When comparing two independent groups, psychology researchers commonly use Student's t-tests. Assumptions of normality and homogeneity of variance underlie this test. More often than not, when these conditions are not met, Student's t-test can be severely biased and lead to invalid statistical inferences. Moreover, we argue that the assumption of equal variances will seldom hold in psychological research, and choosing between Student's t-test and Welch's t-test based on the outcomes of a test of the equality of variances often fails to provide an appropriate answer. We show that the Welch's t-test provides a better control of Type 1 error rates when the assumption of homogeneity of variance is not met, and it loses little robustness compared to Student's t-test when the assumptions are met. We argue that Welch's t-test should be used as a default strategy. Keywords:Welch's t-test; Student's t-test; homogeneity of variance; Levene's test; Homoscedasticity; statistical power; type 1 error; type 2 error Independent sample t-tests are commonly used in the psychological literature to statistically test differences between means. There are different types of t-tests, such as Student's t-test, Welch's t-test, Yuen's t-test, and a bootstrapped t-test. These variations differ in the underlying assumptions about whether data is normally distributed and whether variances in both groups are equal (see, e.g., Rasch, Kubinger, & Moder, 2011;Yuen, 1974). Student's t-test is the default method to compare two groups in psychology. The alternatives that are available are considerably less often reported. This is surprising, since Welch's t-test is often the preferred choice and is available in practically all statistical software packages.In this article, we will review the differences between Welch's t-test, Student's t-test, and Yuen's t-test, and we suggest that Welch's t-test is a better default for the social sciences than Student's and Yuen's t-tests. We do not include the bootstrapped t-test because it is known to fail in specific situations, such as when there are unequal sample sizes and standard deviations differ moderately (Hayes & Cai, 2007).When performing a t-test, several software packages (i.e., R and Minitab) present Welch's t-test by default. Users can request Student's t-test, but only after explicitly stating that the assumption of equal variances is met. Student's t-test is a parametric test, which means it relies on assumptions about the data that are analyzed. Parametric tests are believed to be more powerful than non-parametric tests (i.e., tests that do not require assumptions about the population parameters; Sheskin, 2003). However, Student's t-test is generally only more powerful when the data are normally distributed (the assumption of normality) and the variances are equal in both groups (homoscedasticity; the assumption of homogeneity of variance; Carroll & Schneider, 1985;Erceg-Hurn & Mirosevich, 2008).When sample sizes are equal between groups, Student's t-test is robust to violations of the assump...

Researchers often lack knowledge about how to deal with outliers when analyzing their data. Even more frequently, researchers do not pre-specify how they plan to manage outliers. In this paper we aim to improve research practices by outlining what you need to know about outliers. We start by providing a functional definition of outliers. We then lay down an appropriate nomenclature/classification of outliers. This nomenclature is used to understand what kinds of outliers can be encountered and serves as a guideline to make appropriate decisions regarding the conservation, deletion, or recoding of outliers. These decisions might impact the validity of statistical inferences as well as the reproducibility of our experiments. To be able to make informed decisions about outliers you first need proper detection tools. We remind readers why the most common outlier detection methods are problematic and recommend the use of the median absolute deviation to detect univariate outliers, and of the Mahalanobis-MCD distance to detect multivariate outliers. An R package was created that can be used to easily perform these detection tests. Finally, we promote the use of pre-registration to avoid flexibility in data analysis when handling outliers.

When comparing independent groups researchers often analyze the means by performing a Student's t-test or classical Analysis of Variance (ANOVA) F-test (Erceg-Hurn & Mirosevich, 2008; Keselman et al., 1998; Tomarken & Serlin, 1986). Both tests rely on the assumptions that independent and identically distributed residuals (1) are sampled from a normal distribution and (2) have equal variances between groups (or homoscedasticity; see Lix, Keselman, & Keselman, 1996). While a deviation from the normality assumption generally does not strongly affect either the Type I error rates (Glass,

When comparing two independent groups, researchers in Psychology commonly use Student’s t-test. Assumptions of normality and of homogeneity of variance underlie this test. More often than not, when these conditions are not met, Student’s t-test can be severely biased, and leads to invalid statistical inferences. Moreover, we argue that the assumption of equal variances will seldom hold in psychological research and that choosing between Student’s t-test or Welch’s t-test based on the outcomes of a test of the equality of variances often fails to provide an appropriate answer. We show that the Welch’s t-test provides a better control of Type 1 error rates when the assumption of homogeneity of variance is not met, and loses little robustness compared to Student’s t-test when the assumptions are met. We argue that Welch’s t-test should be used as a default strategy.

Student's t-test and classical F-test ANOVA rely on the assumptions that two or more samples are independent, and that independent and identically distributed residuals are normal and have equal variances between groups. We focus on the assumptions of normality and equality of variances, and argue that these assumptions are often unrealistic in the field of psychology. We underline the current lack of attention to these assumptions through an analysis of researchers' practices. Through Monte Carlo simulations we illustrate the consequences of performing the classic parametric F-test for ANOVA when the test assumptions are not met on the Type I error rate and statistical power. Under realistic deviations from the assumption of equal variances the classic F-test can yield severely biased results and lead to invalid statistical inferences. We examine two common alternatives to the F-test, namely the Welch's ANOVA (W-test) and the Brown-Forsythe test (F*-test). Our simulations show that under a range of realistic scenariosthe W-test is a better alternative and we therefore recommend using the W-test by default when comparing means. We provide a detailed example explaining how to perform the W-test in SPSS and R. We summarize our conclusions in practical recommendations that researchers can use to improve their statistical practices.