ANOVA in R – A Comprehensive Guide To Utilization

ANOVA is a test used in statistics to estimate the changes experienced by quantitative dependent variables based on the levels of one or more categorical independent variables.

This statistical test also determines if there is a mean difference in the groups at each independent variable level. This article discusses ANOVA in R and how it is used.

Definition: ANOVA in R

ANOVA in R is a statistical mechanism facilitated by R programming to conduct implementations of statistical concepts of ANOVA.

ANOVA (Analysis of Variance) is a statistical test that allows you to determine if there are mean differences in groups at individual independent variable levels. ANOVA in R tests the relations between continuous and categorical variables in R programming.

It tests the hypothesis for population variance.

How to use ANOVA in R

The first step is downloading R and R studio programs. After downloading, open the R studio by clicking File, then New File, and R script. From there, you can copy and paste your code into the script and run it by highlighting specific lines and clicking on the run button.

You can check if the data is read correctly using the code:

How to perform ANOVA in R

ANOVA is a statistical test that tests if any of the group means differ from the overall data mean by checking the variance of each individual against the overall data variance. The test is considered statistically significant if one or more groups fall outside the variation range anticipated by the null hypothesis.

You can perform ANOVA in R by applying the function:

This function will calculate the ANOVA test statistic and find out if there is a notable variation among the groups formed by the independent variable levels.

One-way ANOVA

This test models crop yield as a function of the soil type.

1. Use aov() to run the model
2. Use summary() to print the model summary

Two-way ANOVA

This example models the crop yield as a function of the type of soil and planting density.

1. Use aov() to run the model
2. Use summary() to print the summary model

ANOVA in R: Best-fit model

You can choose between four ANOVA models for data explanation. The best-fit model best explains the variation in the dependent variable. You can determine the best-fit model using the Akaike information criterion test, which calculated the data value of each model by balancing the explained variation against the number of used parameters.

The AIC model selection compares each model’s information value and selects the one with the smallest AIC value. The lower the AIC value, the more information is required.

The model with the least AIC score is the best-fit model. The results will show you whether the one or two-way model is the best fit.

ANOVA in R: Post hoc test

An ANOVA test determines if there is a difference in the group means. However, it does not tell what the differences are. So, you can find out the specific statistical difference by performing Tukey’s Honestly Significant Difference post hoc test. This is a pairwise comparison test.

The test will determine if there is a statistically significant difference between the soil types and the different planting density levels.

ANOVA in R: Results

The ANOVA in R results must be presented correctly. Here are the guidelines for the result presentation.

Presentation of the results

Finally, you can present the results of the ANOVA in R model test. The results’ presentation should include a brief description of the tested variables, the F value, degrees of freedom, and each independent variable’s p-value. Finally, you must explain what the results mean.

Use a graph

You can present the model results in a graph. The graph should display the raw data, summary information (mean and standard error for the compared groups), and letters or symbols that indicate the group wide differences of the compared groups.