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The ANOVA test family is similar to the Ttest family in that we use it to compare groups to determine if any significant differences exist between those groups. The ANOVA is appropriate when you're comparing more than two groups. Here are some examples of what types of research questions and/or hypotheses may indicate an ANOVA is appropriate:
OneWay ANOVA:
TwoWay ANOVA:
Repeated Measures ANOVA:
*NOTE: each participant experiences each type of chocolate and provides a test performance score for each.*
Suggested Order to Learn About ANOVA Concepts
Learning about and becoming competent in conducting an ANOVA involves several steps and a variety of different skills. Below is the suggested order by the ASC statistics coaches along with resources to assist you in learning these concepts. All of the concepts below can be discussed with a statistics coach in an individual session. Individual sessions can be scheduled by using ASC Chat at the hours listed in ASC Contact Information on the lefthand side of this page. Additionally, students can learn more about conducting an ANOVA during the Inferential Statistics group session Fridays at 4:00 p.m. PST. Students can selfschedule for this session. For more information, see the Relevant FAQs at the bottom of this page.
Topic  Resource 
Introduction to ANOVA from Dr. Jeffry White, Academic Success Center The F ratio test and concept of analysis of variances 

Dr. Jeffry White, Difference in the F and t distributions The Fstatistic, F distribution, and probability 

Degrees of freedom numerator and degrees of freedom denominator  
Dr. Jeffry White, centrality of the assumptions of ANOVA The assumptions of ANOVA and the implications for violation Levels of measures Balanced designs (equal/unequal sample sizes) Normality of the response variability
Dr. Jeffry White, more on the normality assumption Dr. Jeffry White, more on the homogeneity of variances assumption Equality of variances: Levene’s test 
Introduction: Centrality of Assumptions Measurement Levels: What and why? Choosing Between the KolmogorovSmirnov and the ShapiroWilk Tests of Normality using SPSS
Homogeneity of Variances Assumption Conducting and Interpreting a Levene's Test in SPSS

The null and alternative hypotheses for 1way ANOVA 2way (factorial) ANOVA 
Hypothesis testing with OneWay Between Groups ANOVA: Part 1 Hypothesis Testing with OneWay Between Groups ANOVA: Part 2 
Simple main and interaction effects Ordinal and disordinal interactions 
Tests of simple effects in a twoway ANOVA 
Using SPSS to compute 1way ANOVA (between groups) Using SPSS to compute 1way ANOVA (between subjects) Using SPSS to compute 1way ANOVA (repeated measures) Interpreting the 1way ANOVA output in SPSS 
OneWay Between Groups ANOVA: SPSS 
Using SPSS to compute 2way (factorial) ANOVA Interpreting the factorial ANOVA table in SPSS 

Calculating effect sizes for ANOVA  Significance vs. Effect Size for OneWay ANOVA Using SPSS 
Calculating observed power for ANOVA  Understanding and Calculating Power after TwoWay ANOVA Using SPSS 
Post hoc and multiple comparison tests in ANOVA  PostHoc Tests for OneWay ANOVA Using SPSS 
Probability of Type I/II errors Dr. Jeffry White, more about the concept of alpha error inflation The concept of alpha error inflation and familywise error (e.g. multiple hypothesis testing)  alpha error adjustment strategies 

Dr. Jeffry White, an alternative approach when the normality assumption has been violated Nonparametric alternatives for ANOVA (KruskalWallis test) 
ANOVA vs. KruskalWallis Test in SPSS with Assumption Testing 
Dr. Jeffry White, introduction to an alternative approach when the homogeneity of variances assumption has been violated Alternative when homogeneity of variances have been violated (BrownForsythe & Welch tests) 
Recommended Reading
The articles below will assist you in understanding several of the concepts presented above including but not limited to assumptions, equal variances, and normality.