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.