How to Calculate the F-Ratio

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  • 0:03 Comparing Multiple…
  • 1:39 Calculating the Variance
  • 4:04 Interpreting the F-Ratio
  • 6:15 Lesson Summary
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Lesson Transcript
Instructor: Betsy Chesnutt

Betsy teaches college physics, biology, and engineering and has a Ph.D. in Biomedical Engineering

In statistics, the F-ratio is used to determine if there are differences between groups in an experiment. In this lesson, learn how to calculate the F-ratio and interpret the result.

Comparing Multiple Groups in Stats

James works for an advertising agency, and his team has developed four potential new advertisements for a product. As part of the evaluation process, James shows the ads to a focus group of potential customers and has each person rate (on a 0-10 scale) how likely they are to purchase the product after watching each ad. The data he collected is shown in the table:


data table


How can he tell if one ad was more effective than another? Simply looking at the mean score of each is not enough because there might be a lot of variability in the data, and the means might appear to be different, when statistically, they aren't. A statistical test that he could use to determine if there were any differences between the four groups is called analysis of variance (or ANOVA). ANOVA is a test used to detect differences between continuous variables when there are more than two groups, so it would be ideal to use in this situation.

As part of performing an ANOVA on this data, James will need to calculate an F-ratio. The F-ratio is defined as the ratio of the between group variance (MSB) to the within group variance (MSW).

F = between group variance / within group variance = MSB / MSW

The calculated F-ratio can be compared to a table of critical F-ratios to determine if there are actually any differences between groups or not.

Let's look in a little more detail at all the steps involved in calculating and interpreting the F-ratio.

Calculating the Variance

To calculate the variance within the groups, first calculate the sum of the squared deviations from the mean for each group. To find the sum of the squared deviations for a single group, follow these steps:

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