Academic journal article Psychonomic Bulletin & Review

Sample Size Bias in the Estimation of Means

Academic journal article Psychonomic Bulletin & Review

Sample Size Bias in the Estimation of Means

Article excerpt

The present research concerns the hypothesis that intuitive estimates of the arithmetic mean of a sample of numbers tend to increase as a function of the sample size; that is, they reflect a systematic sample size bias. A similar bias has been observed when people judge the average member of a group of people on an inferred quantity (e.g., a disease risk; see Price, 2001; Price, Smith, & Lench, 2006). Until now, however, it has been unclear whether it would be observed when the stimuli were numbers, in which case the quantity need not be inferred, and "average" can be precisely defined as the arithmetic mean. In two experiments, participants estimated the arithmetic mean of 12 samples of numbers. In the first experiment, samples of from 5 to 20 numbers were presented simultaneously and participants quickly estimated their mean. In the second experiment, the numbers in each sample were presented sequentially. The results of both experiments confirmed the existence of a systematic sample size bias.

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People must often make judgments about the average or typical member of a group on a single quantitative dimension. For example, a teacher might be asked by his students what the class average was on an exam. Or a survey respondent might be asked to report the average number of times she engages in a given behavior (e.g., consumes an alcoholic drink) per day, week, or year. Although previous research has found that such central tendency judgments tend to be accurate-a conclusion that we do not dispute-we hypothesize that they also reflect a systematic sample size bias. That is, they tend to increase as a function of the sample size, so that larger groups are judged to have greater central tendencies than smaller groups are. Furthermore, we believe that this is a fairly general bias that has implications for understanding a variety of judgment phenomena and also basic processes involved in quantitative reasoning and judgment.

Early researchers who studied central tendency judgments conceptualized people as "intuitive statisticians" (Peterson & Beach, 1967) and found them to be quite accurate when estimating the arithmetic mean of a sample of numbers (Anderson, 1964; Beach & Swenson, 1966; Levin, 1975; Spencer, 1961, 1963). For example, Spencer's (1963) participants estimated the mean of several sets of either 10 or 20 numbers that varied in terms of their variance and skewness. His overall finding was that "mean errors were remarkably low for all conditions" (p. 256). Beach and Swenson conducted a similar study with similar results, leading them to conclude that "the most important result of this experiment is the high degree of accuracy evidenced in [participants'] estimates" (p. 162).

Recently, however, we have found evidence of a systematic sample size bias in people's central tendency judgments. 1 For example, Price (2001) showed participants descriptions of several fictional employees in terms of their risk factors for having a heart attack and asked the participants to judge the heart attack risk of the average employee. He found that the risk of the average employee was judged to be higher as the company size increased from 5 to 10 employees, then again as the company size increased from 10 to 15 employees. In an extensive set of follow-up studies, Price, Smith, and Lench (2006) found a similar sample size bias when the stimulus people were presented in photographs and participants judged the likelihood that the average group member would experience a wide variety of negative, positive, and even neutral events. In their final study, Price et al. observed the sample size bias when the stimuli were identical stick figures and participants estimated their average height. This result is important, because it casts doubt on two plausible explanations of the sample size bias. One is that people misunderstand their task to be that of judging the likelihood that at least one person in the group will experience the event in question. …

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