Skip to Main Content
It looks like you're using Internet Explorer 11 or older. This website works best with modern browsers such as the latest versions of Chrome, Firefox, Safari, and Edge. If you continue with this browser, you may see unexpected results.

Statistics Resources

This guide contains all of the ASC's statistics resources. If you do not see a topic, suggest it through the suggestion box on the Statistics home page.

Comparing Means using ANOVA

The ANOVA test family is similar to the T-test 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:

One-Way ANOVA:

  • RQ: What effect, if any, does grade level have on problem-solving efficiency?
    • H0: There is no effect of grade level on problem-solving efficiency.
    • Ha: At least two grades have significantly different levels of problem-solving efficiency.

Two-Way ANOVA:

  • RQ1: What differences in BMI, if any, exist based on alcohol consumption (drinkers vs. non-drinkers)?
    • H0: There are no differences in BMI based on alcohol consumption.
    • Ha: There are significant differences in BMI based on alcohol consumption.
  • RQ2: What differences in BMI, if any, exist based on tobacco consumption (smokers vs. non-smokers)?
    • H0: There are no differences in BMI based on tobacco consumption.
    • Ha: There are significant differences in BMI based on tobacco consumption.
  • RQ3: What interaction, if any, occurs between alcohol consumption (drinkers vs. non-drinkers) and tobacco consumption (smokers vs. non-smokers) in affecting BMI?
    • H0: No interaction occurs between alcohol consumption and tobacco consumption in affecting BMI.
    • Ha: There is an interaction that occurs between alcohol consumption (drinkers vs. non-drinkers) and tobacco consumption (smokers vs. non-smokers) that significantly affects BMI.

Repeated Measures ANOVA:

  • RQ: What effect, if any, does the type of chocolate consumed (milk chocolate, dark chocolate, white chocolate) have on test performance?
    • H0: Test performance is not affected by the type of chocolate consumed.
    • Ha: Test performance is significantly affected by the type of chocolate consumed.

*NOTE: each participant experiences each type of chocolate and provides a test performance score for each.*

ANOVA Concepts and Resources

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 left-hand 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 self-schedule 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

Introduction to ANOVA

Analysis of Variance

Dr. Jeffry White, Difference in the F and t distributions

The F-statistic, F distribution, and probability

Introduction: Difference in the F and t distributions

An introduction to the F distribution

Degrees of freedom numerator and degrees of freedom denominator

Degrees of Freedom

Degrees of Freedom in One Factor ANOVA

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

  • Shapiro-Wilk & Kolmogorov-Smirnov tests
  • Skew/kurtosis
  • Histograms/Q-Q plots

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

ANOVA Use and Assumptions

Measurement Levels: What and why?

2-way ANOVA: Balance

Choosing Between the Kolmogorov-Smirnov and the Shapiro-Wilk Tests of Normality using SPSS

Normality assumption

Homogeneity of Variances Assumption

Conducting and Interpreting a Levene's Test in SPSS

 

The null and alternative hypotheses for 1-way ANOVA

2-way (factorial) ANOVA

Hypothesis testing with One-Way Between Groups ANOVA: Part 1

Hypothesis Testing with One-Way Between Groups ANOVA: Part 2

2 Two-Way ANOVA - Research Questions and Hypotheses

Simple main and interaction effects

Ordinal and disordinal interactions

Tests of simple effects in a two-way ANOVA

Main and Interaction Effects in ANOVA using SPSS

Ordinal and Disordinal

Using SPSS to compute 1-way ANOVA (between groups)

Using SPSS to compute 1-way ANOVA (between subjects)

Using SPSS to compute 1-way ANOVA (repeated measures)

Interpreting the 1-way ANOVA output in SPSS

1-way ANOVA: SPSS

One-Way Between Groups ANOVA: SPSS

One-Way Repeated Measures ANOVA: SPSS

Interpreting an SPSS ANOVA Output

Using SPSS to compute 2-way (factorial) ANOVA

Interpreting the factorial ANOVA table in SPSS

Two-Way ANOVA: SPSS

Interpreting and Reporting SPSS Output The Two Way ANOVA

Calculating effect sizes for ANOVA Significance vs. Effect Size for One-Way ANOVA Using SPSS
Calculating observed power for ANOVA Understanding and Calculating Power after Two-Way ANOVA Using SPSS
Post hoc and multiple comparison tests in ANOVA Post-Hoc Tests for One-Way 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

Visualizing Type I and Type II Error

Alpha Error Inflation

Type I Error Inflation and Bonferroni Correction

Dr. Jeffry White, an alternative approach when the normality assumption has been violated

Nonparametric alternatives for ANOVA (Kruskal-Wallis test)

Alternative to ANOVA

ANOVA vs. Kruskal-Wallis Test in SPSS with Assumption Testing

One-Way Non-Parametric ANOVA (Kruskal-Wallis Test) in SPSS

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 (Brown-Forsythe & Welch tests)

Introduction to an alternative approach

ANOVA: Unequal Variances (Brown-Forsythe and 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.

Was this resource helpful?