@article {Rousselet383935, author = {Guillaume A. Rousselet and Rand R. Wilcox}, title = {Reaction times and other skewed distributions: problems with the mean and the median}, elocation-id = {383935}, year = {2018}, doi = {10.1101/383935}, publisher = {Cold Spring Harbor Laboratory}, abstract = {To summarise skewed (asymmetric) distributions, such as reaction times, typically the mean or the median are used as measures of central tendency. Using the mean might seem surprising, given that it provides a poor measure of central tendency for skewed distributions, whereas the median provides a better indication of the location of the bulk of the observations. However, the sample median is biased: with small sample sizes, it tends to overestimate the population median. This is not the case for the mean. Based on this observation, Miller (1988) concluded that {\textquotedblright}sample medians must not be used to compare reaction times across experimental conditions when there are unequal numbers of trials in the conditions.{\textquotedblright} Here we replicate and extend Miller (1988), and demonstrate that his conclusion was ill-advised. In particular, we show that the main source of bias is not a difference in sample size but a difference in skewness. We also demonstrate that bias can be corrected using a percentile bootstrap bias correction. More importantly, a careful examination of the sampling distributions reveals that the sample median is not median biased, whereas the mean is median biased, which implies that in a typical experiment, the median provides a better estimate of central tendency than the mean. All the code and data to reproduce the figures and analyses in the article are available online.}, URL = {https://www.biorxiv.org/content/early/2018/08/10/383935}, eprint = {https://www.biorxiv.org/content/early/2018/08/10/383935.full.pdf}, journal = {bioRxiv} }