# How do you compare two population variances?

## How do you compare two population variances?

F-Test to Compare Two Population Variances

1. The F-test: This test assumes the two samples come from populations that are normally distributed.
2. Bonett’s test: this assumes only that the two samples are quantitative.
3. Levene’s test: similar to Bonett’s in that the only assumption is that the data is quantitative.

## What is a two variance test?

A test of two variances hypothesis test determines if two variances are the same. The distribution for the hypothesis test is the F distribution with two different degrees of freedom. Assumptions: The populations from which the two samples are drawn are normally distributed.

What test is used to determine if there is difference between the two variances of the group?

Multiple ANOVA
Multiple ANOVA (MANOVA): This tests a group or groups to determine if there are differences on two or more variables.

### How do you test multiple variances?

Steps:

1. Select the Analyze menu > Parametric > Click on Multiple Variances Test:
2. Drag each route variable onto the Data variable drop zones which appear on the study. Click Continue: Note: the only alternative is ‘Not Equal’.
3. The Multiple Variances test output is shown:

### How do you know if variance is equal or unequal?

There are two ways to do so:

1. Use the Variance Rule of Thumb. As a rule of thumb, if the ratio of the larger variance to the smaller variance is less than 4 then we can assume the variances are approximately equal and use the Student’s t-test.
2. Perform an F-test.

How do you know if variance is correct?

A chi-square test ( Snedecor and Cochran, 1983) can be used to test if the variance of a population is equal to a specified value. This test can be either a two-sided test or a one-sided test.

#### How do I know if variances are equal?

If the variances are equal, the ratio of the variances will equal 1. For example, if you had two data sets with a sample 1 (variance of 10) and a sample 2 (variance of 10), the ratio would be 10/10 = 1. You always test that the population variances are equal when running an F Test.

#### Which test is used for testing the equality of variances?

Levene’s test ( Levene 1960) is used to test if k samples have equal variances. Equal variances across samples is called homogeneity of variance.

When should you use the Z test?

The z-test is best used for greater-than-30 samples because, under the central limit theorem, as the number of samples gets larger, the samples are considered to be approximately normally distributed. When conducting a z-test, the null and alternative hypotheses, alpha and z-score should be stated.

## Why is multiple testing a problem?

What is the Multiple Testing Problem? If you run a hypothesis test, there’s a small chance (usually about 5%) that you’ll get a bogus significant result. If you run thousands of tests, then the number of false alarms increases dramatically.

## How to test if variances from two populations are equal?

Test if variances from two populations are equal An F-test (Snedecor and Cochran, 1983) is used to test if the variances of two populations are equal. This test can be a two-tailed test or a one-tailed test. The two-tailed version tests against the alternative that the variances are not equal.

When is the test of two variances biased?

If the two distributions are not normal, or close, the test can give a biased result for the test statistic. Suppose we sample randomly from two independent normal populations. Let and be the unknown population variances and and be the sample variances. Let the sample sizes be n1 and n2.

### When to reject null for two population variances?

Regardless, the hypotheses would be the same for any of the test options and the decision method is the same: if the p -value is less than alpha, we reject the null and conclude the two population variances are not equal.

### How to do a F test of two variances?

A supermarket might be interested in the variability of check-out times for two checkers. In order to perform a F test of two variances, it is important that the following are true: The populations from which the two samples are drawn are normally distributed. The two populations are independent of each other.