Spearman Rank Correlation Coefficient Quiz
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Questions and Answers

Which test statistic is used to test the hypothesis for the Spearman rank correlation?

  • normal distribution
  • F-distribution
  • chi-square distribution
  • t-distribution (correct)

    • For a two-tailed test with a 5 percent significance level and 33 degrees of freedom, what are the critical values for the t-test?

  • ±1.645
  • ±2.576
  • ±2.0345 (correct)
  • ±1.96

    • What is the null hypothesis in the test of the Spearman rank correlation?

  • H0: rS < 0
  • H0: rS ≠ 0
  • H0: rS = 0 (correct)
  • H0: rS > 0

    • What is the formula for the test statistic in the chi-square test of independence?

    <p>χ 2 = ∑i=1 m (Oij − Eij) _ 2 Eij</p> Signup and view all the answers

    How many degrees of freedom does the chi-square test of independence have in a contingency table with r rows and c columns?

    <p>(r - 1)(c - 1)</p> Signup and view all the answers

    What is the expected number of observations in each cell of a contingency table assuming independence?

    <p>Eij = (Total row i)× (Total column j) / Overall total</p> Signup and view all the answers

    What is the rejection region for the test of independence using a contingency table?

    <p>Right side</p> Signup and view all the answers

    How is the chi-square statistic calculated in the chi-square test of independence?

    <p>By summing the values of (Oij − Eij) _ 2 Eij for each of the m cells</p> Signup and view all the answers

    What is the number of cells in a contingency table with r rows and c columns?

    <p>r × c</p> Signup and view all the answers

    What is the name of the graphic that reflects the comparison between the observed and expected frequencies in a contingency table?

    <p>Mosaic</p> Signup and view all the answers

    Which of the following best describes the interpretation of the standardized residual in the ETF example?

    <p>The standardized residual indicates the difference between the observed and expected values, scaled by the expected values.</p> Signup and view all the answers

    What does the width of the rectangles in Exhibit 10 represent?

    <p>The proportion of ETFs that are small, medium, and large.</p> Signup and view all the answers

    What does the height of the rectangles in Exhibit 10 represent?

    <p>The proportion of ETFs that are value, growth, and blend.</p> Signup and view all the answers

    What does the darker shading in Exhibit 10 indicate?

    <p>The number of observations that are more than expected under the null hypothesis of independence.</p> Signup and view all the answers

    What does the lighter shading in Exhibit 10 indicate?

    <p>The number of observations that are less than expected under the null hypothesis of independence.</p> Signup and view all the answers

    What is the formula for calculating the standardized residual?

    <p>Standardized residual = Oij − Eij √ Eij</p> Signup and view all the answers

    What does a positive standardized residual indicate in the ETF example?

    <p>There are more observations than expected.</p> Signup and view all the answers

    What does a negative standardized residual indicate in the ETF example?

    <p>There are fewer observations than expected.</p> Signup and view all the answers

    What is the interpretation of the standardized residual in the ETF example?

    <p>There are more medium-size growth ETFs and fewer large-size growth ETFs than expected.</p> Signup and view all the answers

    What is another name for the standardized residual in the ETF example?

    <p>Pearson residual</p> Signup and view all the answers

    Which of the following statements is true about the Spearman rank correlation coefficient, rS?

    <p>It is calculated on the ranks of the two variables within their respective samples.</p> Signup and view all the answers

    What is the formula for calculating the Spearman rank correlation coefficient, rs?

    <p>$rs = 1 - \frac{6\sum_{i=1}^n d_i^2}{n(n^2 - 1)}$</p> Signup and view all the answers

    What are the hypotheses for testing Spearman rank correlations?

    <p>H0: rS = 0 and Ha: rS ≠ 0</p> Signup and view all the answers

    What is the first step in calculating the Spearman rank correlation coefficient?

    <p>Rank the observations on X from largest to smallest.</p> Signup and view all the answers

    What is the second step in calculating the Spearman rank correlation coefficient?

    <p>Calculate the difference, di, between the ranks for each pair of observations on X and Y.</p> Signup and view all the answers

    What is the third step in calculating the Spearman rank correlation coefficient?

    <p>Calculate the squared difference, di^2, between the ranks for each pair of observations on X and Y.</p> Signup and view all the answers

    When would the use of the Spearman rank correlation coefficient be appropriate?

    <p>When the population under consideration departs from normality.</p> Signup and view all the answers

    What does the Spearman rank correlation coefficient measure?

    <p>The strength and direction of the monotonic relationship between two variables.</p> Signup and view all the answers

    What is the sample size, n, in the formula for the Spearman rank correlation coefficient?

    <p>The number of pairs of observations on X and Y.</p> Signup and view all the answers

    What does it mean if the Spearman rank correlation coefficient, rs, is equal to 1?

    <p>There is a perfect monotonic relationship between the two variables.</p> Signup and view all the answers

    Study Notes

    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.

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    Description

    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.

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