D5.1 Interpreting Chi‐Square. In Output 8.1 is the (Pearson) chi‐square statistically significant? Explain your answer and what it means. Are the expected values in at least 80% of the cells greater than or equal to 5? Explain how you know and why it is important.
D5.2 Measure Strength of the Relationship. Because ‘father’s education revised’ and ‘mother’s education revised’ are at least ordinal data, which of the statistics used in Problem 8.3 is the most appropriate to measure the strength of the relationship; phi, Cramer’s V, or Kendall’s tau‐b? Explain your choice. Why are Kendall’s tau‐b and Cramer’s V different?
D5.3 Interpreting Correlations. In Output 9.2, what do the correlation coefficients tell us? What is the r^2 for the Pearson correlation and what does it mean? Compare the Pearson and Spearman correlations on both correlation size and significance level and explain your comparison. Explain when you should use which type of correlation in this case.
D5.4 Interpreting Regressions. Using Output 9.4, find the regression coefficient (weight) and the standardized regression (Beta) coefficient. How do these compare to the correlation between the same variables in Output 9.3? What does the regression coefficient (weight) tell you? Using the variables in Problem 9.4, develop a research question in which the Pearson correlation would be more appropriate than the bivariate regression. Using the variables in Problem 9.4, develop a research question in which the bivariate regression would be more appropriate than the Pearson correlation.