PSY 201 1 Introduction to Statistics in Psychology PSY 201 Greg Francis PhD Department of Psychological Sciences Psychological Sciences Building Room 3174 765 494 6934 email gfrancis purdue edu http www1 psych purdue edu gfrancis Classes PSY201 Homework 14 Due 8 December 2009 Hand in your answers on a separate sheet of paper 1 A research study comparing three treatment conditions produced means of X 1 2 X 2 4 and X 3 6 a Compute the variance for the set of three means Treat the means as a sample of n 3 values and compute the sample variance b Change the third mean to X 3 15 Notice that we have substantially increased the differences among the three means Compute the variance for the new set of n 3 means c Explain how variance provides a measure of the size of the mean differences 2 A researcher reports an F ratio with df 2 24 for an independent measures research study a How many treatment conditions were compared in the study b How many subjects participated in the entire study 3 The following data represent the results from an independent measures experiment comparing three treatment conditions Use an analysis of variance with 0 05 to determine whether these data are sufficient to conclude that there are significant differences between the treatments Treatment 1 2 3 0 2 5 0 4 6 2 0 4 1 1 7 2 3 8 PSY 201 2 4 The following data are constructed so that all three treatments have exactly the same mean Treatment 1 2 3 0 2 3 6 6 2 4 4 5 6 4 6 a Before you begin any calculations predict what value should be obtained for SSB Hint how big are the differences between treatments b Calculate SST and SSW You should find that all of the variability in the data is withintreatments variability SST SSW c Complete the analysis of variance with 0 05 to determine whether there are any significant differences among the three treatments Does your answer agree with your prediction in part a 5 There is some evidence that high school students justify cheating in class on the basis of poor teacher skills or low levels of teacher caring Murdock Miller Kohlhardt 2004 Students appear to rationalize their illicit behavior based on perceptions of how their teachers view cheating Poor teachers are thought not to know or care whether students cheat so cheating in their classes is okay Good teachers on the other hand do care and are alert to cheating so students tend not to cheat in their classes Following are hypothetical data similar to the actual research results The scores represent judgments of the acceptability of cheating for the students in each sample Use an ANOVA with 0 05 to determine whether there are significant differences in student judgments depending on how they see their teachers nk Xk P 2 i Xik Poor teacher 6 6 246 Average teacher 8 2 65 Good teacher 10 2 82 6 A developmental psychologist is examining the development of language skills from age 2 to age 5 Four different groups of children are obtained one for each age with n 15 children in each group Each child is given a language skills assessment test The resulting data were analyzed with an ANOVA to test for mean differences between age groups The results of the ANOVA are presented in the following table Fill in all the missing values marked by Source Between Within Total SS 81 249 df MS F PSY 201 3 7 The following data represent the results from an independent measures study comparing two treatment conditions nk Xk s2 P k 2 i Xik Treatment 1 2 8 2 7 3 6 3 5 5 9 2 5 5 7 3 2 5 1 5 255 51 a Use an independent t test with 0 05 to determine whether there is a significant mean difference between the two treatments b Use an ANOVA with 0 05 to determine whether there is a significant mean difference between the two treatments c Compare the F statistic with the t2 statistic 8 A published report of a repeated measures research study includes the following description of the statistical analysis The results show significant differences among the treatment conditions F 2 20 6 10 p 0 01 a How many treatment conditions were compared in the study b How many individuals participated in the study 9 Loss of hearing can be a significant problem for older adults Although hearing aids can correct the physical problem people who have lived with hearing impairment often develop poor communication strategies and social skills To address this problem a home education program has been developed to help people who are receiving hearing aids for the first time The program emphasizes communication skills To evaluate the program overall quality of life and satisfaction were measured before treatment and again at the end of the training program and once more at a 6 month follow up Kramer et al 2005 Data similar to the results obtained in the study are shown below Do the data indicate a significant improvement in quality of life following the training program Test with 0 05 Person A B C D T P k 2 i Xik Quality of Life Scores Before After 6 Months 3 7 8 0 5 7 4 9 5 1 7 4 8 28 24 26 204 154 PSY 201 4 10 The endorphins released by the brain act as natural painkillers For example Gintzler 1970 monitored endorphin activity and pain thresholds in pregnant rats during the days before they gave birth The data showed an increase in pain thresholds as the pregnancy progressed The change was gradual until 1 or 2 days before birth at which point there was an abrupt increase in pain threshold Apparently a natural painkilling mechanism was preparing the animals for the stress of giving birth The following data represent pain threshold scores similar to the results obtained by Gintzler Do these data indicate a significant change in pain threshold Use a repeated measures ANOVA with 0 05 Subject A B C D E Days Before Giving Birth 9 7 5 3 1 35 39 41 49 52 33 38 40 44 55 39 41 44 47 57 37 40 45 46 56 36 37 40 44 55