Exam 15: Nonparametric Tests

"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 standard deviation of,W⁺,the Wilcoxon signed rank test statistic?

"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 continuity correction,what is the probability that needs to be calculated in order to obtain the P-value used to test the null hypothesis of no difference using the Wilcoxon signed rank test statistic?

The Wilcoxon signed rank test is for use with ________.

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 negative differences,what would be the value of z,the standardized value of 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 The objective of this study is to assess if diet and intense exercise increase triglyceride levels.According to the SPSS output,what is the value of the appropriate P-value for this test?

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 observed value of W?

When ranking the absolute values of the difference of observations from smallest to largest for use with the Wilcoxon signed rank test and there is a tie,it is best to ___________.

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.The null hypothesis is that income has the same distribution for married and unmarried people.What is the appropriate alternative hypothesis?

The distribution of the Wilcoxon rank sum,W,will be closer to a Normal distribution when using the ___________.

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 expected value of W under the null hypothesis that the two distributions are the same?

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 standard deviation of W under the null hypothesis that the two distributions are the same?

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 male group?

When using the Wilcoxon test and assuming the distribution of the population is not Normal,the null hypothesis would be best stated in terms of the ______.

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.What is the observed value of W⁺?

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.Using the Normal approximation,what is the value of the test statistic used in testing the null hypothesis?

The exact distribution of the Wilcoxon rank sum,W,will not change much in the presence of many tied observations.

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 null hypothesis is that triglyceride levels have the same distribution at the beginning and at the end of the study.What is the appropriate alternative hypothesis?