Advanced Statistics

What is an advantage of using Nonparametric Statistics?

• a. It can handle data that is not normally distributed.
• b. It requires a smaller sample size than Parametric Statistics.
• c. It can be used to test hypotheses about population parameters.
• d. It is less time-consuming than Parametric Statistics.

A researcher is interested in assessing the relationship between two variables, X and Y, in a population. The researcher selects a random sample of 100 individuals and measures X and Y for each person. Which of the following is a reason why the researcher might choose to use Kendall's Tau correlation coefficient instead of Spearman's rank correlation coefficient?

• a. Kendall's Tau is more appropriate when the data are continuous.
• b. Kendall's Tau is more appropriate when the sample size is small.
• c. Kendall's Tau is more appropriate when the data are highly skewed.
• d. Kendall's Tau is more appropriate when the data are ranked on an ordinal scale.

A researcher is interested in comparing the median scores of two groups of students, Group A and Group B, on a standardized test. After conducting the Mann-Whitney U test, the researcher obtains a test statistic of U = 55 and a critical value of U_crit = 70. What is the researcher's decision regarding the null hypothesis?

• a. Reject the null hypothesis because U < U_crit
• b. Fail to reject the null hypothesis because U > U_crit
• c. Fail to reject the null hypothesis because U < U_crit
• d. Reject the null hypothesis because U > U_crit

A researcher is interested in determining the relationship between the age of employees and their job performance ratings. After conducting Spearman's Rank Correlation Coefficient test, the researcher obtains a correlation coefficient of 0.75 and a critical value of 0.632. What is the researcher's decision regarding the null hypothesis?

• a. Reject the null hypothesis because the correlation coefficient is greater than the critical value.
• b. Fail to reject the null hypothesis because the correlation coefficient is greater than the critical value.
• c. Reject the null hypothesis because the correlation coefficient is less than the critical value.
• d. Fail to reject the null hypothesis because the correlation coefficient is less than the critical value.

A researcher is interested in determining the relationship between two variables using Kendall's Tau correlation coefficient. The researcher obtains a correlation coefficient of -0.4. Which of the following conclusions can the researcher draw from this result?

• a. There is a strong positive correlation between the two variables.
• b. There is a moderate negative correlation between the two variables.
• c. There is a weak negative correlation between the two variables.
• d. There is no correlation between the two variables.

A researcher is examining the relationship between two variables, X and Y, using Kendall's Tau correlation coefficient. The researcher obtains a correlation coefficient of 0.7. Which of the following conclusions can the researcher draw from this result?

• a. Variable X causes variable Y.
• b. There is a strong positive correlation between X and Y.
• c. There is a weak positive correlation between X and Y.
• d. There is no relationship between X and Y.

A researcher wants to determine if there is a significant difference in the time taken to complete a task using three different software programs: Program A, Program B, and Program C. After conducting the Friedman test, the researcher obtains a test statistic of 9.5 and a critical value of 6.25. What is the researcher's decision regarding the null hypothesis?

• a. Reject the null hypothesis because the test statistic is greater than the critical value.
• b. Fail to reject the null hypothesis because the test statistic is greater than the critical value.
• c. Reject the null hypothesis because the test statistic is less than the critical value.
• d. Fail to reject the null hypothesis because the test statistic is less than the critical value.

A researcher is interested in determining if there is a significant difference in the median salaries of employees across three different departments in a company: Sales, Marketing, and HR. After conducting the Kruskal-Wallis test, the researcher obtains a test statistic of H = 7.8 and a critical value of H_crit = 5.99. What is the researcher's decision regarding the null hypothesis?

• a. Reject the null hypothesis because H > H_crit
• b. Fail to reject the null hypothesis because H > H_crit
• c. Reject the null hypothesis because H < H_crit
• d. Fail to reject the null hypothesis because H < H_crit.

A study is conducted to compare the effectiveness of two different treatments on reducing pain levels in patients. A Wilcoxon signed-rank test is conducted with a significance level of 0.01, and the calculated test statistic is 37. The critical value for a two-tailed test with 25 paired differences at a significance level of 0.01 is 42. Which of the following is the correct conclusion to draw from the test?

• a. There is a significant difference in pain reduction between the two treatments.
• b. There is no significant difference in pain reduction between the two treatments.
• c. The Wilcoxon signed-rank test cannot be used to compare two treatments.
• d. The sample size is too small to draw any conclusions about pain reduction

How is the significance level determined in a Chi-Square Test of Independence?

• a. By comparing the observed value to the expected value
• b. By calculating the p-value
• c. By using the z-test statistic
• d. By using the t-test statistic