Exam 15: Nonparametric Tests

Which of the following statements about the two-sample Wilcoxon rank sum test is/are FALSE?

When using the Wilcoxon signed rank test and the absolute difference for a pair of observations is zero,it is best to _________________.

Laureysens,et al.(2004)studied the concentration of aluminum in wood from a number of clones of poplar growing in an area with heavy pollution.The same clone was sampled and tested once in August and again in November.The researchers believed that the concentration of aluminum would be shown to be increasing over time and hence higher in November than in August.The following table gives the aluminum concentrations for twelve of the clones. The data are to be analyzed using the Wilcoxon signed rank test.The null hypothesis they established was that the values of aluminum concentrations in the 2 months have the same distribution.What should the researchers establish as the appropriate alternative hypothesis?

A private university is trying to determine if there is pay equity among the male and female faculty.A simple random sample of six faculty members was selected from each gender group and the salary was recorded.The data (in thousands)are shown below. What is the standard deviation for the sum of the ranks for the male faculty?

As part of a large,ongoing diet study,some subjects of the study are taking part in an intensive exercise program for four weeks.Several variables are measured on these subjects,both at the beginning and at the end of the four-week period.Some of these variables are weight,cholesterol,and triglyceride level.One objective of this particular study is to assess the effect of diet and intense exercise on increasing triglyceride levels.The data for a simple random sample of nine of these subjects are given in the table below. The data are to be analyzed using the Wilcoxon signed rank test.Under the null hypothesis that triglyceride levels have the same distribution at the beginning and at the end of the study,what is the standard deviation of the test statistic W⁺?

As part of a large,ongoing diet study,some subjects of the study are taking part in an intensive exercise program for four weeks.Several variables are measured on these subjects,both at the beginning and at the end of the four-week period.Some of these variables are weight,cholesterol,and triglyceride level.One objective of this particular study is to assess the effect of diet and intense exercise on increasing triglyceride levels.The data for a simple random sample of nine of these subjects are given in the table below. The data are to be analyzed using the Wilcoxon signed rank test.The data were entered into SPSS,and the following output was obtained. Wilcoxon Signed Rank Test If the test statistic W⁺ were to be based on positive differences,what would be the value of W⁺?

Some researchers have conjectured that stem-pitting disease in peach-tree seedlings might be controlled with weed and soil treatment.An experiment was conducted to compare peach-tree seedling growth with soil and weeds treated with one of two herbicides.In a field containing twelve seedlings,six were randomly selected throughout the field and assigned to receive Herbicide A.The remaining six were to receive Herbicide B.Soil and weeds for each seedling were treated with the appropriate herbicide,and at the end of the study period the height in centimeters was recorded for each seedling.The following results were obtained. Let W be the Wilcoxon rank sum test statistic equal to the sum of the ranks assigned to the Herbicide A group.What is the value of z,the standardized value of W?

At what age do babies learn to crawl? Does it take longer to learn in the winter when babies are often bundled in clothes that restrict their movement? Data were collected from parents who brought their babies into the University of Denver Infant Study Center to participate in one of a number of experiments between 1988 and 1991.Parents reported the birth month and the age at which their child was first able to creep or crawl a distance of 4 feet within 1 minute.The resulting data were grouped by month of birth: January,May,and September. The data are to be analyzed with the Kruskal-Wallis test.The null hypothesis is that the crawling ages have the same distribution in all groups.What is the alternative hypothesis?

A private university is trying to determine if there is pay equity among the male and female faculty.A simple random sample of six faculty members was selected from each gender group and the salary was recorded.The data (in thousands)are shown below. What is the mean of the sum of the ranks for the male faculty?

Laureysens,et al.(2004)studied the concentration of aluminum in wood from a number of clones of poplar growing in an area with heavy pollution.The same clone was sampled and tested once in August and again in November.The researchers believed that the concentration of aluminum would be shown to be increasing over time and hence higher in November than in August.The following table gives the aluminum concentrations for twelve of the clones. The data are to be analyzed using the Wilcoxon signed rank test.The null hypothesis they established was that the values of aluminum concentrations in the 2 months have the same distribution.Under the null hypothesis,what are the values of the mean and standard deviation,respectively,of the statistic W⁺?

