An “F Test” may be a catch-all term for any test that uses the F-distribution. In most cases, when people mention the F-Test, what they’re actually talking about is that the F-Test to match Two Variances. However, the f-statistic is employed during a sort of tests including multivariate analysis , the Chow test and therefore the Scheffe Test (a post-hoc ANOVA test).

General Steps for an F Test

If you’re running an F Test, you ought to use Excel, SPSS, Minitab or another quite technology to run the test. Why? Calculating the F test by hand, including variances, is tedious and time-consuming. Therefore you’ll probably make some errors along the way.

If you’re running an F Test using technology (for example, an F Test two sample for variances in Excel), the sole steps you actually got to do are Step 1 and 4 (dealing with the null hypothesis). Technology will calculate Steps 2 and three for you.

State the null hypothesis and therefore the alternate hypothesis.

Calculate the F value. The F Value is calculated using the formula F = (SSE1 – SSE2 / m) / SSE2 / n-k, where SSE = residual sum of squares, m = number of restrictions and k = number of independent variables.

Find the F Statistic (the critical value for this test). The F statistic formula is:

F Statistic = variance of the group means / mean of the within group variances.

You can find the F Statistic within the F-Table.

Support or Reject the Null Hypothesis.

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F Test to match Two Variances

A Statistical F Test uses an F Statistic to match two variances, s1 and s2, by dividing them. The result’s always a positive number (because variances are always positive). The equation for comparing two variances with the f-test is:

F = s21 / s22

If the variances are equal, the ratio of the variances will equal 1. For instance , 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.

Assumptions

Several assumptions are made for the test. Your population must be approximately normally distributed (i.e. fit the form of a bell curve) so as to use the test. Plus, the samples must be independent events. Additionally, you’ll want in touch in mind a couple of important points:

The larger variance should enter the numerator (the top number) to force the test into a right-tailed test. Right-tailed tests are easier to calculate.

For two-tailed tests, divide alpha by 2 before finding the proper critical value.

If you’re given standard deviations, they need to be squared to urge the variances.

If your degrees of freedom aren’t listed within the F Table, use the larger critical value. This helps to avoid the likelihood of Type I errors.

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F Test to match two variances by hand: Steps

Warning: F tests can get really tedious to calculate by hand, especially if you’ve got to calculate the variances. You’re far better off using technology (like Excel — see below).

F-Test

Hypothesis Testing > F-Test

Contents:

What is an F Test?

General Steps for an F Test

F Test to match Two Variances

By hand

Two-tailed F test

Excel instructions

See also: F Statistic in ANOVA/Regression

What is an F Test?

An “F Test” may be a catch-all term for any test that uses the F-distribution. In most cases, when people mention the F-Test, what they’re actually talking about is that the F-Test to match Two Variances. However, the f-statistic is employed during a sort of tests including multivariate analysis , the Chow test and therefore the Scheffe Test (a post-hoc ANOVA test).

General Steps for an F Test

If you’re running an F Test, you ought to use Excel, SPSS, Minitab or another quite technology to run the test. Why? Calculating the F test by hand, including variances, is tedious and time-consuming. Therefore you’ll probably make some errors along the way.

If you’re running an F Test using technology (for example, an F Test two sample for variances in Excel), the sole steps you actually got to do are Step 1 and 4 (dealing with the null hypothesis). Technology will calculate Steps 2 and three for you.

State the null hypothesis and therefore the alternate hypothesis.

Calculate the F value. The F Value is calculated using the formula F = (SSE1 – SSE2 / m) / SSE2 / n-k, where SSE = residual sum of squares, m = number of restrictions and k = number of independent variables.

Find the F Statistic (the critical value for this test). The F statistic formula is:

F Statistic = variance of the group means / mean of the within group variances.

You can find the F Statistic within the F-Table.

Support or Reject the Null Hypothesis.

Back to Top

F Test to match Two Variances

A Statistical F Test uses an F Statistic to match two variances, s1 and s2, by dividing them. The result’s always a positive number (because variances are always positive). The equation for comparing two variances with the f-test is:

F = s21 / s22

If the variances are equal, the ratio of the variances will equal 1. For instance , 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. In other words, you usually assume that the variances are adequate to 1. Therefore, your null hypothesis will always be that the variances are equal.

Assumptions

Several assumptions are made for the test. Your population must be approximately normally distributed (i.e. fit the form of a bell curve) so as to use the test. Plus, the samples must be independent events. additionally , you’ll want in touch in mind a couple of important points:

The larger variance should enter the numerator (the top number) to force the test into a right-tailed test. Right-tailed tests are easier to calculate.

For two-tailed tests, divide alpha by 2 before finding the proper critical value.

If you’re given standard deviations, they need to be squared to urge the variances.

If your degrees of freedom aren’t listed within the F Table, use the larger critical value. This helps to avoid the likelihood of Type I errors.

Back to Top

F Test to match two variances by hand: Steps

Warning: F tests can get really tedious to calculate by hand, especially if you’ve got to calculate the variances. You’re far better off using technology (like Excel — see below).

These are the overall steps to follow. Scroll down for a selected example (watch the video underneath the steps).

Step 1: If you’re given standard deviations, attend Step 2. If you’re given variances to match , attend Step 3.

Step 2: Square both standard deviations to urge the variances. for instance , if σ1 = 9.6 and σ2 = 10.9, then the variances (s1 and s2) would be 9.62 = 92.16 and 10.92 = 118.81.

Step 3: Take the most important variance, and divide it by the littlest variance to urge the f-value. for instance , if your two variances were s1 = 2.5 and s2 = 9.4, divide 9.4 / 2.5 = 3.76.

Why? Placing the most important variance on top will force the F-test into a right tailed test, which is far easier to calculate than a left-tailed test.

Step 4: Find your degrees of freedom. Degrees of freedom is your sample size minus 1. As you’ve got two samples (variance 1 and variance 2), you’ll have two degrees of freedom: one for the numerator and one for the denominator.

Step 5: check out the f-value you calculated in Step 3 within the f-table. Note that there are several tables, so you’ll got to locate the proper table for your alpha level. Unsure the way to read an f-table? Read what’s an f-table?.

Step 6: Compare your calculated value (Step 3) with the table f-value in Step 5. If the f-table value is smaller than the calculated value, you’ll reject the null hypothesis.