CJUS K300 1nd Edition Exam 4 Study Guide Lectures 15 19 Lecture 16 October 29 Hypothesis Testing with 2 means Example Does peer approval or disapproval of stealing from employers effect how often individuals steal Group 1 Peers do not approve of stealing from employers n1 40 x 1 5 1 s 1 1 8 Group 2 Peers approve of stealing from employers n2 25 x 2 8 2 s 2 1 9 t obt are x 1 x 2 2 2 s1 s2 n1 n 2 For these we always use the t distribution no matter what the sample sizes Choose an alpha of 01 H 0 u 1 u2 H i u 1 u2 t obt 5 1 8 2 1 82 1 92 40 25 6 6 df n1 n2 2 df 40 25 2 63 Tcrit 2 3 so we reject the null We are 99 confident that the population of peers who do not approve steal less often than the population of those who approve Lecture 17 Matched Sample T Test Two types 1 Paired participants on a specific characteristic 2 The same group tested before and after an intervention Research question Do adult men who were abused as children commit more violent acts than men who were not abused as children Person Pair Abused Not Abused 1 4 0 2 0 1 3 3 2 4 5 1 5 2 0 6 9 3 7 3 0 8 2 2 9 4 1 10 1 0 Full formula x D x D 2 but it is easier to do it step by step in a table to make sure n 1 you do not forget a piece of the equation 1 SD X D X 2 X 1 Next calculation it is easier to just add it on to your table rather than doing them all separately XD X D X D 2 X D X D Person Pair Abused Not Abused 1 4 0 4 1 7 2 89 2 0 1 1 3 3 10 89 3 3 2 1 1 3 1 69 4 5 1 4 1 7 2 89 5 2 0 2 0 3 09 6 9 3 6 3 7 13 69 7 3 0 3 0 7 49 8 2 2 0 2 3 5 29 9 4 1 3 0 7 49 10 1 0 1 1 3 1 69 X D SD 40 1 2 11 9 Lecture 18 November 5 ANOVA Analysis of Variance Ho There are no differences among the 3 groups Hi The three groups do differ H 0 u 1 u2 u 3 40 1 H i u 1 u2 u3 Always just memorize this x 2 SStotal X 2 Total amount of variability in the whole data set x x 2 ij nk SSbetween Variability between groups SSwithin SStotal SSbetween Variability within the groups SS b d f b obt SS w d fw F ANOVA is to test for statistical significance among means by comparing levels of variance ANOVA is concerned with inferences The null and research hypotheses are always the same so just memorize those equations SStotal will always have the greatest value so keep that in mind If it is not the greatest of the 3 then you ve done something wrong in the calculations The tests will also always be 1 tailed to the right side X ij the i indicates individual values the j indicates group values Lecture 19 November 10 New Equations Tukey s Honest Significant Difference Test HSD which is necessary if you reject the null hypothesis SSwithin d f within CD q nk To find q you need to have the alpha level the d f within and k eta 2 SS between SS total Example Research question Do girls who hang around mostly boys boys and girls or mostly girls have more frequency of delinquent acts Mostly Boys x 2 Boys Girls x 2 x Mostly Girls 5 25 7 49 2 4 8 64 5 25 3 9 9 81 4 16 0 0 4 16 9 81 3 9 7 49 6 36 1 1 10 100 4 16 3 9 6 36 7 49 2 4 49 371 42 272 14 H o u1 u2 u 3 H o u1 u2 u3 alpha 05 always d f between 3 1 2 d f within 21 3 18 SStotal 679 11025 154 21 2 36 SSbetween 2 2 2 49 42 14 525 98 7 7 7 SSw 154 98 56 98 2 obt 15 8 56 18 F 15 8 3 55 so we reject the null which says that there is no difference which means that we need to calculate the extent to which this is true through the HSD tukeys honesty Take the means of each group and subtract them from the other one then compare the ABSOLUTE VALUE no negatives to the CD 56 18 CD 3 61 2 4 7 H o uboys uboys girls 7 6 1 2 4 fail to reject the null H i u boys uboys girls H o uboys u girls 7 2 5 2 4 reject the null H i u boys ugirls H o uboys girls u girls 6 2 4 2 4 reject the null H i u boys girls u girls Conclusion ub ubg u g 95 certain that in this population girls friends with boys or boys and girls commit more delinquent acts than girls only friends with girls eta 2 98 64 154 The eta 2 indicates the intensity of the relationship between the independent and dependent variables 65 of the variance in frequency in delinquent activity is explained by the gender of a girls friends in this population