Insensitivity to Sample Size

Insensitivity to sample size is the tendency to judge the likelihood or reliability of a sample statistic, such as an average or a proportion, without properly accounting for how much more variable that statistic tends to be when it comes from a small sample rather than a large one. The psychologists Daniel Kahneman and Amos Tversky documented the bias in a series of studies in the early 1970s, including a well known example in which participants judged a hospital with fifteen births a day exactly as likely as a hospital with forty five births a day to record more than sixty percent boys born on a given day, even though the smaller hospital is statistically far more likely to show such an extreme daily proportion by chance alone. The bias is discussed as one of the clearest illustrations of a broader failure to apply statistical reasoning about variance and sample size intuitively, even among participants who could correctly state the relevant statistical principle when asked directly.