Hypothesis Testing: Two-Sample Case for the Mean
Hypothesis Testing: Two-Sample Case for the Mean
Many cases in the social sciences involve a hypothesis about the difference between two groups (i.e. men and women, control and experiment). We analyze statistics from two samples, and the hypothesis and confidence interval would deal with the difference between two population means. The following factors are important in hypothesis testing:
1. probability theory 2. the sampling distribution of the statistic 3. the errors inherent in hypothesis testing and estimation 4. the level of significance and the level of confidence 5. the directional nature of the alternative hypothesis
General Procedure
1. State the hypotheses. 2. Set the criterion for rejecting H0. 3. Compute the test statistic. 4. Construct the confidence interval. 5. Interpret the results.
Hypothesis of Differences
• There is no difference between mean of group 1 and the mean of group 2. • [pic] or [pic] o to test this difference, we determine the difference between the statistic (the difference between the means), and the hypothesized value for the parameter (0). o if the population variance is known, the sampling distribution of differences is normally distributed. o if the population variance is UNKNOWN, the sampling distribution of differences is the t distribution, for the appropriate degrees of freedom.
Assumptions that must be considered:
1. Independence. The samples must be independent, that is, the scores of one sample in no way influence the scores of the other sample. a. Random selection from the population, then random assignment to the groups b. Random selection from two populations 2. Homogeneity of Variance. Since a pooled estimate of the sample variance is used, we must assume that the variance in population 1 is equal to the variance in population 2. a. If the two samples are of
Many cases in the social sciences involve a hypothesis about the difference between two groups (i.e. men and women, control and experiment). We analyze statistics from two samples, and the hypothesis and confidence interval would deal with the difference between two population means. The following factors are important in hypothesis testing:
1. probability theory 2. the sampling distribution of the statistic 3. the errors inherent in hypothesis testing and estimation 4. the level of significance and the level of confidence 5. the directional nature of the alternative hypothesis
General Procedure
1. State the hypotheses. 2. Set the criterion for rejecting H0. 3. Compute the test statistic. 4. Construct the confidence interval. 5. Interpret the results.
Hypothesis of Differences
• There is no difference between mean of group 1 and the mean of group 2. • [pic] or [pic] o to test this difference, we determine the difference between the statistic (the difference between the means), and the hypothesized value for the parameter (0). o if the population variance is known, the sampling distribution of differences is normally distributed. o if the population variance is UNKNOWN, the sampling distribution of differences is the t distribution, for the appropriate degrees of freedom.
Assumptions that must be considered:
1. Independence. The samples must be independent, that is, the scores of one sample in no way influence the scores of the other sample. a. Random selection from the population, then random assignment to the groups b. Random selection from two populations 2. Homogeneity of Variance. Since a pooled estimate of the sample variance is used, we must assume that the variance in population 1 is equal to the variance in population 2. a. If the two samples are of