approach would form a straight line (e.g., close to the first five points of subject M, bottom right), and values estimated using the hyperbolic approach would have the concave form seen for subject C (top middle) (code+data).

Normalised returned required for various elapsed years.

Subject B is asking for less, not more, over a longer time period (several other subjects have the same pattern of response). Why did Subject E (and most of subject G’s responses) not vary with time? Perhaps they were tired and were not willing to think hard about the problem, or perhaps they did not think the answer made much difference. The subjects from company C2 showed a greater amount of variety. Company C1 had some involvement with financial applications, while company C2 was involved in simulations. Did this domain knowledge spill over into company C1’s developers being more likely to give roughly consistent answers?

The experiment was run online, rather than an experimenter being in the room with subjects. It is possible that subjects would have invested more effort if a more formal setting, with an experimenter who had made the effort to be present. Also, if an experimenter had been present, it would have been possible to ask question to clarify any issues.

Both exponential and hyperbolic equations can be fitted to the data, but given the diversity of answers, it is difficult to put any weight in either regression model. Some subjects clearly gave responses fitting a hyperbolic equation, while others gave responses fitted approximately well by either approach, and other subjects used. It was possible to fit the combined data from all of company C1 subjects to a single hyperbolic equation model (the most significant between subject variation was the value of the intercept); no such luck with the data from company C2.

I’m very please to see there has been a replication of this study, but the current version of the paper is a jumble of ideas, and is thin on experimental procedure. I’m sure it will improve.

What do we learn from this study? Perhaps that developers need to learn something about calculating expected future payoffs.

Modular vs. monolithic programs: a big performance difference

For a long time now I have been telling people that no experiment has found a situation where the treatment (e.g., use of a technique or tool) produces a performance difference that is larger than the performance difference between the subjects.

The usual results are that differences between people is the source of the largest performance difference, successive runs are the next largest (i.e., people get better with practice), and the smallest performance difference occurs between using/not using the technique or tool.

This is rather disheartening news.

While rummaging through a pile of books I had not looked at in many years, I (re)discovered the paper “An empirical study of the effects of modularity on program modifiability” by Korson and Vaishnavi, in “Empirical Studies of Programmers” (the first one in the series). It’s based on Korson’s 1988 PhD thesis, with the same title.

There were four experiments, involving seven people from industry and nine students, each involving modifying a 900(ish)-line program in some way. There were two versions of each program, they differed in that one was written in a modular form, while the other was monolithic. Subjects were permuted between various combinations of program version/problem, but all problems were solved in the same order.

The performance data (time to complete the task) was published in the paper, so I fitted various regressions models to it (code+data). There is enough information in the data to separate out the effects of modular/monolithic, kind of problem and subject differences. Because all subjects solved problems in the same order, it is not possible to extract the impact of learning on performance.

The modular/monolithic performance difference was around twice as large as the difference between subjects (removing two very poorly performing subjects reduces the difference to 1.5). I’m going to have to change my slides.

Would the performance difference have been so large if all the subjects had been experienced developers? There is not a lot of well written modular code out there, and so experienced developers get lots of practice with spaghetti code. But, even if the performance difference is of the same order as the difference between developers, that is still a very worthwhile difference.

Now there are lots of ways to write a program in modular form, and we don’t know what kind of job Korson did in creating, or locating, his modular programs.

There are also lots of ways of writing a monolithic program, some of them might be easy to modify, others a tangled mess. Were these programs intentionally written as spaghetti code, or was some effort put into making them easy to modify?

The good news from the Korson study is that there appears to be a technique that delivers larger performance improvements than the difference between people (replication needed). We can quibble over how modular a modular program needs to be, and how spaghetti-like a monolithic program has to be.

Impact of group size and practice on manual performance

How performance varies with group size is an interesting question that is still an unresearched area of software engineering. The impact of learning is also an interesting question and there has been some software engineering research in this area.

I recently read a very interesting study involving both group size and learning, and Jaakko Peltokorpi kindly sent me a copy of the data.

