Nonparametric Tests BPS 7e Chapter 28 © 2015 W. H. Freeman and Company

Rank Tests Rank tests are _________ tests based on the ______ of observations, their positions in the list ordered from smallest (rank 1) to largest. Tied observations receive the ________ of their ranks. nonparametric; ranks; sum nonparametric; values; minimum parametric; ranks; maximum nonparametric; ranks; average

Rank Tests (answer) Rank tests are _________ tests based on the ______ of observations, their positions in the list ordered from smallest (rank 1) to largest. Tied observations receive the ________ of their ranks. nonparametric; ranks; sum nonparametric; values; minimum parametric; ranks; maximum nonparametric; ranks; average

Rank Test True or False: We should use rank tests when the data come from random samples or randomized comparative experiments and the populations have either continuous or categorical distributions. True False

Rank Test (answer) True or False: We should use rank tests when the data come from random samples or randomized comparative experiments and the populations have either continuous or categorical distributions. True False (continuous distributions)

The Wilcoxon Rank Sum Test True or False: The Wilcoxon rank sum test rejects the hypothesis that the two populations have identical distributions when the rank sum W is far from its mean. True False

The Wilcoxon Rank Sum Test (answer) True or False: The Wilcoxon rank sum test rejects the hypothesis that the two populations have identical distributions when the rank sum W is far from its mean. True False

Continuity Correction To apply the continuity correction in a Normal approximation for a variable that takes only whole-number values, act as if each whole number occupies the entire interval from ____ below the number to ___ above it. 0.5; 0.5 0.5; 1.0 1.0; 1.0 0.75; 0.5

Continuity Correction (answer) To apply the continuity correction in a Normal approximation for a variable that takes only whole-number values, act as if each whole number occupies the entire interval from ____ below the number to ___ above it. 0.5; 0.5 0.5; 1.0 1.0; 1.0 0.75; 0.5

Wilcoxon Statistic W Researchers compare the strengths of cotton fabric treated with two “durable press” processes. Here are the breaking strengths in pounds: Researchers want to test if there is a significant difference between the two processes by using the Wilcoxon statistic (W). What would be the null and alternative hypotheses? a) H0: no difference in distribution of “durable press” processes Ha: the strength of fabric treated with “Permafresh” is systematically higher than “Hylite” b) H0: no difference in distribution of “durable press” processes Ha: there is a systematic difference between fabric strengths treated with “Hylite” and “Permafresh”

Wilcoxon Statistic W (answer) Researchers compare the strengths of cotton fabric treated with two “durable press” processes. Here are the breaking strengths in pounds: Researchers want to test if there is a significant difference between the two processes by using the Wilcoxon statistic (W). What would be the null and alternative hypotheses? a) H0: no difference in distribution of “durable press” processes Ha: the strength of fabric treated with “Permafresh” is systematically higher than “Hylite” b) H0: no difference in distribution of “durable press” processes Ha: there is a systematic difference between fabric strengths treated with “Hylite” and “Permafresh”

Wilcoxon Statistic W Researchers compare the strengths of cotton fabric treated with two “durable press” processes. Here are the breaking strengths in pounds: What would be the Wilcoxon statistic (W ) for the Permafresh group? (5 + (10 + 1)) / 2 = 8 (5)* (10) /2 = 25 (5 * (10 + 1)) / 2 = 27.5 (5 * (10 − 1)) / 2 = 22.5

Wilcoxon Statistic W (answer) Researchers compare the strengths of cotton fabric treated with two “durable press” processes. Here are the breaking strengths in pounds: What would be the Wilcoxon statistic (W) for the Permafresh group? (5 + (10 + 1)) / 2 = 8 (5)* (10) /2 = 25 (5 * (10 + 1)) / 2 = 27.5 (5 * (10 − 1)) / 2 = 22.5

Wilcoxon Statistic W Researchers compare the strengths of cotton fabric treated with two “durable press” processes. Here are the breaking strengths in pounds: What would be the standard deviation of W? (5*5*10) / 12 (5*5*11) / 12 (5*5*0) / 12 (5*5*11) / 2

Wilcoxon Statistic W (answer) Researchers compare the strengths of cotton fabric treated with two “durable press” processes. Here are the breaking strengths in pounds: What would be the standard deviation of W? (5*5*10) / 12 (5*5*11) / 12 (5*5*0) / 12 (5*5*11) / 2

Wilcoxon Signed Rank Statistic The following data present the percent of nitrogen in bubbles of ancient air trapped in amber: 63.4 65.0 64.4 63.3 54.8 64.5 60.8 49.1 51.0 The researchers wonder if ancient air differs significantly from the present atmosphere, which is 78.1% nitrogen. In order to test a hypothesis about the median percent of nitrogen in ancient air (the population), the null hypothesis would be: H0: median = 0. H0: median = 78.1. H0: mean ≠ 0. H0: median ≠ 78.1.

Wilcoxon Signed Rank Statistic (answer) The following data presents the percent of nitrogen in bubbles of ancient air trapped in amber: 63.4 65.0 64.4 63.3 54.8 64.5 60.8 49.1 51.0 The researchers wonder if ancient air differs significantly from the present atmosphere, which is 78.1% nitrogen. In order to test a hypothesis about the median percent of nitrogen in ancient air (the population), the null hypothesis would be: H0: median = 0. H0: median = 78.1. H0: mean ≠ 0. H0: median ≠ 78.1.

Wilcoxon Signed Rank Statistic The following data presents the percent of nitrogen in bubbles of ancient air trapped in amber: 63.4 65.0 64.4 63.3 54.8 64.5 60.8 49.1 51.0 The researchers wonder if ancient air differs significantly from the present atmosphere, which is 78.1% nitrogen. In order to test a hypothesis about the median percent of nitrogen in ancient air (the population), the alternative hypothesis would be: Ha: median = 78.1. Ha: mean = 78.1. Ha: mean ≠ 0. Ha: median ≠ 78.1.

Wilcoxon Signed Rank Statistic (answer) The following data presents the percent of nitrogen in bubbles of ancient air trapped in amber: 63.4 65.0 64.4 63.3 54.8 64.5 60.8 49.1 51.0 The researchers wonder if ancient air differs significantly from the present atmosphere, which is 78.1% nitrogen. In order to test a hypothesis about the median percent of nitrogen in ancient air (the population), the alternative hypothesis would be: Ha: median = 78.1. Ha: mean = 78.1. Ha: mean ≠ 0. Ha: median ≠ 78.1.

Rank Test in ANOVA Setting The _____________ test compares several populations on the basis of independent random samples from each population. This is the one-way analysis of variance setting. Wilcoxon signed rank Kruskal-Wallis Wilcoxon rank Mann-Whitney

Rank Test in ANOVA Setting (answer) The _____________ test compares several populations on the basis of independent random samples from each population. This is the one-way analysis of variance setting. Wilcoxon signed rank Kruskal-Wallis Wilcoxon rank Mann-Whitney