Exam 17: Nonparametric Statistics

When only ordinal-level data are available, Spearman's rank correlation rather than the Pearson product-moment correlation coefficient must be used to analyze the association between two variables.

A researcher wants to determine whether the means of two independent populations are the same.She has two independent random samples, one from each population, shown in the following table: $\quad$ $\quad$ $\quad$ $\quad$ Sample I $\quad$ $\quad$ $\quad$ $\quad$ $\quad$ $\quad$ $\quad$ Sample II 11.5 15.7 22.8 22.5 12.6 13.8 17.5 10.7 13.5 12.4 25.3 16.1 25.1 14.8 11.8 14.7 10.8 12.7 She uses the Mann-Whitney U test and a significance level of 0.05.This is a ______ test, and the critical ______.

The attention span of kindergarteners are measured in minutes.A teacher wants to see if there are differences in the attention span of kindergarteners at different times of day.Using a sample of five such children, their attention spans are measured at five different times throughout the day.Using the data in the table below and an alpha of 0.05, what is the null hypothesis? 9 am 11am nown 1pm 3pm Child 1 12 5 10 7 8 Child 2 10 6 9 8 12 Child 3 7 10 6 8 13 Child 4 11 8 5 4 10 Child 5 12 4 11 5 8

What is the Spearman rank correlation coefficient for the following set of data? 21 22 35 32 33 18 24 28 22 35

Performance records for 18 salespersons are selected to investigate whether compensation methods are a significant motivational factor. Compensation Method Sales Straight Salary 18 12 22 28 28 Straight Commission 27 34 34 27 20 16 24 Salary plus Commission 11 17 27 14 30 22 A Kruskal-Wallis test is to be performed with $\alpha$ = 0.01.The null hypothesis is _______.

A local pediatrician office is interested in the 'no-show' appointment count for each of the 4 pediatricians.'No-show' appointments represent lost revenues because the physician will be Idle when patients do not show for their scheduled appointments.Using the data in the table Below and an alpha of 0.10, what is the critical value of $\chi$ ²? Physician A Physician B Physician C Physician D week 1 8 4 6 7 week 2 7 3 4 6 week 3 8 2 5 4 week 4 8 6 7 9 week 5 4 2 5 10

A Kruskal-Wallis test is to be performed.There will be four categories, and alpha is chosen to be 0.10.The critical chi-square value is _______.

A researcher wants to study the effects of physical exercise on depression.She randomly selects a group of 24 individuals who are equally depressed.None of these individuals currently exercises.She then randomly assigns them in one of three groups: group 1 stays without exercising (sedentary group), group 2 exercises once a week, and group 3 exercises two times a week.Individuals in groups 2 and 3 meet with a personal trainer so they carry out a very similar exercising program, both in kinds of exercises and in intensity.After two months, the researcher has all individuals take a depression-assessment test.The score of the test goes from 0 = totally miserable to 100 = complete satisfaction. The scores are shown in the following table: Group 1 Group 2 Group 3 25 24 35 15 16 22 20 19 31 17 24 32 23 25 31 21 25 29 19 21 33 18 18 35 The researcher uses a Kruskal-Wallis test and a significance level $\alpha$ = 0.05.The critical chi-square value is ______.

In a Wilcoxon matched-pairs signed rank test with 20 matched-pairs of observations, the observed value of the T statistic based on sample data is 76.33.The corresponding observed z-value is ___________.

Which of the following tests might be used to compare the means of two populations if the samples are related?

Charles Clayton monitors the daily performance of his investment portfolio by recording a "+" or a "-" sign to indicate whether the portfolio's value increased or decreased from the previous day.His record for the last eighteen business days is "- + + - - - + - - + + + + + + + + -".The number of runs in this sample is _________.

A Mann-Whitney U test was performed to determine if there were differences in the cost of tuition at a Texas state university versus an Oklahoma state university.The total cost, including room, board, and books for 24 freshmen attending a Texas university were computed and compared to the total cost for 20 Oklahoma state university students.The U statistic was calculated to be 38.78 based on the sample sizes of 24 and 20.What is the z value for this test?

A researcher wants to determine the efficacy of a training program directed at improving concentration, focus, and memory on college students.She selects a random sample of 16 individuals and has them take an initial assessment test before the training program.Then the individuals complete the training program, and at the end they take a final test that's comparable to the initial test.The results are shown in the following table: Individ. Before After 1 79 81 2 74 73 3 81 82.5 4 75 82.5 5 72.5 85 6 75 90 7 67.5 83.5 8 57.5 72.5 9 62.5 87.5 10 77.5 80 11 61.5 92.5 12 57.5 80 13 61.5 71 14 72.5 84 15 64 78.5 16 71 97.5 The analyst uses a Wilcoxon matched-pairs signed rank test with a 0.05 significance level.The value of $\mu$ _T is ______.

Nonparametric statistics are sometimes called distribution-dependent statistics.

A quality control supervisor wishes to determine whether the following measurements are random: 68.2 65 66.5 65 67.5 68 66 64.5 65.3 64.2 67.6 66.5 66.8 68.9 67 65 65 67 68 71 68.5 63.6 64.7 71.5 70.7 66 68.5 70.5 69.5 70.1 For this purpose, the supervisor uses a previous median of 67.9 and compares each measurement to the median to perform a runs test.She determines the number of runs and finds that the critical values of the Rscore are ______ and ________.

Four types of bicycle tires are ridden in six different cities to see if the tires lasted about the same number of miles.If there are differences, then that tire could promote its durability to potential customers.Using the data in the table below and an alpha of 0.05, what is the observed value of $\chi$ ²? Tire A Tire B Tire C Tire D City 1 105 157 112 119 City 2 142 124 132 144 City 3 133 121 138 130 City 4 98 136 110 119 City 5 114 141 95 128 City 6 117 138 129 140

Performance records for 18 salespersons are selected to investigate whether compensation methods are a significant motivational factor. Compensation Method Sales Straight Salary 18 12 22 28 28 Straight Commission 27 34 34 27 20 16 24 Salary plus Commission 11 17 27 14 30 22 A Kruskal-Wallis test is to be performed with $\alpha$ = 0.01.The critical chi-square value is _______.

The Kruskal-Wallis test is to be used to determine whether there is a significant difference in the satisfaction rating (alpha = 0.05)between three brands of boxed cake mix.Shoppers were asked to rate their satisfaction on various attributes and an aggregate satisfaction score ranging from 1-50 was computed.The following data were obtained: Cake Mix A 19 21 25 22 33 Cake Mix B 30 24 28 31 35 Cake Mix C 39 32 41 42 27 For this test, how many degrees of freedom should be used?

The appropriate test for comparing the means of two populations using ordinal-level data from two independent samples is the Mann-Whitney U test.

The nonparametric alternative to linear regression is the Kruskal-Wallis test.