Development of integrated quantity judgments: means of distributions appear more different than they are

Inferential statistics are used to decide whether two or more samples are from the same or different distributions, a decision that is generally difficult to make by visual inspection of sample frequency distributions. We investigate how children (8, 10, and 12 year old) and adults compare two sets of five vertical bars, similar in appearance to histograms, to determine which set represents a greater quantity or whether they were equal quantities. Our bars are conceptually simpler than histograms because only bar lengths matter, not their position. Participants of all ages correctly identified about 75% of the sets with greater quantity. Judgment accuracy was, however, strongly affected by age when sets contained equal quantities, increasing from 13% correct for 8 year olds to 61% for adults. Recognizing equality is difficult when integrating across multiple bars, and difficulty increases with variability. Implications for comparing statistical distributions are discussed.