Tests equality of means of 3+ metric variables in population. Simple ANOVA involves 3 outcome variables on single group. Within-subjects factor distinguishes variables, often time of measurement
ANOVA analyzes differences between means of more than two groups. Two-way ANOVA examines quantitative variable changes with two categorical variables. ANOVA tests significance using F test comparing group means to overall variance
Two-way ANOVA compares effects of two categorical variables on continuous dependent variable. Dependent variable must be continuous, independent variables should have multiple groups. Independence of observations and no significant outliers are required. Data normality and homogeneity of variances must be checked
Two-way ANOVA compares mean differences between groups based on two independent variables. Test determines if there is an interaction between independent variables and dependent variable. Three-way ANOVA needed for three independent variables or two-way ANCOVA for continuous covariates
Pooled standard deviation combines multiple sample data sets into one overall measure. Calculated as square root of pooled variance, weighted average of individual standard deviations. Assumes equal variances within groups before calculation
ANOVA is used to compare means of three or more groups. R.A. Fisher introduced ANOVA in 1920 for agronomical data analysis. ANOVA separates variance due to assignable and chance causes