Question 1

Why is it the case that skewed data poses a problem for parametric tests?
A) There mean is larger than the median.
B) The assumption of normality is violated.
C) The data does not represent the population.
D) The assumption of independence is violated.

Accepted Answer

Parametric tests assume normality, meaning that the data follows a bell-shaped curve. Skewed data violates this assumption and can lead to incorrect conclusions.

Question 2

Which of the following is not an assumption of parametric tests?
A) Observations are independent
B) The data are either on an interval or ratio scale
C) Central limit theorem holds
D) The data are skewed positive.

Accepted Answer

Parametric tests assume that the data is normally distributed, but they do not assume that the data is skewed positive.

Question 3

Which of the following characteristics would lead you to choose a non-parametric test over a parametric test?
A) Skewed data
B) Having data that is not normally distributed
C) Data that are ranked
D) All of the above

Accepted Answer

Non-parametric tests do not make any assumptions about the population distribution or variance, and are suitable for data that may not meet the assumptions of parametric tests. Skewed data and non-normality are both characteristics that indicate a lack of normality in data, which would be reasons to use non-parametric tests. Similarly, ranked data may be best suited for non-parametric tests, as these tests are better at handling ordinal or categorical data, especially where the values may not be evenly distributed.

Question 4

Why might a spearman correlation be appropriate for a given dataset?
A) The data are on a ratio scale
B) The sample size is too large
C) The sample is skewed with a small sample size
D) The data are on a nominal scale

Accepted Answer

Spearman correlation is appropriate when the sample is skewed and has a small sample size, as it does not assume a normal distribution and is less sensitive to outliers compared to Pearson correlation.

Question 5

The Perception of Competitiveness Scale (PCS) developed by Carter and Weissbrod (2011) is a likert scale. If you assume that the scale is ordinal and are examining its relation to age or some other ranked data, you should…
A) use a Spearman correlation
B) use a Mann Whitney U test
C) use a Wilcoxon Signed-Rank test
D) use a Pearson correlation

Accepted Answer

Since the PCS is an ordinal scale, the appropriate correlation method to use when examining its relation to age or other ranked data is a Spearman correlation. This method calculates the strength and direction of the relationship between two ranked variables.

Question 6

In a spearman correlation, how do you determine the strength of the correlation coefficient?
A) Negative correlations are weaker than positive correlations
B) Correlations are weaker as they approach 0.
C) The strength of the correlation depends on the sample size. Smaller samples tend to be stronger
D) Correlations become stronger as they approach 0.

Accepted Answer

The magnitude or strength of a correlation coefficient is determined by how close it is to 1 or -1. The closer the coefficient is to 1 or -1, the stronger the correlation. If the coefficient is close to 0, it indicates a weak correlation. Therefore, correlations are weaker as they approach 0.

Question 7

The Mann-Whitney U test makes assumptions about which of the following?
A) The data are quantitative
B) The data are normally distributed and generalize to the population
C) Observations are independent
D) Equal variances in both groups

Accepted Answer

The Mann-Whitney U test assumes that the observations are independent. It does not assume that the data are quantitative, normally distributed or that there are equal variances in both groups.

Question 8

In which of the following situations should a Wilcoxon signed-rank test be used?
A) When matched data is normally distributed and ranked
B) When observations are non-independent and the data are skewed
C) When you wanted to use an independent samples t-test but the data ends up being heavily skewed.
D) When the sample size is very large and on a ratio scale.

Accepted Answer

The answer of In which of the following situations should...

Question 9

Why is it a problem if data are skewed when considering parametric tests?
A) The assumption of independence is violated
B) The data is qualitative
C) The assumption of normality is violated.
D) There is no method to calculate estimates of population parameters

Accepted Answer

Parametric tests assume normality of the data. Skewed data violates this assumption and can result in misleading conclusions if parametric tests are still applied. Therefore, skewed data may require non-parametric tests instead.

