Decimal Dust, Significant Digits, and the Search for Stars

The practice of rounding statistical results to two decimal places is one of a large number of heuristics followed in the social sciences. In evaluating this heuristic, the authors conducted simulations to investigate the precision of simple correlations. They considered a true correlation of .15 and ran simulations in which the sample sizes were 60, 100, 200, 500, 1,000, 10,000, and 100,000. They then looked at the digits in the correlations' first, second, and third decimal places to determine their reproducibility. They conclude that when n < 500, the habit of reporting a result to two decimal places seems unwarranted, and it never makes sense to report the third digit after the decimal place unless one has a sample size larger than 100,000. Similar results were found with rhos of .30, .50, and .70. The results offer an important qualification to what is otherwise a misleading practice.