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A Complete Guide on ANOVA in R

Published by at September 2nd, 2021 , Revised On August 7, 2023

ANOVA is a statistical test for assessing how the levels of one or more categorical independent variables affect the changes in a quantitative dependent variable. ANOVA determines if the groups’ means differ at each level of the independent variable.

The ANOVA’s null hypothesis (H0) is that there is no difference in means, while the alternate hypothesis (Ha) is that the means differ.

We will walk you through the steps of a one-way ANOVA (one independent variable) and a two-way ANOVA (two independent variables) in this guide.

Quick Recap

One-way ANOVA: A one-way ANOVA is a statistical test that evaluates the variation in group means within a sample while taking just one independent variable or factor into account.

Two-way ANOVA: A two-way ANOVA is a hypothesis-based test, just like a one-way ANOVA. On the other hand, in the two-way ANOVA, each sample is characterized in two ways, resulting in two categorical groups.

Let’s Get Started with R

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All you need to do is:

Click on the File option.

Now place the cursor on New File and select R Script.

You can start copying and pasting the code from the rest of this example in no time in your script.

In order to run the code, highlight all the lines you wish to run and then select the Run option, which is on the top right of the text editor. You can also press ctrl+ enter if you want to use the keyboard.

Now install and load the required packages. Keep in mind that you need first to install the packages required for the analysis and then load them into your R environment. You will have to do this every time the R program is restarted.

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A Step-by-Step Guide: ANOVA in R

The process for one-way ANOVA is as follows:

Step 1: Start loading the data into R. When importing a dataset into R, factors are frequently read as quantitative variables. To avoid this, use the read.csv () command to read the data, indicating whether each variable should be numerical (“numeric”) or categorical (“factor”) within the command.

Step 2: Get started with the ANOVA test. By comparing the variance of each group to the overall variance of the data, ANOVA determines whether any of the group means differ from the overall mean of the data. The test is statistically significant if one or more groups fall outside the range of variation anticipated by the null hypothesis (all group averages are equal).

Step 3: Now assess and choose the most suited model. A suitable test for model fit is the Akaike information criterion (AIC). The information value of each model is calculated by balancing the variation explained against the number of parameters utilized in the model.

Step 4: Checking the homoscedasticity.

Step 5: Run a post-hoc test. ANOVA shows us if there are differences in group means, but it doesn’t tell us what they are. A Tukey’s Honestly Significant Difference (Tukey’s HSD) posthoc test for pairwise comparisons can be used to determine which groups are statistically distinct from one another.

Step 6: Plotting outcomes in a graph. It is critical to provide the following information when charting the results of a model:

1. Summary information, often the mean and standard error of each group being compared
2. Raw data
3. Symbols and letters above each group compared to highlight group-wise differences

Step 7: Reporting the outcomes. It is crucial to state the ANOVA test findings in addition to a graph. Include:

1. Description of the variables you tested in a few words.
2. What the findings imply.
3. Each independent variable’s f-value, degrees of freedom, and p-values.

Analysis of variance is basically a group of statistical models and associated estimate processes (such as “variation” among and between groups) that are used to observe and assess variations in means.

The outcome or impact of two independent factors on a dependent variable is examined using a two-way ANOVA. A two-way ANOVA test examines the effects of independent variables on the expected outcome as well as their relationship to the outcome.

A one-way ANOVA is a statistical test that evaluates the variation in group means within a sample while taking just one independent variable or factor into account.

Following are seven simple steps:
Step 2: Get started with the ANOVA test
Step 3: Now assess and choose the most suited model.
Step 4: Checking the homoscedasticity.
Step 5: Run a post-hoc test.
Step 6: Plotting outcomes in a graph.
Step 7: Reporting the outcomes