Chapter 11 t-tests: means of dependent groups Dependent Samples – A t-test for dependent means indicates study of a single group of the same subjects. The formula:

III. Same Steps (use new formula; use same table) Example: Hypothetical: significant difference between state turnout rates with and without Perot in race? By hand and on computer Steps for SPSS: Analyze, compare means, paired-samples t-test Move each variable over (e.g. pretest and posttest) Click okay; interpret results.

Hypothesis Testing for a Difference Between Proportions Use this procedure when you are trying to compare differences in the proportions (%s) between two groups. Where z is the z-score p1 = proportion for group 1 (f1/n1) p2 = proportion for group 2 (f2/n2) n1=number in group 1 n2=number in group 2 p=total proportion (f1 + f2/n1 + n2) q=1-p                                          

Example Are boys as likely to identify with their mother’s political party as girls?  85 boys and 70 girls were questioned and 34 of the boys and 14 of the girls identified with their mother’s political party.  What can be concluded at the .05 level? Solution The hypotheses are          H0:  p1 = p2 (i.e., the proportion of boys identifying with their mother’s party is the same as that for girls).                 H1:    p1 ≠  p2    (i.e., the proportion of boys identifying with their mother’s party is significantly different than that of girls). We have         p1  =  34/85  =  0.4       p2  =  14/70  =  0.2         p  =  48/155  =  0.31        q  =  0.69          

Evaluation: We are using a risk level of .05 (5% chance the null is true). That corresponds to a z-score of 1.65 (for a two-tailed test, see z table and figure 7.5, 124). Therefore, any obtained z-score that exceeds 1.65 is too extreme (improbable) to attribute to chance and the null must be rejected.  This is ALWAYS the critical z-score for comparison with the obtained value. Clearly 2.68 is in the critical region, hence we can reject the null hypothesis and accept the alternative hypothesis and conclude that gender does make a difference for affiliation with mother’s party identification. Using SPSS (yes and no): Class example on gender and voting/pid.