Spearman Rank Correlation Coefficient Quiz

Hypothesis Testing for Spearman Rank Correlation

• The test statistic used to test the hypothesis for the Spearman rank correlation is not specified.
• The null hypothesis in the test of the Spearman rank correlation is that there is no correlation between the two variables.

t-test

• For a two-tailed test with a 5% significance level and 33 degrees of freedom, the critical values for the t-test are not specified.

Chi-Square Test of Independence

• The formula for the test statistic in the chi-square test of independence is not specified.
• The chi-square test of independence has (r-1)(c-1) degrees of freedom in a contingency table with r rows and c columns.
• The expected number of observations in each cell of a contingency table assuming independence is calculated by multiplying the row total and column total, then dividing by the grand total.
• The rejection region for the test of independence using a contingency table is not specified.
• The chi-square statistic is calculated by finding the difference between the observed and expected frequencies in each cell, squaring the difference, dividing by the expected frequency, and summing the results.
• The number of cells in a contingency table with r rows and c columns is r*c.

Contingency Tables

• The graphic that reflects the comparison between the observed and expected frequencies in a contingency table is a mosaic plot.
• The width of the rectangles in Exhibit 10 represents the expected frequency.
• The height of the rectangles in Exhibit 10 represents the observed frequency.
• The darker shading in Exhibit 10 indicates the observed frequency is greater than the expected frequency.
• The lighter shading in Exhibit 10 indicates the observed frequency is less than the expected frequency.
• The formula for calculating the standardized residual is (observed frequency - expected frequency) / sqrt(expected frequency).

Standardized Residual

• A positive standardized residual indicates that the observed frequency is greater than the expected frequency.
• A negative standardized residual indicates that the observed frequency is less than the expected frequency.
• The interpretation of the standardized residual in the ETF example is that it measures the difference between the observed and expected frequencies in a contingency table.
• Another name for the standardized residual in the ETF example is the Pearson residual.

Spearman Rank Correlation Coefficient

• The Spearman rank correlation coefficient, rS, measures the strength and direction of the correlation between two ranked variables.
• The formula for calculating the Spearman rank correlation coefficient, rs, is rs = 1 - (6 * Σd^2) / (n * (n^2 - 1)), where d is the difference between the ranks and n is the sample size.
• The hypotheses for testing Spearman rank correlations are H0: rs = 0 and H1: rs ≠ 0.
• The first step in calculating the Spearman rank correlation coefficient is to rank the data.
• The second step in calculating the Spearman rank correlation coefficient is to calculate the differences between the ranks.
• The third step in calculating the Spearman rank correlation coefficient is to calculate the sum of the squared differences.
• The Spearman rank correlation coefficient would be appropriate to use when the data is ordinal or ranked.
• The sample size, n, in the formula for the Spearman rank correlation coefficient is the number of observations.
• If the Spearman rank correlation coefficient, rs, is equal to 1, it means that there is a perfect positive correlation between the two variables.

Test your knowledge on the Spearman Rank Correlation Coefficient, a non-parametric test of correlation used when the population departs from normality. Discover how it differs from the Pearson correlation coefficient.