![]() ![]() The degrees of freedom in the table will be the sample size -1, so: Step 3: Calculate the degrees of freedom: Put the highest variance as the numerator and the lowest variance as the denominator:į Statistic = variance 1/ variance 2 = 109.63 / 65.99 = 1.66 Step 1: Write your hypothesis statements: Watch the video for an example of a two-tailed F test: If the f-table value is smaller than the calculated value, you can reject the null hypothesis. Step 6: Compare your calculated value (Step 3) with the table f-value in Step 5. Unsure how to read an f-table? Read What is an f-table?. Note that there are several tables, so you’ll need to locate the right table for your alpha level. Step 5: Look at the f-value you calculated in Step 3 in the f-table. As you have two samples (variance 1 and variance 2), you’ll have two degrees of freedom: one for the numerator and one for the denominator. Degrees of freedom is your sample size minus 1. Why? Placing the largest variance on top will force the F-test into a right tailed test, which is much easier to calculate than a left-tailed test. For example, if your two variances were s 1 = 2.5 and s 2 = 9.4, divide 9.4 / 2.5 = 3.76. Step 3: Take the largest variance, and divide it by the smallest variance to get the f-value. Step 2: Square both standard deviations to get the variances. If you are given variances to compare, go to Step 3. Step 1: If you are given standard deviations, go to Step 2. You’re much better off using technology (like Excel - see below). Warning: F tests can get really tedious to calculate by hand, especially if you have to calculate the variances. Need help with a specific question? Check out our tutoring page! This helps to avoid the possibility of Type I errors.īack to Top F Test to compare two variances by hand: Steps If your degrees of freedom aren’t listed in the F Table, use the larger critical value.If you are given standard deviations, they must be squared to get the variances.For two-tailed tests, divide alpha by 2 before finding the right critical value.Right-tailed tests are easier to calculate. The larger variance should always go in the numerator (the top number) to force the test into a right-tailed test.In addition, you’ll want to bear in mind a few important points: Plus, the samples must be independent events. fit the shape of a bell curve) in order to use the test. Your population must be approximately normally distributed (i.e. Several assumptions are made for the test. Therefore, your null hypothesis will always be that the variances are equal. In other words, you always assume that the variances are equal to 1. You always test that the population variances are equal when running an F Test. 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. If the variances are equal, the ratio of the variances will equal 1. The equation for comparing two variances with the f-test is: The result is always a positive number (because variances are always positive). You can find the F Statistic in the F-Table.īack to Top F Test to Compare Two VariancesĪ Statistical F Test uses an F Statistic to compare two variances, s 1 and s 2, by dividing them. The F statistic formula is:į Statistic = variance of the group means / mean of the within group variances. Find the F Statistic (the critical value for this test).The F Value is calculated using the formula F = (SSE 1 – SSE 2 / m) / SSE 2 / n-k, where SSE = residual sum of squares, m = number of restrictions and k = number of independent variables. State the null hypothesis and the alternate hypothesis.Technology will calculate Steps 2 and 3 for you. If you’re running an F Test using technology (for example, an F Test two sample for variances in Excel), the only steps you really need to do are Step 1 and 4 (dealing with the null hypothesis). Therefore you’ll probably make some errors along the way. Why? Calculating the F test by hand, including variances, is tedious and time-consuming. If you’re running an F Test, you should use Excel, SPSS, Minitab or some other kind of technology to run the test.
0 Comments
Leave a Reply. |
AuthorWrite something about yourself. No need to be fancy, just an overview. ArchivesCategories |