Effect of Violations of Normality Edgell and Noon, 1984 On the Correlation Coefficient t-Test.
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Effect of Violations of Normality Edgell and Noon, 1984 On the Correlation Coefficient t-Test
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Transcript of Effect of Violations of Normality Edgell and Noon, 1984 On the Correlation Coefficient t-Test.
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 Violation of Normality Violation of Independence
Bivariate normal assumptionBivariate normal assumption Both variables come from normal distributionsBoth variables come from normal distributions
• OROR One variable is from a normal distribution and One variable is from a normal distribution and
the variables are independentthe variables are independent Independence assumptionIndependence assumption
Value of one variable is not influenced by the Value of one variable is not influenced by the otherother
t2= r2 / ((1-r2)/df)
Review Violation of Normality Violation of Independence
Run 10,000 samplesRun 10,000 samples Very Non-normal distributionsVery Non-normal distributions Range of sample sizesRange of sample sizes
Determine the proportion of samples that Determine the proportion of samples that were significant at the .05 and .01 levelwere significant at the .05 and .01 level
Method
Review Violation of Normality Violation of Independence
Distributions
Exponential Distribution
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 Independence
Results
Review Violation of Normality Violation of Independence
Method
Run 10,000 samplesRun 10,000 samples Range of sample sizesRange of sample sizes Zero correlations with dependencyZero correlations with dependency
Determine the proportion of samples that Determine the proportion of samples that were significant at the .05 and .01 levelwere significant at the .05 and .01 level
Review Violation of Normality Violation of Independence
Method
Zero-Correlations with dependencyZero-Correlations with dependency
1) Second variable is the square of the First Variable1) Second variable is the square of the First Variable
2) Mixed Bivariate Normal Distributions2) Mixed Bivariate Normal Distributions
- Population is aggregate of smaller subpopulations- Population is aggregate of smaller subpopulations
Review Violation of Normality Violation of Independence
0
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0 2 4 6 8 10 12 140
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0 2 4 6 8 10 12 14
0
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0 2 4 6 8 10 12 14
P=.5 ρ1=.3 P=.5 ρ2= -.3
ρ =0
Mixed Bivariate Normal Distributions
Review Violation of Normality Violation of Independence
Results
Violations of NormalityViolations of Normality Robust at .05Robust at .05 At .01, only sensitive to extreme departures At .01, only sensitive to extreme departures
from normalityfrom 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 RobustNot Robust ButBut
Non independent variables are not likely to have a correlation of zeroNon independent variables are not likely to have a correlation of zero t-Test could be considered a test of the hypothesis of independencet-Test could be considered a test of the hypothesis of independence
