Describes the different types of t-test for comparing the means of groups. These include: one-sample t-tests, unpaired t-test and paired t-test. Parametric methods, such as t-test and ANOVA tests, assume that the dependent (outcome) variable is approximately normally distributed for every groups to be compared. This chapter describes how to transform data to normal distribution in R. Repeated measures ANOVA make the assumption that the variances of differences between all combinations of related conditions (or group levels) are equal. This is known as the assumption of sphericity. The Mauchly’s test of sphericity is used to assess whether or not the assumption of sphericity is met. In this article, you will learn how to: 1) Calculate sphericity; 2) Compute Mauchly's test of sphericity in R; 3) Interpret repeated measures ANOVA results when the assumption of sphericity is met or violated. 4) Extract the ANOVA table automatically corrected for deviation from sphericity. Some statistical tests, such as two independent samples T-test and ANOVA test, assume that variances are equal across groups. This chapter describes methods for checking the homogeneity of variances test in R across two or more groups. These tests include: F-test, Bartlett's test, Levene's test and Fligner-Killeen's test. Many of the statistical methods including correlation, regression, t tests, and analysis of variance assume that the data follows a normal distribution or a Gaussian distribution. In this chapter, you will learn how to check the normality of the data in R by visual inspection (QQ plots and density distributions) and by significance tests (Shapiro-Wilk test). The Friedman test is a non-parametric alternative to the one-way repeated measures ANOVA test. It extends the Sign test in the situation where there are more than two groups to compare. It's recommended when the normality assumptions of the one-way repeated measures ANOVA test is not met or when the dependent variable is measured on an ordinal scale. In this chapter, you will learn how to compute Friedman test in R and to perform pairwise-comparison between groups. The Kruskal-Wallis test is a non-parametric alternative to the one-way ANOVA test. It's recommended when the assumptions of one-way ANOVA test are not met. This chapter describes how to compute the Kruskal-Wallis test using the R software. The Multivariate Analysis Of Variance (MANOVA) is an ANOVA with two or more continuous outcome (or response) variables. The one-way MANOVA tests simultaneously statistical differences for multiple response variables by one grouping variables. This chapter describes how to compute one-way MANOVA in R. The Analysis of Covariance (ANCOVA) is used to compare means of an outcome variable between two or more groups taking into account (or to correct for) variability of other variables, called covariates. In this chapter, you will learn how to compute and interpret the one-way and the two-way ANCOVA in R. The Mixed ANOVA is used to compare the means of groups cross-classified by two different types of factor variables, including: i) between-subjects factors, which have independent categories (e.g., gender: male/female). ii) within-subjects factors, which have related categories also known as repeated measures (e.g., time: before/after treatment). This chapter describes how to compute and interpret the different mixed ANOVA tests in R.