Exam 19: Nonparametric Statistics

The Spearman rank correlation coefficient is equal to the ____________________ correlation coefficient of the ranks of the data.

The z-test approximation to the Wilcoxon rank sum test for two independent samples requires that both sample sizes are larger than 10.

The Kruskal-Wallis test is an extension of the Wilcoxon rank-sum test from two to more than two statistical populations.

A two-sample t-test is the parametric counterpart of the Wilcoxon signed rank sum test for matched pairs.

Frozen TV Dinner The general manager of a frozen TV dinner maker must decide which one of four new dinners to introduce to the market.He decides to perform an experiment to help make a decision.Each dinner is sampled by ten people who then rate the product on a 7-point scale,where 1 = poor,and 7 = excellent.The results are shown below. Tasts Ratings Respondent Dinner 1 Dinner 2 Dinner 3 Dinner 4 1 6 6 4 5 2 5 5 2 4 3 7 7 3 4 4 6 6 5 4 5 7 6 4 3 6 7 5 3 5 7 6 4 3 4 8 5 6 4 6 9 4 4 3 5 10 7 5 6 4 -{Frozen TV Dinner Narrative} Using the appropriate statistical table,what statement can be made about the p-value for this test?

To apply the Wilcoxon rank sum test to determine whether the location of population 1 is different from the location of population 2,the samples must be independent.

The Kruskal-Wallis test is always:

For sample sizes greater than or equal to 5,the test statistic H has an approximate ____________________ distribution.

The Friedman test statistic is approximately chi-squared distributed with (k - 1)degrees of freedom,provided that both the number of blocks b and the number of treatments k are greater than or equal to 5.

Customers' Ages The marketing manager of a Hot Dog Stand chain is in the process of examining some of the demographic characteristics of her customers.In particular,she would like to investigate the belief that the ages of the customers of hot dogs,fast-food hamburger,and fast-food chicken restaurants are different.To test this belief,the ages of eight randomly selected customers from each restaurant type were recorded and listed below.From previous analysis we know that the ages are not normally distributed. Customers' Agas Hot Dogs Hamburger Chicken 23 26 25 19 20 28 25 18 36 17 35 23 36 33 39 25 25 27 28 19 38 31 17 31 -{Customers' Ages Narrative} Using the appropriate statistical table,what statement can be made about the p-value for this test?

The nonparametric counterpart of the parametric t-test of $\mu$ _D for matched pairs is the:

In the case of comparing two population locations,the Friedman test can only determine whether a difference exists.To determine which population,for example,has a higher location requires the use of the ____________________ test.

Nonparametric methods are designed to test ____________________ data.

When n is greater than or equal to 10,the sign test statistic has an approximate ____________________ distribution.

In a normal approximation to the Wilcoxon rank sum test,the standardized test statistic is calculated as z = 1.96.For a two-tail test,the p-value of the test is 0.025.

Customers' Ages The marketing manager of a Hot Dog Stand chain is in the process of examining some of the demographic characteristics of her customers.In particular,she would like to investigate the belief that the ages of the customers of hot dogs,fast-food hamburger,and fast-food chicken restaurants are different.To test this belief,the ages of eight randomly selected customers from each restaurant type were recorded and listed below.From previous analysis we know that the ages are not normally distributed. Customers' Agas Hot Dogs Hamburger Chicken 23 26 25 19 20 28 25 18 36 17 35 23 36 33 39 25 25 27 28 19 38 31 17 31 -The data below are drawn from four independent populations: Sampla 1 2 3 4 13 15 18 9 9 10 15 10 16 15 17 6 12 14 18 6 15 13 8 Test at the 1% significance level to determine whether the population locations differ.

The data for analysis by a Kruskal-Wallis test are either ordinal or interval,but they do not have a(n)____________________ distribution.

Keyboard Speed Ten administration assistants were selected at random from a large university.The keyboard speed (number of words per minute)was recorded for each secretary on two different brands of computer keyboards.Assume that the typing speeds are not normally distributed.The following results were obtained. Computar Kayboard Sacretary Brand A Brand B Barry 72 74 Betty 80 86 Caral 68 72 Cliff 74 70 Ellen 86 85 Fred 75 73 Gwen 78 72 Harry 69 65 Ingrid 76 79 Jerome 65 64 -{Keyboard Speed Narrative} Perform the Wilcoxon signed rank sum test at the 5% significance level.

A nonparametric test for comparing two or more populations should be used instead of its parametric counterpart if:

When the Friedman test is used to test for a difference between two populations,it will produce the same outcome as the ____________________ test.