13-2 Sign Test 649 Claims About Matched Pairs When using the sign test with data that are matched pairs, we convert the raw data to positive and negative signs as follows: 1. Subtract each value of the second variable from the corresponding value of the first variable. 2. Record only the sign of the difference found in Step 1. Exclude ties by deleting any matched pairs in which both values are equal. The main concept underlying this use of the sign test is as follows: If the two sets of data have equal medians, the number of positive signs should be approximately equal to the number of negative signs. Data Contradicting the Alternative Hypothesis EXAMPLE 1 Among 945 couples who used the XSORT method of gender selection, 66 had boys, so the sample proportion of boys is 66>945, or 0.0698 (based on data from the Genetics & IVF Institute). Consider the claim that the XSORT method of gender selection increases the likelihood of baby boys so that the probability of a boy is p 7 0.5. This claim of p 7 0.5 becomes the alternative hypothesis. Using common sense, we see that with a sample proportion of boys of 0.0698, we can never support a claim that p 7 0.5. (We would need a sample proportion of boys greater than 0.5 by a significant amount.) Here, the sample proportion of 66>945, or 0.0698, contradicts the alternative hypothesis because it is not greater than 0.5. YOUR TURN. Exercise 3 “Contradicting H1.” INTERPRETATION An alternative hypothesis can never be supported with data that contradict it. The sign test will show that 66 boys in 945 births is significant, but it is significant in the wrong direction. We can never support a claim that p 7 0.5 with a sample proportion of 66>945, or 0.0698, which is less than 0.5. Is There a Difference Between Measured and Reported Weights? EXAMPLE 2 Listed below are measured and reported weights (lb) of random male subjects (from Data Set 4 “Measured and Reported” in Appendix B). Use a 0.05 significance level to test the claim that for males, the differences “measured weight–reported weight” have a median equal to 0. SOLUTION REQUIREMENT CHECK The only requirement of the sign test is that the sample data are a simple random sample, and that requirement is satisfied. If there is no difference between measured weights and reported weights, the numbers of positive and negative signs should be approximately equal. In Table 13-3 we have 6 positive signs, 3 negative signs, and 1 difference of 0. We discard the difference of 0 and proceed using only the 6 positive signs and 3 negative signs. The sign test tells us whether or not the numbers of positive and negative signs are approximately equal. TABLE 13-3 Measured and Reported Male Weights Measured 220.0 268.7 213.4 201.3 107.1 172.0 187.4 132.5 122.1 151.9 Reported 220 267 210 204 107 176 187 135 122 150 Sign of Difference 0 + + - + - + - + + continued
RkJQdWJsaXNoZXIy NjM5ODQ=