Question 10

After conducting a Mann-Whitney U test, how do you determine statistical significance?
A) If the U-statistic is smaller than the critical value, the result is non-significant.
B) If your calculated U-value is smaller the critical value, than the result is statistically significant.
C) If the U-value is smaller than median rank, the result is statistically significant
D) If the U-value is greater than the median rank, the result is statistically significant.

Accepted Answer

In a Mann-Whitney U test, the calculated U-value is compared with the critical value obtained from the table. If the calculated U-value is smaller than the critical value, then the result is statistically significant. Therefore, option B is the correct answer.

Question 11

How is a Mann-Whitney U test and a Wilcoxon Signed-Rank test different?
A) the Mann Whitney U test is used on matched data and the Wilcoxon Signed-Rank test is not.
B) The Mann-Whitney U test is a parametric procedure, and the Wilcoxon Signed-Rank test is a nonparametric procedure.
C) The Mann-Whitney U test is used on 3 or more groups, and the Wilcoxon Signed-Rank test is used to test for relationships
D) The Mann-Whitney U test is used for two independent groups and the Wilcoxon Signed-Rank test is used for paired or matched data.

Accepted Answer

The Mann-Whitney U test is used for two independent groups, while the Wilcoxon Signed-Rank test is used for paired or matched data. The other options (A, B, and C) are incorrect.

Question 12

If you have 12 pairs of participants what is your critical value for a two-tailed Wilcoxon Signed-rank test at $\alpha$ = .01?
A) 7
B) 3
C) 5
D) 9

Accepted Answer

The critical value for a two-tailed Wilcoxon Signed-rank test with 12 pairs of participants at $\alpha$ = .01 is 7.

Question 13

A researcher has 16 matched pairs for a Wilcoxon Signed-Rank test. For this two-tailed Wilcoxon Signed-Rank test to be significant at $\alpha$ = .05, the test statistic must be…
A) greater than 30
B) less than 30
C) greater than 25
D) less than 25

Accepted Answer

For a two-tailed Wilcoxon Signed-Rank test with 16 matched pairs and a significance level of .05, the critical value must be looked up in a table specific to the Wilcoxon Signed-Rank test. Typically, for n=16, the critical value for a two-tailed test at the .05 level is around 25 or 26. Therefore, for the test to be significant, the test statistic must be less than this critical value, making the correct answer "less than 30," as it is a more conservative (higher) threshold than the actual critical value, ensuring significance if the test statistic is below it.

Question 14

A researcher has two independent groups with ranked data with 20 participants in each group. When using a Mann-Whitney U test (assume assuming α = 0.05), the researcher has data that is statistically significant if…
A) the U statistic is less than 127
B) the U statistic is greater than 127
C) the U statistic is less than 113
D) The U statistic is greater than 113

Accepted Answer

The critical value for a Mann-Whitney U test with 20 participants in each group and α = 0.05 is 127. Therefore, the researcher has data that is statistically significant if the U statistic is less than 127.

Question 15

Consider the following dataset on standardized test scores: 134, 145, 142, 145, 146, 152, 155, 155, 159. There are _______ ties and the score 152 is in the _____ rank.
A) 2; 6
B) 3; 6
C) 2; 5.5
D) 3; 5.5

Accepted Answer

There are 2 ties in the dataset (145 and 155 each appear twice). The score 152 is ranked 6th when the data is ordered from lowest to highest.

Question 16

A researcher conducted a correlational study. He studied the relationship between individuals' perceptions of their own bodies on a rating scale (higher scores meant most positive self-perception) and their perception of the college (higher scores meant more positive perception of the college). He found a spearman correlation of -.68 and the result is statistically significant. What does this mean?
A) Body image and college ratings are positively correlated: those who have better self-perception of their body had worse perceptions of the college.
B) Body image and college ratings are positively correlated: those who have better self-perception of their body had better perceptions of the college
C) Body image and college ratings are negatively correlated: as self-perception of one's body got higher, perception of the college got lower.
D) Body image and college ratings are negatively correlated: as self-perception of one's body got higher, perception of the college got higher.

