Question

Determine whether or not the following variable is a rank and give the units

Student ratings of a course on a 5-point Likert scale

A. The ratings are ranks and the units are Likerts

B. The ratings are not ranks and have no units

C. The ratings are not ranks and the units are Likerts

D. The ratings are ranks and have no units

For which one of the following situtations would a Kruskal-Wallace test be appropriate?

A. Testing whether the distributions of the ratings of a new distance learning course were the same as rated (on the usual 5-point Likert scale) by Freshmen, Sophomores, Juniors, and Seniors who had taken the course

B. Judging whether the height of the water at high tide at a marina increases more or less consistently as the phase of the moon changes from new to full.

C. Estimating the association between the value of homes and their age in a community known To have a number of very expensive mansions

D. Comparing the sweetness of a diet drink (rated from 1 to 10) as judged by a panel of teenage tasters and a panel of adult tasters

E. Comparing the ratings of a new product on a 5-point Likert scale by a panel of consumers to their ratings of a competitor’s product on the same scale

Determine whether or not the following variable is a rank and give the units

The change in your pocket by year minted

A. The mint dates are ranks and have no units

B. The mint dates are ranks and the units are years

C. The mint dates are not ranks and the units are years

D. The mint dates are not ranks and have no units

For which one of the following situations would a Wilcoxon Rank-Sum (or Mann-Whitney) test be appropriate?

A. During its initial release, is there an association between the number of downloads of a new smartphone game and the number of hours since it has been released?

B. Each member of a group of professional chef rates the quality of a basket of organic vegetables on a 5-point scale. The same chefs then rate the quality of a basket of non-organic vegetables on the same scale. Are the organic veggies rated higher?

C. The Richter scale measures the damage potential of earthquakes. Some scientists think it is best used for judging the relative size of earthquakes and not their absolute size. Are earthquakes around the Pacific “ring of fire” rim stronger in general than those found in the Atlantic? Compare earthquakes over a recent 5-year period.

D. The Mohs scale rates the hardness of minerals. If one mineral can scratch another, it is judged to be harder. ( Diamond, the hardest mineral, is a 10.) Is hardness related to the weight of a 1x1x1 cm cube of the material

E. A dog’s intelligence can be judged roughly by how many times a new command must be repeated until it is learned. A researcher trained several dogs of each of 4 different breeds, teaching them 3 new commands. Are the breeds equally “intelligent”?

For which one of the following situations would a Kruskall- Wallace test be appropriate?

A. Estimating the association between the value of homes and their age in a community known to have a number of very expensive mansions

B. Comparing the ratings of a new product on a 5-point Likert scale by a panel of consumers to their ratings of a competitor’s product on the same scale

C. Comparing the sweetness of a diet drink (rated from 1-10) as judged by a panel of teenage tasters and a panel of adult tasters

D. Testing whether the distributions of the ratings of a new distance learning course were the same as rated (on the usual 5-point Likert scale) by Freshmen, Sophomores, Juniors, and Seniors who had taken the course.

E. Judging whether the height of the water at high tide at a marina increases more or less consistently as the phase of the moon changes from new to full.

For which one of the following situations would a Kruskal- Wallace test be appropriate?

A. The Mohs scale rates the hardness of minerals. If one mineral can scratch another, it is judged to be harder. ( Diamond, the hardest mineral, is a 10.) Is hardness related to the weight of a 1x1x1 cm cube of the mineral

B. The Richter scale measures the damage potential of earthquakes. Some scientists think it is best used for judging the relative size of earthquakes and not their absolute size. Are earthquakes around the Pacific “ring of fire” rim stronger in general than those found in the Atlantic? Compare earthquakes over a recent 5-year period

C. Each member of a group of professional chef rates the quality of a basket of organic vegetables on a 5-point scale. The same chefs then rate the quality of a basket of non-organic vegetables on the same scale. Are the organic veggies rated higher?

D. A dog’s intelligence can be judged roughly by how many times a new command must be repeated until it is learned. A researcher trained several dogs of each of 4 different breeds, teaching them 3 new commands. Are the breeds equally “intelligent”?

E. During its initial release, is there an association between the number of downloads of a new smartphone game and the number of hours since it has been released?

