Sign Test Access tech supplements, videos, and data sets at www.TriolaStats.com TECH CENTER continued 13-2 Sign Test 655 R R does not have a function dedicated to the sign test, but the binom.test command can be used to find the P-value for a sign test. R command: binom.test(x, n, p=0.5, alternative=c(“less” or “two.sided”) where x is the number of the less frequent sign and n is the number of positive and negative signs. TIP: The final result is the P-value, so reject the null hypothesis if the P-value is less than or equal to the significance level. Otherwise, fail to reject the null hypothesis. A complete list of R statistical commands is available at TriolaStats.com Excel XLSTAT Add-In 1. Click on the XLSTAT tab in the Ribbon and then click Nonparametric tests. 2. Select Comparison of two samples from the dropdown menu. 3. Enter the data range for each sample in the Sample 1 & 2 boxes. Check the Column labels box if the data range includes labels. 4. Select Paired samples under Data format. 5. Check the Sign test option only. 6. Click the Options tab. 7. Under Alternative hypothesis select Sample 1−Sample 2 3 D. Confirm Hypothesized difference (D) is 0. 8. Enter a significance level and check the Exact p-value box. 9. Click OK. Excel Excel does not have a function dedicated to the sign test, but can be used to find the P-value for a sign test. 1. Click on the Insert Function ƒx button, select the category Statistical, and select the function BINOM.DIST and click OK. 2. For Number_s enter the number of times the less frequent sign occurs. For Trials enter the total number of positive and negative signs. For probability_s enter 0.5. For Cumulative enter 1 for “True.” 3. Click OK. The single-tail P-value will be displayed. Double this value for two-tailed tests. TIP: The final result is the P-value, so reject the null hypothesis if the P-value is less than or equal to the significance level. Otherwise, fail to reject the null hypothesis. Statistical Literacy and Critical Thinking 1.Is Friday the 13th Unlucky? Listed below are numbers of hospital admissions in one region due to traffic accidents on different Fridays falling on the 6th day of a month and the following 13th day of the month (based on data from “Is Friday the 13th Bad for Your Health,” by Scanlon et al., British Medical Journal, Vol. 307). Assume that we plan to use the sign test to test the claim of no difference between traffic accidents that occur on Friday the 6th and those that occur on the following Friday the 13th. a. What requirements must be satisfied for this test? b. Is there any requirement that the samples must be from populations having a normal distribution or any other specific distribution? c. In what sense is this sign test a “distribution-free test”? Friday 6th 9 6 11 11 3 5 8 Friday 13th 13121410 4 12 8 2.Identifying Signs For the sign test described in Exercise 1, identify the number of positive signs, the number of negative signs, the number of ties, the sample size n that is used for the sign test, and the value of the test statistic. 13-2 Basic Skills and Concepts
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