When you have completed this chapter, you will be able to: Conduct the sign test for single and dependent samples using the binomial and standard normal distributions as the test statistics, conduct a test of hypothesis for dependent samples using the Wilcoxon signed-rank test, conduct and interpret the Wilcoxon rank-sum test for independent samples,...
16 1 Copyright © 2004 by The McGrawHill Companies, Inc. All rights reserved. 16 2 When you have completed this chapter, you will be able to: Conduct the sign test for single and dependent samples using the binomial and standard normal distributions as the test statistics Conduct a test of hypothesis for dependent samples using the Wilcoxon signedrank test Conduct and interpret the Wilcoxon ranksum test for independent samples Copyright © 2004 by The McGrawHill Companies, Inc. All rights reserved. 16 3 Conduct and interpret the KruskalWallis test for several independent samples Compute and interpret Spearman’s coefficient of rank correlation Conduct a test of hypothesis to determine whether the correlation among the ranks in the population is different from zero Copyright © 2004 by The McGrawHill Companies, Inc. All rights reserved. Terminology Range …is the difference between the …is the difference between the largest and the and the smallest smallest value value largest Only two values are used in its calculation Only two values are used in its calculation It is influenced by an extreme value It is influenced by an extreme value It is easy to compute and understand It is easy to compute and understand Copyright © 2004 by The McGrawHill Companies, Inc. All rights reserved. 16 4 The Sign Test The Sign Test is based on the sign of a difference between two related observations no assumption is necessary regarding the shape of the population of differences … the binomial distribution is the test statistic for small samples and the standard normal (z) for large samples … the test requires dependent (related) samples Copyright © 2004 by The McGrawHill Companies, Inc. All rights reserved. 16 5 The Sign Test 16 6 …continued Procedure to conduct the test: Determine the sign of the Determine the sign of the difference difference between related pairs between related pairs Determine the number of usable pairs Compare the number of positive (or negative) differences to the critical value n is the number of usable pairs (without ties), x is the number of pluses or minuses, and the binomial probability p=.5 Copyright © 2004 by The McGrawHill Companies, Inc. All rights reserved. Normal Approximation Normal Approximation …if both and are greater than 5, n(1 p ) np the z distribution is appropriate 16 7 …if the number of pluses or minuses is more than n/2, then z ( x ) n n …if the number of pluses or minuses is less than n/2, then z ( x ) n n Copyright © 2004 by The McGrawHill Companies, Inc. All rights reserved. Normal Approximation Normal Approximation 16 8 The Gagliano Research Institute for Business Studies is comparing the Research and Development expense (R&D) as a percent of income for a sample of glass manufacturing firms for 2000 and 2001 At the .05 significance level has the R&D expense declined? Use the sign test Copyright © 2004 by The McGrawHill Companies, Inc. All rights reserved. Normal Approximation Normal Approximation Company Continued… 2000 2001 Difference Sign Company 2000 2001 Difference 16 9 Sign Savoth Glass 20 16 4 + Savoth Glass 20 16 4 + Ruisi Glass 14 13 1 + Ruisi Glass 14 13 1 + Rubin Inc 23 20 3 + Rubin Inc 23 20 3 + Vaught 24 17 7 + Vaught 24 17 7 + Lambert Glass 31 22 9 + Lambert Glass 31 22 9 + Pimental 22 20 2 + Pimental 22 20 2 + Olson Glass 14 20 6 Olson Glass 14 20 6 Flynn Glass 18 11 7 + Flynn Glass 18 11 7 + Copyright © 2004 by The McGrawHill Companies, Inc. All rights reserved. Normal Approximation Normal Approximation 16 10 Continued… Step 1: H0: p=.5 H1: p