Calculating the ANOVA Test Statistic (F)

Summary statistics from the problem

TSS	=	482.6897
SSB	=	53.9674
SSW	=	428.7222
\( \nu_t \)	=	28
\( \nu_b \)	=	2
\( \nu_w \)	=	26

In the box below, please enter the test statistics for the data and model, then click on the “Check your answer!” button. Please round your answer to the ten-thousandths place.

Your guess:

You got the correct answer of F = 1.6364. Congratulations!

Unfortunately, your answer was not correct. Either try again or click on “Show Solution” below to see how to obtain the correct answer.

Show Formula

Hide Formula

Here is the formula you can use to calculate the within sum of squares.

In this formula, there are a few symbols to know:

Show Solution

Hide Solution

From these calculations, the test statistic is F = 1.6364. As with all test statistics, one would compare this observed value to the table value. Here, if α = 0.05, one would compare 1.6364 to the critical value from the \( F(2, 26) \) distribution with 0.05 area in the right tail.

Show the R Code

Hide the R Code

First, to calculate the critical value for an α = 0.05 level test, you would run:

Next, for calculating the test statistic (and the associated p-value). As with all ANOVA problems, there are two ways of performing these calculations in R. The method you select will depend on how your data are stored.

Method 1: Wide Format

Copy and paste the following code into your R script window, then run it from there.

In the R output, the value of the test statistic is located just below F value. If you want R to return only that value, run:

Here, the number outputted is value of the test statistic. How did you get the number? The summary table (also known as an ANOVA table) is just a table. Thus, the first line saves the table as the variable modSummary the last line looks inside that variable, selects the ANOVA table ([[1]]), and then returns the value in the cell at row 1, column 4.

Method 2: Long Format

Copy and paste the following code into your R script window, then run it from there.

As above, the value of the test statistic is located just below F value. If you want R to return only that value, run:

Here, the number outputted is value of the test statistic. How did you get the number? The summary table (also known as an ANOVA table) is just a table. Thus, the first line saves the table as the variable modSummary the last line looks inside that variable, selects the ANOVA table ([[1]]), and then returns the value in the cell at row 1, column 4.