HYPOTHESIS TESTS COMPARING TWO POPULATIONS I. Comparing the means of two independent populations. A. State the null hypothesis. B. Choose a statistical test. C. Check Assumptions. 1. Two independent random probability samples. 2. Interval level measurement of variable being compared. 3. Groups defined by catergorical variable with two categories. 4. For a z-test, the sampling distribution must be normal, which can be assumed to be true if each sample contains 100 or more cases. 5. If either of the sample sizes is less than 30, a t-test must be used, requiring the additional assumptions that: a. the populations from which the samples are drawn are normal. b. the variance of the two populations is equal, if an equal variances t-test is used. D. Select an alpha level. E. Calculate the test statistic and decide about the null. 1. Calculate the statistic. 2. Determine the probability associated with the statistic. 3. Compare probability to alpha level. 4. Decide about the null. II. Comparing means in two dependent (matched, paired) populations. A. State the null hypothesis. B. Choose at statistical test. C. Check Assumptions. 1. Two dependent random probability samples such that scores from one can be mathed with scores from the other. 2. Interval level of measurement on variable being compared. 3. Sampling distribution is normally distributed which can be assumed if the populations are normally distributed. D. Select and alpha level. E. Calculate the test statistic and decide about the null. 1. Calculate the statistic. 2. Determine the probability associated with the statistic. 3. Compare probability to alpha level. 4. Decide about the null.