That is the good news; the not so good news is that the experiment was not about software engineering, but the manual assembly of a contraption of the experimenters devising. Still, this experiment is an example of the impact of group size and learning (through repeating the task).

Subjects worked in groups of one to four people and repeated the task four times. Time taken to assemble a bespoke, floor standing rack with some odd-looking connections between components (the image in the paper shows an image of something that might function as a floor standing book-case, if shelves were added, apart from some component connections getting in the way) was measured.

The following equation is a very good fit to the data (code+data). There is theory explaining why log(repetitions) applies, but the division by group-size was found by suck-it-and-see (in another post I found that time spent planning increased with teams size).

There is a strong repetition/group-size interaction. As the group size increases, repetition has less of an impact on improving performance.

time = 0.16+ 0.53/{group size} - log(repetitions)*[0.1 + {0.22}/{group size}]

The following plot shows one way of looking at the data (larger groups take less time, but the difference declines with practice):

Time taken (hours) for various group sizes, by repetition.

and here is another (a group of two is not twice as fast as a group of one; with practice smaller groups are converging on the performance of larger groups):

Time taken (hours) for various repetitions, by group size.

Would the same kind of equation fit the results from solving a software engineering task? Hopefully somebody will run an experiment to find out :-)

Students vs. professionals in software engineering experiments

Experiments are an essential component of any engineering discipline. When the experiments involve people, as subjects in the experiment, it is crucial that the subjects are representative of the population of interest.

Academic researchers have easy access to students, but find it difficult to recruit professional developers, as subjects.

If the intent is to generalize the results of an experiment to the population of students, then using student as subjects sounds reasonable.

If the intent is to generalize the results of an experiment to the population of professional software developers, then using student as subjects is questionable.

What it is about students that makes them likely to be very poor subjects, to use in experiments designed to learn about the behavior and performance of professional software developers?

The difference between students and professionals is practice and experience. Professionals have spent many thousands of hours writing code, attending meetings discussing the development of software; they have many more experiences of the activities that occur during software development.

The hours of practice reading and writing code gives professional developers a fluency that enables them to concentrate on the problem being solved, not on technical coding details. Yes, there are students who have this level of fluency, but most have not spent the many hours of practice needed to achieve it.

Experience gives professional developers insight into what is unlikely to work and what may work. Without experience students have no way of evaluating the first idea that pops into their head, or a situation presented to them in an experiment.

People working in industry are well aware of the difference between students and professional developers. Every year a fresh batch of graduates start work in industry. The difference between a new graduate and one with a few years experience is apparent for all to see. And no, Masters and PhD students are often not much better and in some cases worse (their prolonged sojourn in academia means that have had more opportunity to pick up impractical habits).

It’s no wonder that people in industry laugh when they hear about the results from experiments based on student subjects.

Just because somebody has “software development” in their job title does not automatically make they an appropriate subject for an experiment targeting professional developers. There are plenty of managers with people skills and minimal technical skills (sub-student level in some cases)

In the software related experiments I have run, subjects were asked how many lines of code they had read/written. The low values started at 25,000 lines. The intent was for the results of the experiments to be generalized to the population of people who regularly wrote code.

Psychology journals are filled with experimental papers that used students as subjects. The intent is to generalize the results to the general population. It has been argued that students are not representative of the general population in that they have spent more time reading, writing and reasoning than most people. These subjects have been labeled as WEIRD.

I spend a lot of time reading software engineering papers. If a paper involves human subjects, the first thing I do is find out whether the subjects were students (usual) or professional developers (not common). Authors sometimes put effort into dressing up their student subjects as having professional experience (perhaps some of them have spent a year or two in industry, but talking to the authors often reveals that the professional experience was tutoring other students), others say almost nothing about the identity of the subjects. Papers describing experiments using professional developers, trumpet this fact in the abstract and throughout the paper.

I usually delete any paper using student subjects, some of the better ones are kept in a subdirectory called students.

Software engineering researchers are currently going through another bout of hand wringing over the use of student subjects. One paper makes the point that a student based experiment is a good way of validating an experiment that will later involve professional developers. This is a good point, but ignored the problem that researchers rarely move on to using professional subjects; many researchers only ever intend to run student-based experiments. Also, they publish the results from the student based experiment, which are at best misleading (but academics get credit for publishing papers, not for the content of the papers).

