CH 12 PSY 110

Analysis of Variance (ANOVA)

A procedure used to evaluate the differences between two or more treatments (groups), allowing comparison of means across multiple groups.

Null Hypothesis (H0)

In ANOVA, it states that the means of all groups are equal (μ1 = μ2 = μ3).

Alternative Hypothesis (H1)

The statement that at least one group mean is different from the others, thus rejecting the Null Hypothesis.

F-ratio

A test statistic used in ANOVA to compare the variance between groups to the variance within groups.

Within-Treatments Variability

The variability of subjects within the same treatment group, caused solely by chance or experimental error.

Between-Treatments Variability

The differences between sample means, which may be due to treatment effects or chance.

Mean Square (MS)

Variance estimates used in ANOVA, calculated from Sums of Squares (SS) divided by their respective degrees of freedom.

Degrees of Freedom (df) for ANOVA

The number of independent values that can vary in the analysis, critical for calculating Mean Squares and F-ratios.

Total Sums of Squares (SSTotal)

A measure of total variability in the data, calculated from the squared differences between each score and the grand mean.

Post-hoc Tests

Additional hypothesis tests conducted after an ANOVA to determine which specific group means are significantly different from one another.

Grand Mean (MG)

The average of all scores in a study, used as a reference point in ANOVA.

Homogeneity of Variance

An assumption of ANOVA stating that the populations from which the samples are drawn must have equal variances.

F-distribution

The distribution of the F-ratio, characterized by positive values and clustering close to 1.00 when the null hypothesis is true.

Critical Region

The area of the F-distribution that defines the threshold for rejecting the null hypothesis, based on a specified alpha level (e.g., α = .05).

Variance

A method of measuring how much the scores in a dataset differ from the mean, used in calculating ANOVA.