# 13: Analysis of Variance

• • David Lane
• Rice University
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• 13.1: Introduction to ANOVA
Analysis of Variance (ANOVA) is a statistical method used to test differences between two or more means. It may seem odd that the technique is called "Analysis of Variance" rather than "Analysis of Means." As you will see, the name is appropriate because inferences about means are made by analyzing variance.
• 13.2: ANOVA Designs
There are many types of experimental designs that can be analyzed by ANOVA. This section discusses many of these designs and defines several key terms used.
• 13.3: One-Factor ANOVA
This section shows how ANOVA can be used to analyze a one-factor between-subjects design.
• 13.4: One-Way Demo
• 13.5: Multi-Factor Between-Subjects
• 13.6: Unequal Sample Sizes
Whether by design, accident, or necessity, the number of subjects in each of the conditions in an experiment may not be equal.  Since n is used to refer to the sample size of an individual group, designs with unequal sample sizes are sometimes referred to as designs with unequal n. Table 1. Sample Sizes for "Bias Against Associates of the Obese" Study.
• 13.7: Tests Supplementing
The null hypothesis tested in a one-factor ANOVA is that all the population means are equal. When the null hypothesis is rejected, all that can be said is that at least one population mean is different from at least one other population mean.
• 13.8: Within-Subjects
Within-subjects factors involve comparisons of the same subjects under different conditions.  A within-subjects factor is sometimes referred to as a repeated-measures factor since repeated measurements are taken on each subject. An experimental design in which the independent variable is a within-subjects factor is called a within-subjects design.
• 13.9: Power of Within-Subjects Designs Demo
This simulation demonstrates the effect of the correlation between measures in a one-way within-subjects ANOVA with two levels. This test is equivalent to a correlated t test.
• 13.10: Statistical Literacy
• 13.E: Analysis of Variance (Exercises)