EffectofViolationsofNormality-HarvardUniversity影响的违反常态-哈佛大学.ppt

1、Effect of Violations of Normality,Edgell and Noon, 1984,On the Correlation Coefficient t-Test,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 Independence Assumption,Review

2、 Violation of Normality Violation of Independence,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,t2= r2 / (1-r2)/df,

3、Review Violation of Normality Violation of Independence,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,Method,Review Violation of Normality Violation of Independence,Distributions,Exponential D

4、istribution,Review Violation of Normality Violation of Independence,Distributions,Uniform Distribution,Review Violation of Normality Violation of Independence,Distributions,Cauchy Distribution,Review Violation of Normality Violation of Independence,Results,Review Violation of Normality Violation of

5、Independence,Results,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,Review Violation of Normality Violation of Independence,Me

6、thod,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,Review Violation of Normality Violation of Independence,P=.51=.3,P=.5 2= -.3,=0,Mixed Bivariate Normal Distributio

7、ns,Review Violation of Normality Violation of Independence,Results,Violations of Normality Robust at .05 At .01, only sensitive to extreme departures from normality,Conclusion,Is the t-test for correlation coefficients robust to violations of normality,Conclusion,Is the t-test for correlation coefficients robust to violations of independence,Not Robust,But Non independent variable