CJUS K300 1nd Edition Exam 3 Study Guide Lectures 11 14 Lecture 11 October 8 2 Tailed Tests Null hypothesis Ho There s no difference between the two variables Research hypothesis 2 tailed non directional H1 There is a difference between the two variables But not providing information on what the difference is Starting off with an example Domestic Violence Attitude Scale Possible range of scores 1 50 where higher scores indicate officers taking domestic violence more seriously For the population of police officers 20 For a sample of 75 officers x 29 s 4 Ho The sample of officers who have been through the 2 day training program come from a population of officers whose mean score on the Domestic Violence Attitude Scale is 20 H1 The sample of officers who have been through the 2 day training program come from a population of officers whose mean score on the Domestic Violence Attitude Scale is not 20 We typically express these in symbol form Ho 20 H1 20 Steps to test a null hypothesis 2 tailed 1 State your null and research hypotheses 2 Decide on your alpha level 10 05 or 01 3 Look up your critical value e g zcrit draw a graph picture it s easier to visualize 4 Calculate your zobt 5 Compare Is zcrit zobt zcrit refer to your graph picture 6 State your conclusion Critical regions for alpha 05 1 96 Equation Z obt x s n Is 1 96 Zobt 1 96 or in other words is the Zobt outside of the critical zone No Reject the null hypothesis and find in favor of the research hypothesis Since zobt is in the critical region we reject the Ho and find instead in favor of the H1 Conclusion We are 95 certain that the sample of officers who have been through the 2 day training program come from a population whose mean score on the Domestic Violence Attitude Scale is not 20 Lecture 12 October 13 1 Tailed Tests Why Reasons to specify a directional hypothesis 1 It fits the theory 2 It gives a mathematical advantage In a two tailed test both the tails or extremities are included 2 5 in each tail For a one tailed test we combine the tails making it 5 in one of the tails How do we know which tail to use As a good rule of thumb you can follow the sign of the null hypothesis Means right hand tail Means left hand tail usually Steps in testing a null hypothesis with a 1 tailed test so similar to the 2 tailed test 1 State your null research hypotheses 2 Decide on your alpha level usually given to you 3 Look up the critical value Zcrit and draw a graph if you wish x Z obt s 4 Calculate n 5 Compare Zobt and Zcrit 6 State your conclusion in words Using the same example from last class with 2 tailed tests we will look again at the Violence Attitude Scale Possible range 1 50 higher score taking domestic violence more seriously Population of police officers 20 Sample of 75 officers x 20 8 s 4 H o 20 H 1 20 H 1 interpreted The sample of officers who have been through the 2 day training program come from a population of officers whose mean score on the Domestic Violence Attitude Scales is GREATER than 20 Alpha 05 corresponds to 1 65 Zobt 1 74 Reject the null Another example Do teenage shoplifters steal less valuable items than the general population of shoplifters You can find hints in the research question about the direction of the test Population of all shoplifters the mean value of stolen items 83 so 83 For a sample of 97 shoplifters ages 13 17 years the mean value of stolen items was 81 so X 81 s 11 alpha 05 look up alpha in the 1 tailed test column 1 65 Zobt 1 80 Lecture 13 October 15 Test of Best Fit Time of day Observed frequency Expected frequency 12am 6am 20 25 6am 12pm 7 25 12pm 6pm 31 25 6pm 12am 42 25 Total 100 100 H o x 2 0 In the population of all ambulance calls at Green College the calls are distributed evenly across the 4 time of day categories H i x 2 0 In the population of all ambulance calls at Green College the calls are not distributed evenly across the 4 time of day categories alpha 05 Degrees of freedom K 1 K most likely stands for categories in german d f 4 1 3 at an alpha of 05 X 2crit 7 815 2 X o e e 2 obt This is the equation in theory and we have to understand this equation in order to understand what our answer means but we will be using a somewhat more simple equation to work with day to day X 2obt 26 96 o Time of day o e e o e 2 o e 2 e 12am 6am 20 25 5 25 1 6am Noon 7 25 18 324 12 96 Noon 6pm 31 25 7 49 1 44 6pm 12am 42 25 17 289 11 56 Total 100 26 96 Is 26 96 7 815 Yes so we Reject Ho Conclusion We are 95 certain that in the population of all Green College ambulance calls the ambulance calls are not evenly distributed across the 4 times of day categories You will absolutely need to know how to write this out Chi Squared Computational Formula aka the formula we will actually be using 2 o X n e 2 obt Using the same example with this equation we would do 20 2 25 72 312 25 25 422 100 26 96 25 Lecture 14 October 20 Test of Independence Expected Frequency Table Lables White Non White Row Marginals Non Capital Cell A 118 Cell B 70 118 Capital Cell C 97 Cell D 17 114 Column Marginals 215 87 302 Independent Events P A and B P A x P B P non cap 188 302 622 P white victim 215 302 712 P non cap and white victim 622 X 712 443 443 X 302 134 what you put in the cell This is how we COULD get the expected frequencies but there is an easier way Row marginal x column marginal and dividing by total n fe RM x CM n So for Cell A f e 118 x 215 84 302 Testing the hypothesis Alpha of 05 d f Rows 1 Columns 1 2 1 2 1 1 x 1 1 Chi square crit 3 841 Observed 118 70 97 17 Expected 134 54 81 33 N 302 X obt 2 2 o n e 103 9 90 7 116 2 8 75 319 55 302 17 55 So we reject Ho Conclusion We are 95 certain that in the population race of victim and whether or not a homicide case is charges as a noncapital or capital offense are NOT independent Are gender of victim and how a case is charged independent Male Female RM Non capital …