Statistics in Applied Science and Technology

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

2. 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

3. 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!

4. 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.

5. 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.

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

7. 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).

8. 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

9. 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!

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

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

12. 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)

13. 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.

14. 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!

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