Wednesday, November 11, 2015

Assumptions Underlying the Pearson Product Moment Correlation Coefficient....

Assumptions Underlying the PPMCC: PPMCC is appropriate when three conditions exists: underlying measurement scales for the variables being correlated must be interval or ratio level, Scores for each variable should be normally distributed (no skewness should be there), relationship between the two variables should be fundamentally linear.

1.     The underlying measurement scales for the variables being correlated must be interval or ratio level (i.e., they are continuous).
Examples of variables that meet this criterion include revision time (measured in hours), intelligence (measured using IQ score), exam performance (measured from 0 to 100), weight (measured in kg), and so forth.
2.     Bivariate Normality (Bivariate normal distribution): Scores for each variable should be normally distributed. No skewness, neither positive nor negative should be there.
3.     Relationship between the two variables should be fundamentally linear.
4.     There should be no significant outliers (single data points within the data that do not follow the usual pattern).
5.     Homoscedasticity: It means variance around regression line should be same for all values of predictor variable (X). A relation is called heteroscedastic when all the points very (bunched up) near the regression line. Homoscedasticity is violated when there is much more variability (points are scattered away from the regression line) around the regression line. 

Serious violations in homoscedasticity (assuming a distribution of data is homoscedastic when in actuality it is heteroscedastic) result in underemphasizing the Pearson coefficient.  Assuming homoscedasticity assumes that variance is fixed throughout a distribution.

Heteroscedasticity is caused by non-normality of one of the variables, an indirect relationship between variables, or to the effect of a data transformation.  Heteroscedasticity is not fatal to an analysis, the analysis is weakened, not invalidated.  Homoscedasticity is detected with scatterplots and is rectified through transformation.

These notes are written by S C Joshi during EPSY 635 Course, Fall 2015, Texas A&M University. Acknowledgements to Dr. Bob Hall, Professor, EPSY, Texas A&M University for his assistance in understanding these terms during the course

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