Answer 1

I)  The Kruskal-Wallis test is a nonparametric (distribution free) test, and is used when the assumptions of one-way ANOVA are not met.The Kruskal-Wallis test can be used for both continuous and ordinal-level dependent variables. Therefore,

A. Testing whether the distributions of the ratings of a new distance learning course were the same as rated (on the usual 5-point Likert scale) by Freshmen, Sophomores, Juniors, and Seniors who had taken the course Ans:  Kruskal-Wallace test is appropriate

B. Judging whether the height of the water at high tide at a marina increases more or less consistently as the phase of the moon changes from new to full. Ans:  Kruskal-Wallace test is appropriate

C. Estimating the association between the value of homes and their age in a community known To have a number of very expensive mansions Ans:  Kruskal-Wallace test is not appropriate

D. Comparing the sweetness of a diet drink (rated from 1 to 10) as judged by a panel of teenage tasters and a panel of adult tasters Ans:  Kruskal-Wallace test is appropriate

E. Comparing the ratings of a new product on a 5-point Likert scale by a panel of consumers to their ratings of a competitor’s product on the same scale Ans:  Kruskal-Wallace test is appropriate

II) Wilcoxon Rank-Sum (or Mann-Whitney) test is a nonparametric test of the null hypothesis that it is equally likely that a randomly selected value from one sample will be less than or greater than a randomly selected value from a second sample.

A. During its initial release, is there an association between the number of downloads of a new smartphone game and the number of hours since it has been released? Ans: Wilcoxon Rank-Sum (or Mann-Whitney) test is not appropriate

B. Each member of a group of professional chef rates the quality of a basket of organic vegetables on a 5-point scale. The same chefs then rate the quality of a basket of non-organic vegetables on the same scale. Are the organic veggies rated higher? Ans: Wilcoxon Rank-Sum (or Mann-Whitney) test is appropriate

C. The Richter scale measures the damage potential of earthquakes. Some scientists think it is best used for judging the relative size of earthquakes and not their absolute size. Are earthquakes around the Pacific “ring of fire” rim stronger in general than those found in the Atlantic? Compare earthquakes over a recent 5-year period. Ans: Wilcoxon Rank-Sum (or Mann-Whitney) test is appropriate

D. The Mohs scale rates the hardness of minerals. If one mineral can scratch another, it is judged to be harder. ( Diamond, the hardest mineral, is a 10.) Is hardness related to the weight of a 1x1x1 cm cube of the material. Ans: Wilcoxon Rank-Sum (or Mann-Whitney) test is not appropriate

E. A dog’s intelligence can be judged roughly by how many times a new command must be repeated until it is learned. A researcher trained several dogs of each of 4 different breeds, teaching them 3 new commands. Are the breeds equally “intelligent”?  Ans: Wilcoxon Rank-Sum (or Mann-Whitney) test is appropriate

III) The Kruskal-Wallis test is a nonparametric (distribution free) test, and is used when the assumptions of one-way ANOVA are not met.The Kruskal-Wallis test can be used for both continuous and ordinal-level dependent variables. Therefore,

A. Estimating the association between the value of homes and their age in a community known to have a number of very expensive mansions.  Ans:  Kruskal-Wallace test is not appropriate

B. Comparing the ratings of a new product on a 5-point Likert scale by a panel of consumers to their ratings of a competitor’s product on the same scale. Ans:  Kruskal-Wallace test is appropriate

C. Comparing the sweetness of a diet drink (rated from 1-10) as judged by a panel of teenage tasters and a panel of adult tasters. Ans:  Kruskal-Wallace test is appropriate

D. Testing whether the distributions of the ratings of a new distance learning course were the same as rated (on the usual 5-point Likert scale) by Freshmen, Sophomores, Juniors, and Seniors who had taken the course. Ans:  Kruskal-Wallace test is appropriate

E. Judging whether the height of the water at high tide at a marina increases more or less consistently as the phase of the moon changes from new to full.  Ans:  Kruskal-Wallace test is appropriate

IV) The Kruskal-Wallis test is a nonparametric (distribution free) test, and is used when the assumptions of one-way ANOVA are not met.The Kruskal-Wallis test can be used for both continuous and ordinal-level dependent variables. Therefore,

A. The Mohs scale rates the hardness of minerals. If one mineral can scratch another, it is judged to be harder. ( Diamond, the hardest mineral, is a 10.) Is hardness related to the weight of a 1x1x1 cm cube of the mineral.  Ans:  Kruskal-Wallace test is appropriate

B. The Richter scale measures the damage potential of earthquakes. Some scientists think it is best used for judging the relative size of earthquakes and not their absolute size. Are earthquakes around the Pacific “ring of fire” rim stronger in general than those found in the Atlantic? Compare earthquakes over a recent 5-year period.  Ans:  Kruskal-Wallace test is appropriate

C. Each member of a group of professional chef rates the quality of a basket of organic vegetables on a 5-point scale. The same chefs then rate the quality of a basket of non-organic vegetables on the same scale. Are the organic veggies rated higher? Ans:  Kruskal-Wallace test is not appropriate

D. A dog’s intelligence can be judged roughly by how many times a new command must be repeated until it is learned. A researcher trained several dogs of each of 4 different breeds, teaching them 3 new commands. Are the breeds equally “intelligent”? Ans:  Kruskal-Wallace test is appropriate

E. During its initial release, is there an association between the number of downloads of a new smartphone game and the number of hours since it has been released?. Ans:  Kruskal-Wallace test is not appropriate