How many decimals? Rounding descriptive and inferential statistics based on measurement precision

Reporting descriptive statistics requires rounding the results. Experienced researchers typically round the numbers to one or two decimals, following the APA manual. However, this general recommendation ignores the sample size and the instrument's precision. Herein, expressions are derived that indicate how many decimals are reliable and so at what point the results should be rounded. The derivations are based on the measurement precision, that is, the precision of the raw data and uses propagation of error techniques. Two scenarios are considered, one in which systematic measurement error is possible and one in which only non-systematic measurement error is assumed. An example is provided showing how to round means, standard deviations and t values, among others, and an R library is available to automatize calculations. (C) 2020 Elsevier Inc. All rights reserved.