12: Analysis of Variance – ANOVA
- Page ID
- 57590
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- Know when to use an ANOVA
- Understand the design setup for an ANOVA
- Know when to use an ANOVA instead of multiple t-tests
- Interpret an ANOVA result
- Read a journal article that uses ANOVAs
Key Terms
- Assumptions of an ANOVA
- ANOVA as a ratio
- Post-hoc tests
- Experimenter-wise error rate
On to the ANOVA, or Analysis of Variance. Analysis of Variance is a term that describes a family of analyses. Statistics is about analyzing and understanding variance; suffice to say, it is probably accurate to say that Analysis of Variance is what statistics is all about.
To begin, the purpose of the ANOVA is to analyze the variance of three or more groups on a single dependent variable. You are trying to detect if one group is higher or lower than the other two groups, or if the three or more groups are similar? The ANOVA contrasts with the independent t-test, which examines two groups only on a single dependent variable. Keep in mind that the two groups versus one group is not the best way to describe the difference between the ANOVA and the independent t-test. A better way to describe the difference is that the ANOVA examines variance, while the t-test examines mean scores. Because the ANOVA examines variance, it is a flexible statistical test that can be used for additional purposes, which will be described at the end of this chapter.
- 12.1: When to Use the ANOVA
- This page discusses the Analysis of Variance (ANOVA), which compares means across three or more groups, often considering demographic differences. It establishes null and alternative hypotheses regarding mean scores. While ANOVA is effective for continuous dependent variables, analyzing ordinal outcomes with it is complex; logistic regression is suggested for ordinal interpretations.
- 12.2: The Concept Behind Analysis of Variance
- This page discusses Analysis of Variance (ANOVA), a statistical method used to compare differences among groups by partitioning variance into true and error variance. It employs the F-test, which assesses the ratio of between-group to within-group variance to determine significance. A significant result is indicated when the F-test value exceeds established thresholds, such as 1.96 for the F-test and a p-value of .05, signaling notable differences among group means.
- 12.3: - Interpreting the F-test and Post-Hoc Comparisons
- This page discusses the F-test, which identifies differences between groups without specifying which ones. It highlights the importance of post-hoc comparisons to pinpoint specific group differences, using adjusted t-tests to mitigate Type I error risks. Common post-hoc tests include Tukey, Sidak, and Bonferroni. Notably, a significant F-test does not ensure significant post-hoc results, suggesting that consulting a statistician may be necessary for proper interpretation.
- 12.4: Commentary
- This page covers key ANOVA terminology and applications in statistical research, detailing interchangeable terms, independent variables (IVs), and factorial ANOVA distinctions. It discusses ANCOVA's role in controlling for covariates, the importance of theoretical foundations in selecting them, and differentiates between ANOVA and MANOVA usage.
- 12.5: Reading Articles – ANOVA
- This page discusses the analysis of journal articles, emphasizing steps like identifying research questions and understanding statistical methods. It centers on a study by Erermis et al. (2004), which finds no significant link between obesity and psychological issues but notes that clinically obese adolescents exhibit higher aggression than their peers.
- 12.6: Summary
- This page discusses ANOVA, a statistical method used to compare differences among three or more groups, applicable to various demographics and clinical populations. Although ANOVA may oversimplify complexity by clustering individuals, its comparisons, when grounded in sound concepts, can provide significant insights into the data.
- 12.7: Discussion Questions
- This page explains the differences between t-tests and ANOVA, highlighting that t-tests compare means of two groups while ANOVA evaluates variances among three or more groups. ANOVA is favored to manage Type I error rates, and post-hoc tests help to identify specific group differences after significant ANOVA results. It also describes different types of t-tests, including independent, paired, one-sample, and two-sample, which cater to various comparison situations.