Statistics · BEGINNER LESSON
ANOVA
ANOVA, analysis of variance, is a statistical method for testing whether the means of two or more groups differ when the outcome is continuous. It does this by comparing variation between groups with variation within groups.
What ANOVA measures
ANOVA stands for analysis of variance. It is used when the outcome is a continuous variable, meaning a measured value like height, concentration, or response size, and the groups are defined by a categorical factor such as treatment type or time point. The main question is whether the group means are all the same or whether the differences among the group means are larger than expected from random variation.
[1] Analysis of Variance: Is There a Difference in Means and What Does ...
How ANOVA works
ANOVA separates total variation in the outcome into variation explained by the factor of interest and variation due to random error. The F-test compares the variance between groups with the variance within groups, producing an F-ratio. A larger F-ratio means the group means are farther apart relative to the spread inside the groups, so the factor explains more of the outcome. In a one-way ANOVA there is one factor with two or more levels.
[1] Analysis of Variance: Is There a Difference in Means and What Does ...
Repeated-measures and blocked designs
Some ANOVA versions handle related measurements. In repeated-measures ANOVA, the same subjects are measured more than once, such as at several time points or under several conditions, so the factor is within-subject. A randomized block ANOVA separates variation between blocks, such as experiments or subjects, from the treatment effect. These approaches can be more powerful when measurements are correlated within a subject or block.
[2] Repeated Measures Designs and Analysis of Longitudinal Data - PMC [3] Good statistical practice in pharmacology Problem 2 - PMC
Assumptions and limits
ANOVA has important assumptions: the outcome should be roughly normally distributed within each group, group variances should be similar, and observations should be independent in ordinary ANOVA. Repeated-measures ANOVA adds strong requirements such as similar correlation patterns across time points and complete measurements for each subject at each time point. Standard ANOVA also does not identify which specific group pairs differ, and it does not handle continuous covariates or time-varying covariates well in the forms described here.
[1] Analysis of Variance: Is There a Difference in Means and What Does ... [2] Repeated Measures Designs and Analysis of Longitudinal Data - PMC [3] Good statistical practice in pharmacology Problem 2 - PMC
SEE THE IDEA
How ANOVA compares groups
Measure one value per observation, such as a response or score.
Classify observations into levels such as treatment, time, or experiment.
Spread among observations inside the same group or block.
Differences among the group means after accounting for random spread.
Compares between-group and within-group variation to judge whether the mean differences are larger than expected by chance.
ANOVA uses the factor to split total variation, then the F-test compares the two parts.
A simple ANOVA asks whether differences among group means are large compared with the variation inside the groups.
TRY IT YOURSELF
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Sources and further reading
This general lesson was generated from public source material. It explains a concept; it does not interpret a private paper or provide medical advice.