# F-test - Test for the Differences Between Two Population Variances

The tests concerning the differences between two population variances are called F-test. We are testing the equality of two variances.

For this test, we calculate a F-distributed test statistic that follows the F-distribution.

Here also we assume that the samples are normally distributed and are independent.

The hypothesis is formed as follows:

Assume we have two samples with n1 and n2 observations. The test statistic for F-test is calculated as follows:

We use the degrees of freedom to identify the critical value from the F-table.

The F distribution is an asymmetric distribution that has a minimum value of 0, but no maximum value. The curve reaches a peak not far to the right of 0, and then gradually approaches the horizontal axis the larger the F value is. The F distribution approaches, but never quite touches the horizontal axis.

All the other steps in conducting the hypothesis test are the same, except the calculation of test statistic.

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- What is Hypothesis Testing
- Test Statistic, Type I and type II Errors, and Significance Level
- Decision Rule in Hypothesis Testing
- p-Value in Hypothesis Testing
- Selecting the Appropriate Test Statistic
- Hypothesis Testing with t-statistic
- Hypothesis Testing with z-statistic
- Tests Concerning Differences in Means
- Paired Comparision Tests - Mean Differences When Populations are Not Independent
- Hypothesis Tests Concerning Variances
- Chi-square Test – Test for value of a single population variance
- F-test - Test for the Differences Between Two Population Variances
- Non-parametric Tests

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