Abstract Characteristics of a population are often unknown. To estimate such characteristics, random sampling must be used. Sampling is the process by which a subgroup of a population is examined in order to infer the values of the population's true characteristics. Estimates based on samples are approximations of the population's true value; therefore, it is often useful to know the reliability of such estimates. Standard errors are measures of reliability of a given sample's descriptive statistics with respect to the population's true values. This article reviews some widely used descriptive statistics as well as their standard error estimators and their confidence intervals. The statistics discussed are: the arithmetic mean, the median, the geometric mean, the harmonic mean, the variance, the standard deviation, the median absolute deviation, the quantile, the interquartile range, the skewness, as well as the kurtosis. Evaluations using Monte-Carlo simulations show that standard errors estimators, assuming a normally distributed population, are almost always reliable. In addition, as expected, smaller sample sizes lead to less reliable results. The only exception is the estimate of the confidence interval for kurtosis, which shows evidence of unreliability. We therefore propose an alternative measure of confidence interval based on the lognormal distribution. This review provides easy to find information about many descriptive statistics which can be used, for example, to plot error bars or confidence intervals.

The study of mental processes is at the forefront of research in cognitive psychology. However, the ability to identify the architectures responsible for specific behaviors is often quite difficult. To alleviate this difficulty, recent progress in mathematical psychology has brought forth Systems Factorial Technology (SFT; Townsend and Nozawa, 1995). Encompassing a series of analyses, SFT can diagnose and discriminate between five types of information processing architectures that possibly underlie a mental process. Despite the fact that SFT has led to new discoveries in cognitive psychology, the methodology itself remains far from intuitive to newcomers. This article therefore seeks to provide readers with a simple tutorial and a rudimentary introduction to SFT. This tutorial aims to encourage newcomers to read more about SFT and also to add it to their repertoire of analyses.

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