Inferences from Two Standard Deviations Access tech supplements, videos, and data sets at www.TriolaStats.com TECH CENTER continued R R command not available at time of publication. R is rapidly evolving, and an updated list of statistical commands is available at TriolaStats.com. Excel XLSTAT Add-In Requires original sample data, does not work with summary data. 1. Click on the XLSTAT tab in the Ribbon and then click Parametric tests. 2. Select Two-sample comparison of variances from the dropdown menu. 3. Under Sample 1 & 2 enter the range of cells containing the sample data. For Data format select One column per sample. If the first row of data contains a label, also check the Column labels box. 4. Select Fisher’s F-test. 5. Click the Options tab. 6. Under Alternative hypothesis select the desired format (3 for two-tailed test, * for left-tailed test, + for right-tailed test). Enter the Hypothesized ratio (usually 1) and enter the desired significance level (enter 5 for 0.05 significance level). Select Asymptotic p-value. 7. Click OK to display the test statistic (labeled F Observed value) and P-value. Excel (Data Analysis Add-In) 1. Click on Data in the ribbon, then click on the Data Analysis tab. 2. Select F-Test Two-Sample for Variances and click OK. 3. Enter the data range for each variable in the Variable Range boxes. If the first row contains a label, check the Labels box. 4. Enter the desired significance level in the Alpha box and click OK. The results include the F test statistic, P-value for a one-tail test, and critical value for a one-tail test. TIP: For a two-tailed test make two adjustments: (1) Enter the value that is half the significance level (Step 4) and (2) double the P-value given in the results. Statistical Literacy and Critical Thinking 1. F Test Statistic a. If s2 1 represents the larger of two sample variances, can the F test statistic ever be less than 1? b. Can the F test statistic ever be a negative number? c. If testing the claim that s 2 1 ≠ s 2 2, what do we know about the two samples if the test statistic F is very close to 1? d. Is the F distribution symmetric, skewed left, or skewed right? 2. F Test Using sample data from Data Set 2 “ANSUR I 1988” and Data Set 3 “ANSUR II 2012” for a test of the claim that heights of female U.S. Army personnel in 1988 and 2012 have different amounts of variation, we find that s = 63.6 cm for 1988 and s = 64.2 cm for 2012. a. Find the values of s2 1 and s 2 2 and express them with appropriate units of measure. b. Identify the null and alternative hypotheses. c. Find the value of the F test statistic and round it to four decimal places. d. The P-value for this test is 0.6695. What do you conclude about the stated claim? 9-4 Basic Skills and Concepts 486 CHAPTER 9 Inferences from Two Samples
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