Parametric and Non-Parametric Tests of Independence

Which of the following conditions most strongly suggests the use of a non-parametric test rather than a parametric test?

Calculate the degrees of freedom for a t-test of a Pearson correlation coefficient with a sample size of 25.

Given a sample correlation coefficient (r) of 0.50 and a sample size (n) of 18, what is the calculated t-statistic for testing the null hypothesis that the population correlation is zero?

Which of the following is an assumption required for the t-test of the Pearson correlation coefficient?

The Spearman rank correlation coefficient is best described as:

When calculating the Spearman rank correlation, if two observations have the same value, how should their ranks be assigned?

Calculate the Spearman rank correlation coefficient given n=5 and the sum of squared differences in ranks is 8.

For a sample size of 40, which test statistic is used to test the significance of the Spearman rank correlation?

Which test is most appropriate for determining if 'Investment Strategy' (Growth vs. Value) is independent of 'Fund Size' (Small vs. Large)?

In a contingency table, how is the expected frequency for a cell calculated?

What are the degrees of freedom for a Chi-Square test of independence on a contingency table with 3 rows and 4 columns?

Consider a contingency table cell with an Observed Frequency of 50 and an Expected Frequency of 40. What is the contribution of this cell to the Chi-Square statistic?

The Chi-Square test of independence is typically:

In a Mosaic plot, what does the size (area) of each tile represent?

What does the standardized residual in a Mosaic plot analysis help identify?

Calculate the standardized residual for a cell with Observed = 100 and Expected = 81.

Under what circumstance would the Spearman rank correlation be preferred over Pearson even if the data is continuous?

What is the critical t-value for a two-tailed Pearson correlation test at a 5% significance level with n=25? (Approximate using standard t-distribution knowledge)

A Chi-Square test results in a statistic of 15.5 with 4 degrees of freedom. If the critical value at 5% significance is 9.49, what is the conclusion?

If the Spearman rank correlation is 1.0, what does this indicate about the two variables?

In the context of hypothesis testing for correlation, the null hypothesis H0 usually states:

If a sample size is small (n < 30) for a Spearman rank correlation test, what is required to determine the critical value?

Calculate the Chi-Square contribution for a cell where Observed = 20 and Expected = 25.

If a contingency table has 2 rows and 2 columns, what is the degrees of freedom?

Which of the following describes a 'Type I Error' in the context of these tests?

Given: Row 1 Total = 30, Column 1 Total = 20, Grand Total = 50. Calculate the Expected Frequency for cell (1,1).

In a Pearson correlation t-test, if the calculated t-value is 1.5 and the critical value is 2.1, what is the decision?

When transforming data to ranks for the Spearman correlation, the smallest value is typically assigned rank:

What is the primary advantage of using a Mosaic plot over a simple contingency table?

Given n=50 and r=0.3. Calculate the t-statistic.

If variables X and Y are independent, the population correlation coefficient rho is:

Which distribution does the Chi-Square statistic follow?

In a Spearman rank calculation, if d=0 for all pairs, then:

What is the range of possible values for the Chi-Square statistic?

If a Chi-Square test yields a p-value of 0.03 and we use a 5% significance level, we should:

Calculating Spearman rank: If Sum(d^2) = 20 and n = 6, what is r_s?

Which of the following is NOT a requirement for the Chi-Square test of independence?

For a contingency table with Row Totals of 10 and 20, and Column Totals of 15 and 15 (Grand Total 30), calculate the Expected Frequency for cell (2, 2).

What happens to the critical t-value for a Pearson correlation test as the sample size increases (holding significance level constant)?

A standardized residual of -3.0 in a Mosaic plot indicates:

Pearson correlation is sensitive to:

If a dataset has ranks for X: 1, 2, 3 and ranks for Y: 3, 2, 1. What is the Spearman correlation?

The null hypothesis for a Chi-Square test of independence typically asserts:

What is the denominator in the formula for the t-statistic of the Pearson correlation?

Spearman rank correlation is a specific case of:

Contingency table analysis is typically used for what kind of variables?

If observed frequency equals expected frequency for all cells, the Chi-Square statistic is:

In a 3x3 contingency table, what is the critical value of Chi-Square at 5% significance (approx)?

Which correlation coefficient should be used if the data is ordinal (e.g., credit ratings AAA, AA, A)?

The term 'contingency table' is synonymous with: