646 CHAPTER 13 Nonparametric Tests Basic Concept of the Sign Test The basic idea underlying the sign test is to analyze the frequencies of positive and negative signs to determine whether they are significantly different. For example, consider the results of clinical trials of the XSORT method of gender selection. Among 726 couples who used the XSORT method in trying to have a baby girl, 668 couples did have baby girls. Is 668 girls in 726 births significant? Common sense should suggest that 668 girls in 726 births is significant, but what about 365 girls in 726 births? Or 400 girls in 726 births? The sign test allows us to determine when such results are significant. Figure 13-1 summarizes the sign test procedure. For consistency and simplicity, we will use a test statistic based on the number of times that the less frequent sign occurs. Handling Ties Among Ranks EXAMPLE 1 The golf scores (for one hole) of 4, 5, 5, 5, 10, 11, 12, and 12 are given ranks of 1, 3, 3, 3, 5, 6, 7.5, and 7.5, respectively. The table below illustrates the procedure for handling ties. Sorted Data Preliminary Ranking Rank 4 1 1 5 5 5 2 3 Mean is 3. 4 3 3 3 10 5 5 11 6 6 12 12 7 Mean is 7.5. 8 7.5 7.5 $1%1& $1%1& f f Key Concept This section introduces the sign test, which involves converting data values to positive and negative signs, then testing to determine whether either sign occurs significantly more often than the other sign. 13-2 Sign Test DEFINITION The sign test is a nonparametric (distribution-free) test that uses positive and negative signs to test different claims, including these: 1. Claims involving matched pairs of sample data 2. Claims involving nominal data with two categories 3. Claims about the median of a single population
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