Calculating the ANOVA Test Statistic (F)

Summary statistics from the problem

TSS	=	518.9333
SSB	=	34.1333
SSW	=	484.8
\( \nu_t \)	=	14
\( \nu_b \)	=	2
\( \nu_w \)	=	12

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 = 0.4224. Congratulations!

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

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

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

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From these calculations, the test statistic is F = 0.4224. As with all test statistics, one would compare this observed value to the table value. Here, if α = 0.05, one would compare 0.4224 to the critical value from the \( F(2, 12) \) distribution with 0.05 area in the right tail.

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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.