Exam 16: Nonparametric Tests

Rejection of a hypothesis using a nonparametric test is less convincing than using an equivalent parametric test, since nonparametric tests generally make fewer assumptions.

Rejection of a hypothesis using a nonparametric test is more convincing than using an equivalent parametric test when the data are badly skewed.

The Wilcoxon signed-rank test is an alternative to the one-sample t test for paired observations.

Systolic blood pressure of randomly selected HMO patients was recorded on a particular Wednesday, with the results shown here: Patient Age Group Under 20 20 to 29 30 to 49 50 and Over 105 110 122 139 113 101 114 115 108 112 128 136 114 127 124 124 123 123 125 123 The appropriate hypothesis test to compare the medians is:

Returns on an investor's stock portfolio (n = 19 stocks) are compared for the same stock in each of two consecutive quarters. Since the returns are not normally distributed (normality test p-values were .005 and .126 respectively), a nonparametric test was chosen. The test results are shown below. Spearman Rank Correlation Qtr1 Qtr2 Qtr1 1.000 Qtr2 .577 1.000 19 sample size $\pm .456$ critical value .05 (two-tail) $\pm .575$ critical value .01 (two-tail) Which is the best conclusion?

The Wilcoxon signed-rank test is useful to compare more than two sample medians.

Spearman's rank correlation is named for a British behavioral psychologist who was studying human intelligence.

The Wilcoxon signed-rank test is useful to compare one sample median with a benchmark.

The Wilcoxon signed-rank test is robust to outliers in the data if the population is at least somewhat symmetric.

The Friedman test compares medians when there are two grouping factors (rows, columns).

Spearman's rank correlation coefficient lies within the range 0 to 1.00 inclusive.

Which nonparametric test is used to compare a one-sample median with a benchmark?

The Wilcoxon rank sum test (Mann-Whitney test) can be used even if population variances are unequal.

Nonparametric tests may require special tables for small samples.

Twenty customers are randomly chosen and each is given a sample of Nut Butter ice cream to taste. The customers rank the taste of the ice cream on a 10-point scale. Each is then given a sample of Chewy Gooey ice cream to taste and rank on a 10-point scale. Based on the 20 customers' ratings of each flavor, the research analyst conducting the survey wishes to determine if one flavor is preferred over the other. Which nonparametric test would you use to determine if there is a difference in the ratings?

Which nonparametric test is analogous to a two-factor ANOVA without replication?

Which nonparametric test has no parametric counterpart?

The Kruskal-Wallis test is analogous to the parametric one-factor ANOVA.

The Friedman test is a nonparametric equivalent to two-factor ANOVA without replication.

To compare the cost of three shipping methods, a firm shipped five orders to each of four different destinations over a six-month period. Their total shipping costs are shown below. $\quad$$\quad$$\quad$$\quad$$\quad$$\quad$$\quad$$\quad$$\quad$$\quad$$\quad$$\quad$$\quad$$\text { Destination }$ Shipper Toledo Oshawa Janesville Dallas Speedyship 355 435 422 518 GetItThere 342 441 402 488 WeRTops 361 430 435 528 Which nonparametric test would you use to compare the median shipping costs among destinations and among shippers?