CH 16 SB Jackson

The Spearman's Coefficient of Rank Correlation can range from:

-1.00 to 1.00

Which the of the following statements correctly describe steps of the Wilcoxon signed-rank test?

-Sum the ranks for the negative differences and the positive differences, separately. -Place absolute differences between pairs in rank order. -The smaller sum is the T value.

Which one of the following is the correct set of hypotheses for a one-tailed test of Spearman's coefficient of rank correlation?

H0: The rank correlation is 0. H1: There is a positive association among the ranks.

Which one of the following is the correct set of hypotheses for a two-tailed test of Spearman's coefficient of rank correlation?

H0: The rank correlation is 0. H1: There is an association among the ranks.

A market researcher has 22 persons try two different types of chips. He thinks they will prefer Brand B. What are the appropriate hypotheses for a sign test of this idea?

H0: π ≤ 0.5 H1: π > 0.5

Which of the following are valid hypotheses with a sign test for the median?

Ho: Median = 25 H1: Median ≠ -25 Ho: Median ≤ 25

Which of the following are valid hypotheses with a sign test for the median?

Ho: Median ≥ 110 Ho: Median = - 110

Which of the following assumptions are required for ANOVA but not for the Kruskal-Wallis analysis of variance by ranks?

Interval or Ratio level data Normal population distributions Equal population variances

What kind of data can be used with distribution free tests?

Interval scale data. Ordinal scale data. Ratio scale data.

If a pair of observations that is being used for a sign test are assigned a difference of 0, how is this treated in counting the pluses and minuses?

It is not counted.

Which one of the following tests uses a chi-square distribution for the test statistic?

Kruskal-Wallis test.

What is the shape of the distribution of H, the Kruskal-Wallis statistic for one-way analysis of variance by ranks?

Nearly chi-square for df = k - 1

Hypothesis tests designed for nonparametric data require that the data follow:

No particular distribution.

Which kind of data cannot be used with distribution-free tests?

Nominal scale data.

In doing a Wilcoxon signed-rank test, we find a T of 15. The cutoff value from the table is 17. What is your conclusion?

Reject the null hypothesis, the pairs are from different populations.

The median is often used as the measure of central tendency when the population distribution is skewed. How can you conduct a hypothesis test about the value of the median?

Tests of the median require non-parametric tests, such as the sign test.

What is the name of a non-parametric test used to see if two independent samples came from equivalent populations?

The Wilcoxon Rank-Sum test.

Which of the following are needed to calculate Spearman's Coefficient of Rank Correlation?

The difference between pair ranks. The sample size.

In a sign test, what happens if two paired observations are the same (that is, they have no difference)?

The difference is 0, and the observations are dropped from the sample.

Which statement best describes the ranking of sample data for the Wilcoxon rank-sum test?

The observations from both samples are ranked as if from a single group.

Spearman's correlation coefficient measures the relationship between two interval or ratio level variables. What is the purpose of Spearman's rank-order correlation?

To describe the relationship between sets or ranked data.

Suppose you are conducting a two-tailed Wilcoxon signed-rank test with n=25 and α=0.05. What is the decision rule?

We reject H0 if T ≤ 89.

Which of the following are condition for which Spearman's Coefficient of Rank Correlation is preferred is better suited than Pearson's Coefficient of Correlation?

When the relationship is not linear. When the data is ordinal scale.

Under what conditions can the standard normal distribution be used as the test statistic for the Wilcoxon rank-sum test?

When there are at least 8 observations in each of the two samples.

In calculating the test statistic for the Wilcoxon rank-sum test, W is the sum of ranks for the first sample. How do you decide which sample represents the first population?

You may choose either one, the value of z will be the same.

Suppose you are conducting a sign test (upper tail) with n=13 and no 0 differences. What would be the cutoff level for rejecting the null with α=0.10?

10

What is a "distribution-free" test?

A hypothesis test that does not need to assume anything about the shape of the population distribution.

Which of the following statements explain how the sign test is used to test the population median?

A sample value less than the median is given a minus sign. The null hypothesis is that the median is equal to some chosen value.

Which of the following is an accurate description of the Wilcoxon signed rank test?

A test based on the differences in dependent samples, where the normality assumption is not required.

When ranking sample observations for the Wilcoxon rank-sum test, how do you handle ties?

Average the ranks involved and assign the average rank to both observations.

The sign test has only two outcomes, they are independent, and the probabilities for each trial are the same. What distribution do these attributes describe?

Binomial.

The Wilcoxon signed-rank test can be used as a non-parametric replacement for the paired t-test to overcome which of the following issues?

The population of difference is not normal. The data is ordinal.

How are the samples ranked to compute the Kruskal-Wallis statistic?

The samples are combined and ranked from low to high.

For Kruskal-Wallis one way analysis of variance by ranks, what is the primary requirement for the samples?

The samples must be independent.

Which of the following are true regarding requirements about the samples used for the Kruskal-Wallis test?

The samples must be independent. It can be used for two or more samples.

What information is the basis of a sign test?

The sign of a difference between two related observations.

You have learned about many tests for the population mean or proportion, but what can you do to test the median?

The sign test is one of the few tests that can be used to test the median.

Why is it appropriate to use a binomial distribution to calculate the p-value for a sign test?

The sign test meets all the binomial assumptions.

Which of the following are need to calculate the Kruskal-Wallis test statistic, H?

The size of each sample. The sum of the ranks for each sample.

Which of the following is true about Spearman's Coefficient of Rank Correlation?

The smaller the absolute value is the weaker the correlation. The larger the absolute value is the stronger the correlation.

In doing a sign test, assume the significance level is set to α = 0.05. What number of success should we select from the binomial distribution to arrive at the decision rule for an upper tail test?

The smallest number of success, x, such that the probability of having at least x successes is less than 0.05.

Which statement describes the distribution of the test statistic for the Wilcoxon rank-sum test when each sample contains more than 7 observations?

The standard normal distribution.

The Wilcoxon rank-sum test is a non-parametric test to see whether two independent samples came from equivalent populations. Which of these parametric tests does it replace?

The test of two means. (t-test)

Which of the following t-test requirements does the Wilcoxon rank-sum test eliminate?

The two populations have equal variances. The two populations have normal distributions.