Table of Contents

- 1 When there are more than two treatments in an ANOVA all of the treatment means must be significantly different from each other to reject the null hypothesis?
- 2 What is a large F value?
- 3 When comparing more than two treatment means Why should you use an analysis of variance?
- 4 What is the F ratio?
- 5 What happens to the f ratio when the null hypothesis is true?
- 6 What is the critical value of the F distribution table?

## When there are more than two treatments in an ANOVA all of the treatment means must be significantly different from each other to reject the null hypothesis?

When there are more than two treatments in an ANOVA, rejecting the null hypothesis means that all of the treatment means are significantly different from each other. If the null hypothesis is true, the F-ratio for ANOVA is expected (on average) to have a value of 1.00.

## What is a large F value?

If you get a large f value (one that is bigger than the F critical value found in a table), it means something is significant, while a small p value means all your results are significant. The F statistic just compares the joint effect of all the variables together.

**What values of F indicate H0 is likely true?**

Standard statistics texts indicate that the expected value of the F ratio is 1.0 (more precisely: N/(N−2)) in a completely balanced fixed-effects ANOVA, when the null hypothesis is true.

**What does the numerator of the F ratio measure?**

The numerator of the F-ratio measures between-treatments variability, which consists of treatment effects and random, unsystematic differences. The denominator measures variability that is exclusively caused by random, unsystematic differences.

### When comparing more than two treatment means Why should you use an analysis of variance?

Analysis of Variance (ANOVA) for Comparing Multiple Means Doing multiple two-sample t -tests would result in an increased chance of committing a Type I error. For this reason, ANOVAs are useful in comparing (testing) three or more means (groups or variables) for statistical significance.

### What is the F ratio?

The F-ratio is the ratio of the between group variance to the within group variance. It can be compared to a critical F-ratio, which is determined by rejecting or accepting the null hypothesis, which determines whether or not there are no differences between groups.

**Which is the correct definition of the f ratio?**

The F-ratio is a ratio of two (or more) sample means. b. The F-ratio is a ratio of two variances. c. The F-ratio is a ratio of sample means divided by sample variances. d. None of the above.

**Where is the critical region for the f-ratio?**

In an analysis of variance, if all other factors are held constant, the larger the differences between the sample means, the bigger the value for the F-ratio. true The critical region for the F-ratio from an analysis of variance is located entirely in one tail of the distribution.

#### What happens to the f ratio when the null hypothesis is true?

When the null hypothesis is true, the F-ratio is balanced so that the numerator and the denominator are both measuring exactly the same sources of variance. In an analysis of variance, if all other factors are held constant, the larger the differences between the sample means, the bigger the value for the F-ratio.

#### What is the critical value of the F distribution table?

The F-distribution table lists a critical value of F = 4.26 for an F-ratio with df = 2, 9 and α = .05. If the data produce an F-ratio of F (2,9) = 4.10, the correct decision would be to reject H0 at the .05 level of significance. THIS SET IS OFTEN IN FOLDERS WITH…