CJUS-K300 1nd EditionExam # 4 Study Guide Lectures: 15 - 19Lecture 16 (October 29)Hypothesis Testing with 2 meansExample: 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-x1=¿ 5.1-s1=1.8Group #2: Peers approve of stealing from employers-n2=25-x2=8.2-s2=1.9tobt=x1−x2√s12n1+s22n2 For these we always use the t distribution no matter what the sample sizes areChoose an alpha of .01H0: u1=u2 Hi: u1≠ u2 tobt=5.1−8.2√1.8❑240+1.9❑225 = -6.6df = n1+n2 – 2df = 40 + 25 – 2 = 63Tcrit ≈ 2.3so we reject the nullWe are 99% confident that the population of peers who do not approve steal less often than thepopulation of those who approve. Lecture 17 Matched Sample T-TestTwo types1. Paired participants on a specific characteristic2. The same group tested before and after an interventionResearch 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 13 3 24 5 15 2 06 9 37 3 08 2 29 4 110 1 0Full formula: SD=√∑(xD−´xD)2n− 1 but it is easier to do it step by step in a table to make sureyou do not forget a piece of the equation. 1.XD= X2−X1 (Next calculation, it is easier to just add it on to your table rather than doing them all separately) Person Pair Abused Not AbusedXDXD−´XD(XD−´XD)21 4 0 -4 -1.7 2.892 0 1 1 3.3 10.893 3 2 -1 1.3 1.694 5 1 -4 -1.7 2.895 2 0 -2 0.3 .096 9 3 -6 -3.7 13.697 3 0 -3 -0.7 .498 2 2 0 2.3 5.299 4 1 -3 -0.7 .4910 1 0 -1 1.3 1.69´XD=¿∑¿ 40.1SD=√40.19=2.11 Lecture 18 (November 5) ANOVA – Analysis of VarianceHo: There are no differences among the 3 groupsHi: The three groups do differH0: u1=u2=u3Hi: u1≠ u2≠ u3 Always, just memorize this!x∑¿¿¿2¿¿SStotal=∑X2−¿ (Total amount of variability in the whole data set)∑xx∑¿¿¿2¿¿∑(¿¿ij)nk−¿SSbetween=¿ (Variability between groups)SSwithin=SStotal−SSbetween (Variability within the groups)obt=¿SSbd . fbSSwd . fwF¿ 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. Xij 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. CD=q√SSwithind . f withinnk To find q you need to have the alpha level, the d.f within and k eta2=SS betweenSS total Example: Research question- Do girls who hang around mostly boys, boys and girls or mostly girls have more frequency of delinquent acts?Mostly Boysx2Boys & Girlsx2Mostly Girlsx25 25 7 49 2 48 64 5 25 3 99 81 4 16 0 04 16 9 81 3 97 49 6 36 1 110 100 4 16 3 96 36 7 49 2 4∑¿ 49 ∑¿371 ∑¿ 42 ∑¿272 ∑¿14 ∑¿36 Ho: u1=u2=u3 Ho: u1≠ u2≠u3 alpha = .05 (always)d.f between = 3-1 = 2 SStotal=679−1102521=154d.f within = 21-3 = 18SSbetween=(4927+4227+1427)−525=98 SSw = 154-98=56obt=¿9825618=15.8F¿ 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 CDCD=3.61√56187=2.4 Ho: uboys=uboys∧ girls 7-6 = |1| < 2.4 fail to reject the nullHi: uboys≠ uboys∧girls Ho: uboys=ugirls 7-2= |5| >2.4 reject the null Hi: uboys≠ ugirls Ho: uboys∧girls=ugirls 6-2 =|4| > 2.4 reject the nullHi: uboys∧girls≠ ugirls Conclusion: ub=ubg≠ ug 95% certain that in this population, girls friends with boys or boys and girls commit more delinquent acts than girls only friends with girls. eta2=98154=.64The eta2 indicates the intensity of the relationship between the independent and dependentvariables. 65% of the variance in frequency in delinquent activity is explained by the gender of a girls friends in this