A private university is trying to determine if there is pay equity among the male and female faculty.A simple random sample of six faculty members was selected from each gender group and the salary was recorded.The data (in thousands)are shown below. What is the sum of the ranks for the female group?

In a study to investigate the effect of diet on reducing cholesterol levels,a random sample of five subjects known to have high cholesterol had their cholesterol measured at the beginning of the study and after 6 months on a special diet.The data are given in the table below. The data are to be analyzed using the Wilcoxon signed rank test.The five differences are to be assigned an appropriate rank.What rank should the difference of -7 be assigned?

In a study to investigate the effect of diet on reducing cholesterol levels,a random sample of five subjects known to have high cholesterol had their cholesterol measured at the beginning of the study and after 6 months on a special diet.The data are given in the table below. The data are to be analyzed using the Wilcoxon signed rank test.Under the null hypothesis that the responses have a continuous distribution that is not affected by the treatment,what is the expected value of the test statistic W⁺?

Some researchers have conjectured that stem-pitting disease in peach-tree seedlings might be controlled with weed and soil treatment.An experiment was conducted to compare peach-tree seedling growth with soil and weeds treated with one of two herbicides.In a field containing twelve seedlings,six were randomly selected throughout the field and assigned to receive Herbicide A.The remaining six were to receive Herbicide B.Soil and weeds for each seedling were treated with the appropriate herbicide,and at the end of the study period the height in centimeters was recorded for each seedling.The following results were obtained. Let W be the Wilcoxon rank sum test statistic equal to the sum of the ranks assigned to the Herbicide A group.What is the observed value of W?

"Cramming" is a technique often used by students to prepare for exams,in which they study for extended hours only a few days before the exams.Often students drink caffeinated beverages to help them stay awake while cramming for exams.Five students were randomly selected and asked to drink highly caffeinated beverages before their first midterm exam and then drink only water before their second midterm exam in the same subject.The difference of the scores (midterm 2 - midterm 1)is shown below for the five students. What is the mean of the Wilcoxon signed rank test statistic,W⁺,under the null hypothesis that there is no difference?

The rank sum statistic,W,is approximately _______ as long as the sample size of both SRSs is large.

At what age do babies learn to crawl? Does it take longer to learn in the winter when babies are often bundled in clothes that restrict their movement? Data were collected from parents who brought their babies into the University of Denver Infant Study Center to participate in one of a number of experiments between 1988 and 1991.Parents reported the birth month and the age at which their child was first able to creep or crawl a distance of 4 feet within 1 minute.The resulting data were grouped by month of birth: January,May,and September. The data are to be analyzed with the Kruskal-Wallis test.Under the null hypothesis,what is the approximate distribution of H?

"Cramming" is a technique often used by students to prepare for exams,in which they study for extended hours only a few days before the exams.Often students drink caffeinated beverages to help them stay awake while cramming for exams.Five students were randomly selected and asked to drink highly caffeinated beverages before their first midterm exam and then drink only water before their second midterm exam in the same subject.The difference of the scores (midterm 2 - midterm 1)is shown below for the five students. Using the normal approximation with the continuity correction,compute the P-value used to test the null hypothesis of no difference against the alternative hypothesis that midterm 2 scores are systematically higher than midterm 1 scores using the Wilcoxon signed rank test statistic.Using a significance level of .05,is there evidence against the null hypothesis of no systematic difference in the scores?

Does income increase when you get married? To investigate this,a college student has randomly selected people from his college town and collected income data for these people.They were categorized according to their marital status.The following results (in thousands of dollars)were obtained. The data are to be analyzed using the Wilcoxon rank sum test.Let W be the Wilcoxon rank sum test statistic equal to the sum of the ranks assigned to the married group.What is the value of z,the standardized value of W?

At what age do babies learn to crawl? Does it take longer to learn in the winter when babies are often bundled in clothes that restrict their movement? Data were collected from parents who brought their babies into the University of Denver Infant Study Center to participate in one of a number of experiments between 1988 and 1991.Parents reported the birth month and the age at which their child was first able to creep or crawl a distance of 4 feet within 1 minute.The resulting data were grouped by month of birth: January,May,and September. The data are to be analyzed with the Kruskal-Wallis test.Under the null hypothesis,compute the approximate distribution of H.At the 5% significance level,would we reject the null hypothesis?