Researchers are complaining that reviews are rejecting their papers on student based experiments. I’m pleased to hear that reviewers are rejecting these papers.

Experimental Psychology by Robert S. Woodworth

I have just discovered “Experimental Psychology” by Robert S. Woodworth; first published in 1938, I have a reprinted in Great Britain copy from 1951. The Internet Archive has a copy of the 1954 revised edition; it’s a very useful pdf, but it does not have the atmospheric musty smell of an old book.

The Archives of Psychology was edited by Woodworth and contain reports of what look like ground breaking studies done in the 1930s.

The book is surprisingly modern, in that the topics covered are all of active interest today, in fields related to cognitive psychology. There are lots of experimental results (which always biases me towards really liking a book) and the coverage is extensive.

The history of cognitive psychology, as I understood it until this week, was early researchers asking questions, doing introspection and sometimes running experiments in the late 1800s and early 1900s (e.g., Wundt and Ebbinghaus), behaviorism dominants the field, behaviorism is eviscerated by Chomsky in the 1960s and cognitive psychology as we know it today takes off.

Now I know that lots of interesting and relevant experiments were being done in the 1920s and 1930s.

What is missing from this book? The most obvious omission is equations; lots of data points plotted on graph paper, but no attempt to fit an equation to anything, e.g., an exponential curve to the rate of learning.

A more subtle omission is the world view; digital computers had not been invented yet and Shannon’s information theory was almost 20 years in the future. Researchers tend to be heavily influenced by the tools they use and the zeitgeist. Computers as calculators and information processors could not be used as the basis for models of the human mind; they had not been invented yet.

Replication: not always worth the effort

Replication is the means by which mistakes get corrected in science. A researcher does an experiment and gets a particular result, but unknown to them one or more unmeasured factors (or just chance) had a significant impact. Another researcher does the same experiment and fails to get the same results, and eventually many experiments later people have figured out what is going on and what the actual answer is.

In practice replication has become a low status activity, journals want to publish papers containing new results, not papers backing up or refuting the results of previously published papers. The dearth of replication has led to questions being raised about large swathes of published results. Most journals only published papers that contain positive results, i.e., something was shown to some level of statistical significance; only publishing positive results produces publication bias (there have been calls for journals that publishes negative results).

Sometimes, repeating an experiment does not seem worth the effort. One such example is: An Explicit Strategy to Scaffold Novice Program Tracing. It looks like the authors ran a proper experiment and did everything they are supposed to do; but, I think the reason that got a positive result was luck.

The experiment involved 24 subjects and these were randomly assigned to one of two groups. Looking at the results (figures 4 and 5), it appears that two of the subjects had much lower ability that the other subjects (the authors did discuss the performance of these two subjects). Both of these subjects were assigned to the control group (there is a 25% chance of this happening, but nobody knew what the situation was until the experiment was run), pulling down the average of the control, making the other (strategy) group appear to show an improvement (i.e., the teaching strategy improved student performance).

Had one, or both, low performers been assigned to the other (strategy) group, no experimental effect would have shown up in the results, significantly reducing the probability that the paper would have been accepted for publication.

Why did the authors submit the paper for publication? Well, academic performance is based on papers published (quality of journal they appear in, number of citations, etc), a positive result is reason enough to submit for publication. The researchers did what they have been incentivized to do.

I hope the authors of the paper continue with their experiments. Life is full of chance effects and the only way to get a solid result is to keep on trying.

Experimental method for measuring benefits of identifier naming

I was recently came across a very interesting experiment in Eran Avidan’s Master’s thesis. Regular readers will know of my interest in identifiers; while everybody agrees that identifier names have a significant impact on the effort needed to understand code, reliably measuring this impact has proven to be very difficult.

The experimental method looked like it would have some impact on subject performance, but I was not expecting a huge impact. Avidan’s advisor was Dror Feitelson, who kindly provided the experimental data, answered my questions and provided useful background information (Dror is also very interested in empirical work and provides a pdf of his book+data on workload modeling).

