Question 1

Which of the following best explains how to interpret the test statistic for the Wilcoxon signed-ranks T?

Accepted Answer

The Wilcoxon signed-ranks T test is a non-parametric test used to compare two related samples. The test statistic T is calculated based on the ranks of the differences between pairs. A smaller value of T indicates that the observed differences are not likely to occur by chance, leading to the rejection of the null hypothesis. This is because a small T value suggests a systematic difference between the paired samples, rather than random variation.

Question 2

A researcher computes the Wilcoxon signed-ranks T test.She computes T = 68 using a sample of 24 participants.What is the decision for a two-tailed test at a .05 level of significance?

Accepted Answer

To determine the decision for a two-tailed test using the Wilcoxon signed-ranks T test, we need to compare the calculated T value with the critical values from a table. For a sample size of 24 and a significance level of .05, the critical values are ± 55. Using a two-tailed test, if the calculated T value falls outside of this range, we reject the null hypothesis. Since T = 68 is greater than the critical value of 55, we reject the null hypothesis and conclude that there is a significant difference between the two related groups. Therefore, the answer is B.

Question 3

Tests for ordinal data can ________ the power to detect an effect when data are skewed.

Accepted Answer

B

Question 4

The Wilcoxon signed-ranks T test is used as a nonparametric alternative to which parametric test?

Accepted Answer

The Wilcoxon signed-ranks T test is used as a nonparametric alternative to the related samples t-test, which compares the means of two related groups. Therefore, the best choice is C, related samples t-test. Option A, one-sample t-test, compares the sample mean to a known or hypothesized population mean, and option B, two-independent sample t-test, compares the means of two independent groups. Option D is incorrect because it includes option A, which is not parametrically related to the Wilcoxon signed-ranks T test.

Question 5

A researcher computes a one-sample sign test in which the number of pluses is 8,the number of minuses is 2,and the number of scores equal to the median is 1.The test statistic (x)for the sign test is equal to

Accepted Answer

The test statistic for a one-sample sign test is the smaller of the number of pluses or minuses. In this case, the number of pluses is 8 and the number of minuses is 2, so the test statistic is 2.

Question 6

Which of the following best explains how to find the test statistic for the one-sample sign test?

Accepted Answer

In the one-sample sign test,scores above the median are assigned a plus sign (+);scores below the median are assigned a negative sign (-);the test statistic is the number of pluses or minuses,whichever occurs most often.

Question 7

A researcher finds that the number of scores above the median is 11 and the number of scores below the median is 5 using a sample of 16 participants.Based on these data,what is the decision for a one-sample sign test at a .05 level of significance?

Accepted Answer

The answer of A researcher finds that the number of...

Question 8

The test statistic (x)for the sign test is equal to

Accepted Answer

The sign test is a non-parametric test used to evaluate the median of a continuous distribution. The test statistic for the sign test is determined by counting the number of positive differences (pluses) or negative differences (minuses) between paired observations, and using the count that occurs most often. This makes choice B the correct answer.

Question 9

Tests for ordinal data meaningfully convey information regarding ________.

Accepted Answer

Tests for ordinal data can meaningfully convey information regarding differences, but they do not provide information about variance because the data does not have a numerical value that can be measured for variation. Therefore, choice B is the correct answer.

Question 10

Tests for ordinal data

Accepted Answer

Ordinal data are nonparametric in nature, which means that nonparametric tests are better suited for analyzing such data. These tests do not measure variance to test for significance, and this makes them more robust to the presence of outliers. Hence, option D is the best choice.

Question 11

Which of the following gives the best explanation for why it would be advantageous to convert the following scores to ordinal data?

Accepted Answer

The answer of Which of the following gives the best...

Question 12

A researcher computes a related samples sign test in which the number of positive ranks is 9 and the number of negative ranks is 3.The test statistic (x)is equal to

Accepted Answer

The answer of A researcher computes a related samples sign...

Question 13

A researcher computes the Wilcoxon signed-ranks T test.She finds that the sum of positive ranks is 56 and the sum of negative ranks is 22.What is the value of the test statistic,T?

Accepted Answer

The test statistic T for the Wilcoxon signed-ranks test is the smaller of the sum of positive ranks and the sum of negative ranks. In this case, the sum of negative ranks is 22, which is smaller than the sum of positive ranks (56), making 22 the value of T.

Question 14

Which of the following is not a step to average tied ranks?

Accepted Answer

The step "Rank each score by its effect size" is not a step to average tied ranks. The correct steps are: 
A) Compute the mean of the tied ranks. 
B) Assume the ranks are in order. 
D) Shift the remaining ranks accordingly.

Question 15

Each of the following is an appropriate test for ordinal data,except

Accepted Answer

The chi-square goodness-of-fit test is not appropriate for ordinal data because it is designed to test frequencies of categorical data against expected frequencies, not to analyze the ranks or order of data. The other tests listed are suitable for analyzing ordinal data, which involves rankings or order without assuming a specific distribution.

Question 16

For the Wilcoxon signed-ranks T,when T is less than the critical value,we decide to

Accepted Answer

When T is less than the critical value in a Wilcoxon signed-ranks test, it indicates that the observed data are significantly different from what would be expected under the null hypothesis, leading to the decision to reject the null hypothesis.

Question 17

Which of the following scales of measurement are analyzed using a nonparametric test?

Accepted Answer

Nonparametric tests are used for analysis of non-numerical or categorical data, which includes nominal and ordinal data.

Question 18

The key advantage of measuring ranked data is that it minimizes ________ caused by outliers.

Accepted Answer

Ranking data assigns a numerical value to each observation based on its position in the ordered list. This reduces the impact of extreme values, also known as outliers. By reducing variability, ranked data can help provide a more accurate representation of the underlying relationships between variables. However, it does not directly affect significance or effect size.

Question 19

The sign test is used as a nonparametric alternative to which parametric test?

Accepted Answer

The sign test is a nonparametric alternative to both the one-sample t-test (choice A) and the related samples t-test (choice C). It is not an alternative to the two-independent sample t-test (choice B), which compares the means of two independent samples and assumes normality and equal variances. Instead, the Wilcoxon rank-sum test is a nonparametric alternative to the two-independent sample t-test.

Question 20

A researcher finds that the number of positive ranks is 13 and the number of negative ranks is 4 using a sample of 17 participants.Based on these data,what is the decision for a related samples sign test at a .05 level of significance?

Accepted Answer

To conduct a related samples sign test, we test the null hypothesis that the median of the differences between the two related samples is zero. We count the number of positive and negative differences and use the binomial distribution to calculate the probability of getting the observed number of positive and negative ranks (or a more extreme result) if the null hypothesis is true. In this case, we have 13 positive ranks and 4 negative ranks, which gives a two-tailed p-value of 0.021. Since this p-value is less than .05, we reject the null hypothesis and conclude that there is evidence that the median of the differences is not zero.

Quiz 18: Nonparametric Tests: Tests for Ordinal Data