9-4 Two Variances or Standard Deviations 485 Levene-Brown-Forsythe Test The Levene-Brown-Forsythe test (or modified Levene’s test) is another alternative to the F test, and it is much more robust against departures from normality. This test begins with a transformation of each set of sample values. Within the first sample, replace each x value with x - median , and apply the same transformation to the second sample. Using the transformed values, conduct a t test of equality of means for independent samples, as described in Part 1 of Section 9-2. Because the transformed values are now deviations, the t test for equality of means is actually a test comparing variation in the two samples. See Exercise 18 “Levene-Brown-Forsythe Test.” There are other alternatives to the F test, as well as adjustments that improve the performance of the F test. See “Fixing the F Test for Equal Variances,” by Shoemaker, American Statistician, Vol. 57, No. 2. Inferences from Two Standard Deviations Access tech supplements, videos, and data sets at www.TriolaStats.com TECH CENTER Statdisk 1. Click Analysis in the top menu. 2. Select Hypothesis Testing from the dropdown menu and Standard Deviation Two Samples from the submenu. 3. Using Summary Statistics: Select the Use Summary Statistics tab and enter the sample size and sample standard deviation for each sample. Using Sample Data: Select the Use Data tab and select the desired data columns. 4. Select the desired format for Alternative Hypothesis and enter the significance level. 5. Click Evaluate. Minitab 1. Click Stat in the top menu. 2. Select Basic Statistics from the dropdown menu and select 2 Variances from the submenu. 3. Using Summary Statistics: Select Sample variances or Sample standard deviations from the dropdown menu and enter the sample sizes and sample variances or standard deviations. Using sample data: Select Each sample is in its own column from the dropdown menu and select the desired data columns. 4. Click the Options button and select the desired ratio. Enter the desired confidence level and enter 1 for Hypothesized ratio. Select the desired format for the Alternative hypothesis. 5. Check the box labeled Use test and confidence intervals based on normal distribution. 6. Click OK twice. TIP: Another procedure is to click on Assistant in the top menu, then select Hypothesis Tests and 2-Sample Standard Deviation. Complete the dialog box to get results, including P-value and other helpful information. StatCrunch 1. Click Stat in the top menu. 2. Select Variance Stats from the dropdown menu, then select Two Sample from the submenu. 3. Using Summary Statistics: Select With Summary from the submenu and enter the sample variances and sample sizes. Using Sample Data: Select With Data from the submenu and select the desired data column for each sample. 4. Select Hypothesis test for S1 2, S2 2. Enter 1 for the hypothesized ratio 1H02 and select the desired format for the alternative hypothesis 1HA2. 5. Click Compute! TI-83> 83 84 Plus Calculator 8 us Ca cu ato 1. Press K, then select TESTS in the top menu. 2. Select 2-SampFTest in the menu and press [. 3. Select Data if you have sample data in lists or Stats if you have summary statistics. Press [ and enter the list names (leave Freq = 1) or summary statistics. 4. For s1 select the desired format for the alternative hypothesis. 5. Select Calculate and press [. o st e, Go Figure Every minute there are more than 350,000 tweets, 212 million e-mails, and 16 million text messages. continued
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