83rd Annual Meeting of the Midwestern Psychological Association

Jennifer Golder

Comparing sets of numbers is a critical skill in mathematics, science, and everyday life. Although scientists use statistics to compare number sets formally, informal comparisons are quite common, in considering prices, sports performance, and grades. It is possible that individuals possess intuitive strategies for number set comparison in which sets are represented as summary values with approximations of means and variance. We investigated how college-aged individuals assessed number sets by examining how the properties of the data sets (e.g., mean differences and variance) influence accuracy and confidence in differences. Finally, we used these measures to evaluate participants data comparison strategies.

*Subjects. *Subjects were 30 Psychology students at Grand Valley State University.

Materials. Each subject saw 127 data set pairs with the following properties: (a) set size 2, 4, 6 or 8, (b) ratio of means of either 4:5 or 9:10, and (c) variance 10% or 20% of the mean.

*Procedure.* Subjects were presented a series of data sets on a computer. Participants were asked to determine which of two golfers (LEFT or RIGHT side) hit the ball farther (accuracy) and their reaction times were recorded (milliseconds). After completing the computer tasks, subjects were asked to evaluate the strategies they used to solve the sets.

*Results and Discussion.* As mean ratios decreased and variance increased, accuracy and confidence decreased as indicated through number correct, suggesting that the statistical properties of the sets influenced comparisons (see Figure 1). When the mean ratio was larger, participants responded more quickly than when it was smaller F(1, 30) = 19.15, p < .001. When the coefficient of variation was smaller, participants responded more quickly than when it was larger F(1, 30) = 23.95, p < .001. And participants took longer to respond with each increase in sample size F(3, 28) = 9.54, p < .001). Subjects were also more accurate when mean ration was larger, and when variance and sample size was smaller (F(3, 28) = 2.05, p < .001).

Discussion. These results suggest that participants detected the differences between data sets based on the statistical properties of the sets. The results clearly demonstrated an effect of means, variance, and sample size. More specifically, as mean differences increase and variance decreased, reaction times decreased and accuracy increased. The results suggest that subjects detect differences by creating approximate values that include means and variance.

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