Explain the difference between the type of information given by the tests of sta

Question

Explain the difference between the type of information given by the tests of statistical significance such as t and Chi Square, and information given by measures of association such as Gamma, the Coefficient of Determination (r2), Cramer's V and Pearson’s correlation coefficient (r). What is meant by a PRE measure? Which of the measures listed above are PRE?

Can a test of significance show a statistically significant relationship while a measure of association shows a weak relationship between the variables?

If yes, present an example illustrating how such a situation might occur.

Explanation / Answer

The test of significance is used to test if the differences / association in the observations is simply by chance. A t-test tests a null hypothesis about two means comparsion that is two means are equal, or that the difference between them is zero whereas chi-square test tests that a null hypothesis about the relationship between two variables.

Gamma Test: measures the strength of association of the cross tabulated data when both variables are measured at the ordinal level. It makes no adjustment for either table size or ties.

Coeficient of Determination: interpreted as the proportion of the variance in the dependent variable that is predictable from the independent variable.

Pearson's correlation coefficient: covariance of the two variables divided by the product of their standard deviations.

PRE measures: does knowing the value of a case on one variable help you to predict its value on the other, that is, help you as compared to not knowing its value.

Gamma, Pearson's correlation coefficien measures listed above are PRE

Cramer's V test: For crosstabs with nominal measures we can generally preferred Cramer's V test. It is ranges from 0 to 1, and the closer to 1, the stronger the relationship.

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