Analysis the variance (ANOVA) provides F-tests to statistically assess the equality of method when you have actually three or much more groups. In this post, I’ll prize several common questions around the F-test.

You are watching: Which of the following describes a typical distribution of f-ratios?

*variances*to test

*means*?

I’ll usage concepts and graphs come answer this questions about F-tests in the context of a one-way ANOVA example. I’ll use the same approachthatIuse to define how t-tests work. If you need a inside wall on the basics, review my hypothesis testing overview.

To learn much more about ANOVA tests, including the more facility forms, review my ANOVA Overview.

## Introducing F-tests and F-statistics!

The circulation curve displays the likelihood the F-values for a populace where the 4 group method are equal at the population level. Ns shaded the an ar that synchronizes to F-values higher than or equal to our study’s F-value (3.3). When the null hypothesis is true, F-values loss in this area roughly 3.1% that the time. Utilizing a definition level of 0.05, ours sample data room unusual sufficient to warrant rejecting the null hypothesis. The sample evidence argues that not all group way are equal.

Learn just how to analyze P values correctly and also avoid a usual mistake.

## Why We analyze Variances to test Means

Let’s go back to the question around why we analyze variances to identify whether the group way are different. Emphasis on the “means room different” aspect. This part explicitly requires the sports of the team means. If over there is no sports in the means, castle can’t it is in different, right? Similarly, the larger the differences in between the means, the much more variation should be present.

ANOVA and also F-tests assess the quantity of variability in between the group method in the paper definition of the sport within groups to recognize whether the mean distinctions are statistically significant. While statistically significant ANOVA results indicate that not all method are equal, that doesn’t determine which details differences in between pairs of way are significant. Come make that determination, you’ll have to use write-up hoc test to supplement the ANOVA results.

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If you’d prefer to learn about other hypothesis tests making use of the same basic approach, read:

To view an alternate to classic hypothesis experimentation that go not use probability distributions and test statistics, learn around bootstrapping in statistics!

**Note: I created a different version the this article that appeared elsewhere. I’ve completely rewritten and updated it because that my blog site.**