CARDS Group Differences ANOVA

ANOVA

Analysis of Variance; a statistical method used to test differences between two or more means.

Factor

Independent variable in ANOVA.

Levels

Different groups or categories within a factor.

Response Variable

Dependent variable or the outcome being measured.

Assumptions of ANOVA

Conditions that must be met for ANOVA to be valid, including independence of samples and normality.

Homoscedasticity

The assumption that the variance among different groups is equal.

One-Way ANOVA

ANOVA with one categorical independent variable and a normally distributed continuous dependent variable.

Two-Way ANOVA

ANOVA that includes two or more categorical independent variables.

Repeated Measures ANOVA

ANOVA used when the same subjects are measured multiple times under different conditions.

Mixed-Design ANOVA

ANOVA used when there are two or more dependent variables.

ANCOVA

Analysis of Covariance; combines ANOVA and regression to control for covariates.

Effect Size (η²)

A measure of the strength of the relationship between independent and dependent variables.

Post-hoc Tests

Statistical procedures conducted after rejecting the null hypothesis in ANOVA to explore the differences between group means.

Tukey HSD Test

A post-hoc test that determines which means are significantly different after an ANOVA.

F-value

The test statistic computed in ANOVA, representing the ratio of variance between groups to variance within groups.

Type I Error

The incorrect rejection of a true null hypothesis (false positive).

Independent Samples

Samples in which subjects in one group cannot also be in another group.

Homogeneity of Variance

The assumption that the variances across groups are roughly equal.

Reporting Results of ANOVA

Should include purpose, sample size, descriptive statistics, F-statistic, degrees of freedom, p-value, and effect size.

Kruskal-Wallis Test

A non-parametric alternative to ANOVA that may be used for skewed data.

Example of One-Way ANOVA

Comparing the average test scores of students from three different teaching methods.

Example of Two-Way ANOVA

Examining the effects of both study method and gender on test scores.

Example of Repeated Measures ANOVA

Measuring the same group of patients' blood pressure at three different time points.

Example of Mixed-Design ANOVA

Studying the impact of diet and exercise type on weight loss among subjects monitored over several months.

Example of Post-hoc Test

Using Tukey's HSD test to determine which teaching method yields significantly different average scores after a One-Way ANOVA.

Example of ANCOVA

Comparing test scores while controlling for students' prior knowledge as a covariate.

Example of the Kruskal-Wallis Test

Testing for differences in customer satisfaction ratings across three different store locations without assuming normal distribution.