Statistics in Applied Science and Technology Chapter 13.5 & supplemental: Test of Significance of Measure of Association

Key Concepts in This Section Assumptions involved in each test of significance. t statistics to test significance of measure of association between two interval-ratio variables

How to tell that the association between two interval-ratio variables are “Statistically Significant”? (chapter 13.5) With the null of “no relationship” in the population, the sampling distribution of all possible sample correlation coefficient r’s is approximated by the t distribution. Therefore, test statistics is t test!

Review of the assumptions: Random sampling Level of measurement is interval-ratio Both variables are or approximate a normal distribution The variance of Y scores is uniform for all values of X (Homoscedasticity) Linear relationship.

Review of the assumptions (II) A visual inspection of the scattergram will usually be sufficient to appraise the extent to which the relationship conforms to the assumption of linearity and homoscedasticity. As a rule of thumb, if the data points fall in a roughly symmetrical, cigar-shaped pattern, whose shape can be approximated with a straight line, then it is appropriate to proceed with this test.

Stating the Null Hypothesis H0:  (population correlation coefficient) = 0 H1:  (population correlation coefficient)  0

Test statistics and its distribution Test statistics is t and can be found by: Where: r - sample correlation coefficient n - number of pairs of observations There is a family of t distribution, the one to use depends on the degree of freedom (n-2).

How do I find Critical t? Table B (in the inside back cover), two tailed Reject the null hypothesis when t falls into rejection region/critical region

How to tell that the association between two ordinal variables are “Statistically Significant”? (supplement) With the null of “no relationship” in the population, the sampling distribution of all possible sample Gamma’s is approximated by the Z distribution (for samples of 10 or more). Therefore, test statistics is Z test!

Review of the Assumptions Random sampling Level of measurement is ordinal Sample size is greater than 10.

Stating the Null Hypothesis H0:  (population Gamma) = 0 H1:  (population Gamma)  0

Test Statistics and its distribution Test Statistics is Z and can be found by: Ns, Nd - defined as the same in calculating Gamma (G) N - total number of subject in the study. There is only one Z distribution (Standard normal distribution with mean of 0 and standard deviation of 1)

How do I find Critical Z? The same way you did when you conducting Z test for a population mean! (usually two-tailed. Therefore, for =0.05, Zcrit = 1.96) Reject the null hypothesis when Z falls into rejection region/critical region.

How to tell that the association between two nominal variables are “Statistically Significant”? (supplement) With the null of “no relationship/no association/independence” of two nominal level variables, we can actually use the 2 test! Therefore, test statistics is 2 test! The procedures to conduct 2 test are the same as described in Chapter 12!

Congratulations! You have completed the majority part of the course!