Accepted Answer

The negative Spearman correlation coefficient of -.68 indicates a negative relationship between the two variables. As self-perception of one's body got higher (more positive), perception of the college got lower (less positive). Therefore, option C, "Body image and college ratings are negatively correlated: as self-perception of one's body got higher, perception of the college got lower" is the best choice.

Question 17

Consider the following data: 6, 8, 10, 10, 10, 11, 12, 15, 18, 18, 19, 20, 24, 25. The data in rank 4 is ___ and rank 11 is ____.
A) 10; 19
B) 12; 19
C) 10; 20
D) 12; 20

Accepted Answer

The data in rank 4 is 10 (since 10 is the fourth number when the data is arranged in ascending order), and the data in rank 11 is 19 (since 19 is the eleventh number in the ordered list).

Question 18

If you have quantitative data that is skewed, which of the following can be used to "unskew" it?
A) rank the data
B) use the mode
C) use the median
D) convert it to a ratio or interval scale.

Accepted Answer

Ranking the data can help "unskew" it by organizing the data points according to their value, which can make the distribution more symmetrical or easier to analyze, especially when using non-parametric statistical methods.

Question 19

If using a two-tailed spearman correlation with 10 pairs and an alpha level of .05, what is the critical value?
A) .745
B) .700
C) .564
D) .648

Accepted Answer

To find the critical value for a two-tailed Spearman correlation with 10 pairs and an alpha level of .05, we first need to look up the appropriate table. Using a table of critical values for the Spearman correlation coefficient, we can find that the critical value for 10 pairs at an alpha level of .05 is .648. Therefore, the answer is D.

Question 20

A statistical method to measure hidden or latent variables from observed data is…
A) spearman correlation
B) factor analysis
C) eugenics
D) Wilcoxon sign-ranked test

Accepted Answer

Factor analysis is a statistical method used to identify hidden or latent variables from observed data. It helps in discovering the structure, patterns, and relationships amongst observed variables. Spearman correlation measures the strength of association between two variables. Eugenics is a discredited pseudoscience that advocates for selective breeding to improve the human gene pool. Wilcoxon sign-ranked test is a non-parametric statistical hypothesis test used to compare two paired samples.

Quiz 15: Non-Parametric Tests

Why is it the case that skewed data poses a problem for parametric tests?

Which of the following is not an assumption of parametric tests?

Which of the following characteristics would lead you to choose a non-parametric test over a parametric test?

Why might a spearman correlation be appropriate for a given dataset?

The Perception of Competitiveness Scale (PCS) developed by Carter and Weissbrod (2011) is a likert scale. If you assume that the scale is ordinal and are examining its relation to age or some other ranked data, you should…

In a spearman correlation, how do you determine the strength of the correlation coefficient?

The Mann-Whitney U test makes assumptions about which of the following?

In which of the following situations should a Wilcoxon signed-rank test be used?

Why is it a problem if data are skewed when considering parametric tests?

After conducting a Mann-Whitney U test, how do you determine statistical significance?

How is a Mann-Whitney U test and a Wilcoxon Signed-Rank test different?

If you have 12 pairs of participants what is your critical value for a two-tailed Wilcoxon Signed-rank test at $\alpha$ = .01?

A researcher has 16 matched pairs for a Wilcoxon Signed-Rank test. For this two-tailed Wilcoxon Signed-Rank test to be significant at $\alpha$ = .05, the test statistic must be…

A researcher has two independent groups with ranked data with 20 participants in each group. When using a Mann-Whitney U test (assume assuming α = 0.05) , the researcher has data that is statistically significant if…

Consider the following dataset on standardized test scores: 134, 145, 142, 145, 146, 152, 155, 155, 159. There are ___ ties and the score 152 is in the _ rank.

Consider the following data: 6, 8, 10, 10, 10, 11, 12, 15, 18, 18, 19, 20, 24, 25. The data in rank 4 is _ and rank 11 is __.

If you have quantitative data that is skewed, which of the following can be used to "unskew" it?

If using a two-tailed spearman correlation with 10 pairs and an alpha level of .05, what is the critical value?

A statistical method to measure hidden or latent variables from observed data is…