# Step-by-Step Guide:

# One-way ANOVA

2 or more groups - Parametric & Non-Parametric

## Overview

What you will learn here:

How to run and interpret a One-Way ANOVA; and

how to run a non-parametric Kruskal Wallis Test.

An ANOVA or Analysis of Variance allows you to see if there is a difference in the mean between three or more groups (T-Test's only compare 2 groups). You will also learn when to select a non-parametric version of the ANOVA.

You can also perform an ANOVA on repeated measures. This is not covered here. But a good introduction is available as is a step-by-step guide on how to run a Repeated Measures ANOVA in Jamovi

## Dataset used for One-Way ANOVA

Skoczylis, Joshua, 2021, "Extremism, Life Experiences and the Internet", https://doi.org/10.7910/DVN/ICTI8T, Harvard Dataverse, Version 3.

## One-Way ANOVA (parametric)

## One-Way ANOVA Hypothesis

Ho: Ethnicity has no impact on individuals political leaning.

Ha: Ethnicity has an impact on individuals political leaning.

## One-Way ANOVA variables required

Dependent Variable(s):

Political_LeaningRight_Left: This continuous variable measures where someone is on the Political spectrum

Dependent Variable(s):

Ethnicity: This is the participants ethnicity

Note: The dependent variable must have 3 or more outcomes.

or

In our example we are using the above variable, however, you can use an ordinal variable.

Note: The dependent variable must have 3 or more outcomes.

## Parametric One-Way ANOVA Assumptions

Test's Assumptions:

Independence: Your observations in each sample should be independent.

Independent Variable: This variable must have 3 or more outcomes.

Random Sampling: Your data should be a random sample of the target population.

Equal Variance (Homogeneity): Both groups should have approximately the same variance.

Normality: Your Dependent variable should be approximately normally distributed.

Test Assumptions Not Met:

If your assumptions are not met, use the non-parametric Kruskal Wallis test. We will go through this test below.

Note: There is some discussion amongst statisticians of how stringent one must be with these assumptions as an ANOVA can be relatively robust when the normality assumption is violated. Be aware that ignoring the violation of normality may increase your risk of Type 1 error.

If your sample is small check your Kurtosis in the Descriptive Statistics section. If it is negative, you should not use a Standard ANOVA.

If you decide to ignore the normality assumption, you must make this clear to the reader. It is also always worthwhile double checking your results using the Kruskal Wallis test.

## One-Way ANOVA: Step-by-Step Guide

1.

Select your variables

Navigate to Analyses > ANOVA > One-Way ANOVA

Now select your variables and drag & drop them into the relevant fields

2.

Check your Assumptions

Let's check our assumptions. Select the following test in the Assumptions Section:

Homogeneity Test

Normality Test

The results will appear in the results panel on your right. For each of the assumption tests Jamovi runs multiple tests - so select the one that suits.

As you can see from the tables below, the Homogeneity Assumption is not violated (the p-values range from 0.389 to 0.404).

The Normality Assumption on the other hand is violated (the p-value ranges from <.001 to 0.037).

In this case, we will ignore the violation of the Normality Assumption. However, we will conduct a non-parametric Kruskal Wallis test later to double-check our results (see note in the Assumptions section)

3.

Select your Statistics

If neither assumption is met, consider whether a Kruskal Wallis test is more appropriate.

In this case, we will selected the Assume equal (Fisher's) test. Will will leave the default for missing values in place.

It is always good to get a descriptive table and plot. You can use these to provide context when you are writing up your results.

2.

Conduct a Post-hoc test

ANOVAs will give you an overall p-value. This p-value, however, does not tell you between which groups the difference is significant or not.

To get this information we need to select the appropriate post-hoc test in the Post-hoc Tests section. You have the following options:

Games-Howell: Select this test if there is unequal variance (the homogeneity assumption is violated)

Tukey: Select this test if the variance between groups is equal.

In addition, you might also want to select the following three additional statistics:

Mean Difference: This will give you the mean difference between the groups

Report significance: This will give you the p-value for each grouping

Flag significant comparisons: This will highlight significant results using **. This just makes it easier to see them in a big table.

The plot is not great, so I have will generate a plot using JJStatsPlot (JJStatsPlot > Graphs & Plots).

## Results: Accept Null Hypothesis

1.

One-Way ANOVA output

Based on the output, we accept the Null Hypothesis - there is no significant difference in political leaning between the different ethnic groups (p 0.884).

The table and descriptive plot both confirm that the difference in political leaning between groups is small.

Below you can see the output of the Tukey Test. Note, that usually you would only display this table if your ANOVA result is significant. Here we have only displayed it to show you how it looks.

## One-Way ANOVA (non-parametric - Kruskal Wallis)

## Kruskal Wallis Hypothesis

Ho: Ethnicity has no impact on individuals political leaning.

Ha: Ethnicity has an impact on individuals political leaning.

This is the same hypothesis as above.

## Kruskal Wallis Test variables required

We are using the same variables as in the test above:

Political_LeaningLeft_Right: Dependent Variable

Ethnicity: Inpendent Variable

## Kruskal Wallis test Assumptions

Independence: Your observations in each sample should be independent.

Independent Variable: This variable must have 3 or more outcomes.

Random Sampling: Your data should be a random sample of the target population.

## Kruskal Wallis Test (Non-parametric ANOVA): Step-by-Step Guide

1.

Select your Variables & Statistics

Just note, that the results of the parametric ANOVA returned a non-significant results. As the Normality Assumption was violated, we will also use a Kruskal Wallis test to double-check our results.

Navigate to Analyses > ANOVA > One-Way ANOVA Kruskal Wallis

Now just select Effect Size and DSCF Pairwise comparison.

The pairwise comparison provides you with a table that shows you the differences between groups

Your results should appear in the panel on the right.

## Results: Accept Null Hypothesis

1.

Kruskal Wallis output

The Kruskal Wallis test confirms that we should accept the Null Hypothes - there is no difference in political leaning between ethnic groups (p 0.840). The Effect Size also supports this and suggest that there is no effect of ethnicity on political leaning (0.001).

Below, we see the Pairwise comparison. Note, this is only really of interest if there is a significant difference. If your results are insignificant there is no need to report this.