One-way ANOVA typically evaluates whether there is difference in means of three or more groups, although it also works for two-group analysis. In other words, it investigates the effect a grouping variable on the outcome variable.
ANOVA (ANalysis Of VAriance) is a statistical test to determine whether two or more population means are different. In other words, it is used to compare two or more groups to see if they are significantly different.
Maron: ANOVA, ANOVA Multiple Comparisons & Kruskal Wallis in R | R Tutorial 4.9 | MarinStatsLectures (4:36)
A Language, not a Letter: Learning Statistics in R
The ANOVA test (or Analysis of Variance) is used to compare the mean of multiple groups. The term ANOVA is a little misleading. Although the name of the technique refers to variances, the main goal of ANOVA is to investigate differences in means.
Two-way analysis of variance (two-way ANOVA) is an extension of the one-way ANOVA to examine the influence of two different categorical independent variables on one continuous dependent variable. The two-way ANOVA can evaluate not only the main effect of each independent variable but also the potential interaction between them.
A Language, not a Letter: Learning Statistics in R
The repeated-measures ANOVA is used for analyzing data where same subjects are measured more than once. This test is also referred to as a within-subjects ANOVA or ANOVA with repeated measures. The “within-subjects” term means that the same individuals are measured on the same outcome variable under different time points or conditions.
Repeated-measures designs are often used in psychology in which the same participants are measured multiple times. One popular example is the longitudinal design in which the same participants are followed and measured over time. Another example is the cross-over study in which participants receive a sequence of different treatments. To analyze such data, repeated-measures ANOVA can be used.
Statistics of DOOM: R - Mixed ANOVA (43:26)
Mixed ANOVA is used to compare the means of groups cross-classified by two different types of factor variables, including:
Between-subjects factors, which have independent categories (e.g., gender: male/female)
Within-subjects factors, which have related categories also known as repeated measures (e.g., time: before/after treatment).
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 other words, ANCOVA allows to compare the adjusted means of two or more independent groups.
Tom Sherratt: Analysis of Covariance in RStudio (8:25)
Effect Sizes (Group Differences)