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Effect of Violations of Normality

Effect of Violations of Normality. On the Correlation Coefficient t-Test. Edgell and Noon, 1984. Is the t-test for correlation coefficients robust to violations of its assumptions?. Overview. Review t-test of the Correlation Coefficient Violations Bivariate Normal Assumption

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Effect of Violations of Normality

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  1. Effect of Violations of Normality On the Correlation Coefficient t-Test Edgell and Noon, 1984

  2. Is the t-test for correlation coefficients robust to violations of its assumptions?

  3. Overview • Review t-test of the Correlation Coefficient • Violations • Bivariate Normal Assumption • Independence Assumption

  4. ReviewViolation of Normality Violation of Independence t2= r2 / ((1-r2)/df) • Bivariate normal assumption • Both variables come from normal distributions • OR • One variable is from a normal distribution and the variables are independent • Independence assumption • Value of one variable is not influenced by the other

  5. Review Violation of Normality Violation of Independence Method • Run 10,000 samples • Very Non-normal distributions • Range of sample sizes • Determine the proportion of samples that were significant at the .05 and .01 level

  6. Review Violation of Normality Violation of Independence Distributions Exponential Distribution

  7. Review Violation of Normality Violation of Independence Distributions Uniform Distribution

  8. Review Violation of Normality Violation of Independence Distributions Cauchy Distribution

  9. Review Violation of Normality Violation of Independence Results

  10. Review Violation of Normality Violation of Independence Results

  11. Review Violation of Normality Violation of Independence Method • Run 10,000 samples • Range of sample sizes • Zero correlations with dependency • Determine the proportion of samples that were significant at the .05 and .01 level

  12. Review Violation of Normality Violation of Independence Method Zero-Correlations with dependency 1) Second variable is the square of the First Variable 2) Mixed Bivariate Normal Distributions - Population is aggregate of smaller subpopulations

  13. Review Violation of Normality Violation of Independence Mixed Bivariate Normal Distributions P=.5 ρ1=.3 P=.5 ρ2= -.3 ρ =0

  14. Review Violation of Normality Violation of Independence Results

  15. Conclusion • Violations of Normality • Robust at .05 • At .01, only sensitive to extreme departures from normality Is the t-test for correlation coefficients robust to violations of normality?

  16. Conclusion • Not Robust Is the t-test for correlation coefficients robust to violations of independence? • But • Non independent variables are not likely to have a correlation of zero • t-Test could be considered a test of the hypothesis of independence

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