Avidan’s asked subjects to figure out what a particular method did, timing how long it took for them to work this out. In the control condition a subject saw the original method and in the experimental condition the method name was replaced by xxx and local and parameter names were replaced by single letter identifiers. The hypothesis was that subjects would take longer for methods modified to use ‘random’ identifier names.

A wonderfully simple idea that does not involve a lot of experimental overhead and ought to be runnable under a wide variety of conditions, plus the difference in performance is very noticeable.

The think aloud protocol was used, i.e., subjects were asked to speak their thoughts as they processed the code. Having to do this will slow people down, but has the advantage of helping to ensure that a subject really does understand the code. An overall slower response time is not important because we are interested in differences in performance.

Each of the nine subjects sequentially processed six methods, with the methods randomly assigned as controls or experimental treatments (of which there were two, locals first and parameters first).

The procedure, when a subject saw a modified method was as follows: the subject was asked to explain the method’s purpose, once an answer was given either the local or parameter names were revealed and the subject had to again explain the method’s purpose, and when an answer was given the names of both locals and parameters was revealed and a final answer recorded. The time taken for the subject to give a correct answer was recorded.

The summary output of a model fitted using a mixed-effects model is at the end of this post (code+data; original experimental materials). There are only enough measurements to have subject as a random effect on the treatment; no order of presentation data is available to look for learning effects.

Subjects took longer for modified methods. When parameters were revealed first, subjects were 268 seconds slower (on average), and when locals were revealed first 342 seconds slower (the standard deviation of the between subject differences was 187 and 253 seconds, respectively; less than the treatment effect, surprising, perhaps a consequence of information being progressively revealed helping the slower performers).

Why is subject performance less slow when parameter names are revealed first? My thoughts: parameter names (if well-chosen) provide clues about what incoming values represent, useful information for figuring out what a method does. Locals are somewhat self-referential in that they hold local information, often derived from parameters as initial values.

What other factors could impact subject performance?

The number of occurrences of each name in the body of the method provides an opportunity to deduce information; so I think time to figure out what the method does should less when there are many uses of locals/parameters, compared to when there are few.

The ability of subjects to recognize what the code does is also important, i.e., subject code reading experience.

There are lots of interesting possibilities that can be investigated using this low cost technique.

Linear mixed model fit by REML ['lmerMod']
Formula: response ~ func + treatment + (treatment | subject)
   Data: idxx
 
REML criterion at convergence: 537.8
 
Scaled residuals:
     Min       1Q   Median       3Q      Max
-1.34985 -0.56113 -0.05058  0.60747  2.15960
 
Random effects:
 Groups   Name                      Variance Std.Dev. Corr
 subject  (Intercept)               38748    196.8
          treatmentlocals first     64163    253.3    -0.96
          treatmentparameters first 34810    186.6    -1.00  0.95
 Residual                           43187    207.8
Number of obs: 46, groups:  subject, 9
 
Fixed effects:
                          Estimate Std. Error t value
(Intercept)                  799.0      110.2   7.248
funcindexOfAny              -254.9      126.7  -2.011
funcrepeat                  -560.1      135.6  -4.132
funcreplaceChars            -397.6      126.6  -3.140
funcreverse                 -466.7      123.5  -3.779
funcsubstringBetween        -145.8      125.8  -1.159
treatmentlocals first        342.5      124.8   2.745
treatmentparameters first    267.8      106.0   2.525
 
Correlation of Fixed Effects:
            (Intr) fncnOA fncrpt fncrpC fncrvr fncsbB trtmntlf
fncndxOfAny -0.524
funcrepeat  -0.490  0.613
fncrplcChrs -0.526  0.657  0.620
funcreverse -0.510  0.651  0.638  0.656
fncsbstrngB -0.523  0.655  0.607  0.655  0.648
trtmntlclsf -0.505 -0.167 -0.182 -0.160 -0.212 -0.128
trtmntprmtf -0.495 -0.184 -0.162 -0.184 -0.228 -0.213  0.673