Analysis of Variance (ANOVA) Lecture Notes

This set of vocabulary flashcards covers essential concepts, terms, and statistical symbols introduced in the lecture on one-way between-subjects Analysis of Variance (ANOVA).

ANOVA

Short for Analysis of Variance, a statistical technique used to compare the means of multiple groups or conditions.

Factor

The term used for the independent variable in an ANOVA.

Treatment

A term for the independent variable specifically when it is manipulated by the researcher.

Levels

The individual conditions or groups that make up a single independent variable or factor.

Between subjects design

A research design where different people are placed into each group or condition.

Family wise error rate

The additive chance of making a Type I error when performing multiple t-tests on the same set of data.

Type I error

Falsely rejecting the null hypothesis; saying there is a significant effect or difference when there is actually nothing going on.

Omnibus test

A test that looks for a significant difference somewhere between the means of all groups without specifying exactly which means are different.

Between groups variability

Variance attributed to the level of the independent variable (treatment effect), individual differences, and experimental error.

Within groups variability

Variance attributed to individual differences and experimental error, but not the treatment effect (as all individuals in the group received the same treatment).

F statistic ratio

$\text{Mean Squared Treatment} / \text{Mean Squared Error}$.

Mean Squared Error ($MS_{\text{error}}$)

Also called mean squared residual, this is the within-groups variability that cannot be accounted for by the treatment condition.

Mean Squared Treatment ($MS_{\text{treatment}}$)

Also called mean squared model, this is the variability that can be accounted for based on the group or treatment level the participant belongs to.

Grand mean

The mean of all data points in the entire sample across all conditions combined.

Sums of Squares ($SS$)

A measure of the variability or shifting about of scores; these are additive, meaning $\text{SS}_{\text{total}} = \text{SS}_{\text{treatment}} + \text{SS}_{\text{error}}$.

Degrees of freedom treatment ($df_{\text{treatment}}$)

Calculated as $k - 1$ where $k$ is the number of levels or conditions.

Degrees of freedom error ($df_{\text{error}}$)

Calculated as $N - k$ where $N$ is the total sample size and $k$ is the number of conditions.

One-tailed test

The type of test conducted in ANOVA because the F-distribution is positively skewed and variances cannot be negative.

Effect size

A measure of the magnitude of an effect that indicates the proportion of variance in the dependent variable that can be attributed to the independent variable.

Omega squared ($\omega^2$)

A more appropriate and conservative measure of effect size for ANOVA that estimates variance in the population.

Eta squared ($\eta^2$)

A measure of effect size that is more intuitive but tends to overestimate the magnitude of the effect.