Question

1. Circle the appropriate word choice in each of a thru e below. All else being the same, the chances of getting a "significant result” increases as a. Sample size (increases/decreases) b. Population std deviation (increases/decreases) c. Effect size (increases/decreases) d. Alpha (increases/decreases) e. P-value of a test (increases/decreases) 2. For fixed sample size, decreasing alpha (increases/decreases) beta, and increases/decreases the power of the test? 3. For fixed alpha, decreasing sample size will increase/decrease) power? 4. For fixed alpha and sample size, a test with a larger effect size will have (more/less) power than a test with smaller effect size? 5. As population standard deviation increases, power (increases/decreases).

Answer 1

Solution 1a: As we know test statisic value gets Large when we increase sample size. So Significant result increases as sample size increases.

b) Standard DEVIATION is inversely proportional to test statisic. So to make test statisic Significant we need to decrease sample variation.

c) Effect size increases make the difference between two population means more Significant.

d) On increasing alpha the test become more Significant.

E) p value SMALLER more Significant results we get.

2) For fixed sample size decreasing alpha , decreases beta, increases the power of the test.

3) decreasing sample size leads to decrease the power of the test.

4) Large effect size has more due to more Difference between two means as compared to small effect size.

5) As population standard deviation increases make test statisic less Significant and this will lead to decrease the power of the test.