PSY 201 1Introduction to Statistics in Psychology: PSY 201Greg Francis, PhDDepartment of Psychological SciencesPsychological Sciences Building, Room 3174(765) 494-6934email: [email protected]://www1.psych.purdue.edu/∼gfrancis/Classes/PSY201/Homework 14Due: 8 December 2009Hand in your answers on a separate sheet of paper.(1) A research study comparing three treatment conditions produced means of X1= 2, X2= 4and X3= 6.a) Compute the variance for the set of three means. (Treat the means as a sample of n = 3values and compute the sample variance.)b) Change the third mean to X3= 15. Notice that we have substantially increased the differencesamong 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 comparingthree treatment conditions. Use an analysis of variance with α = 0.05 to determine whether thesedata are sufficient to conclude that there are significant differences between the treatments.Treatment1 2 30 2 50 4 62 0 41 1 72 3 8PSY 201 2(4) The following data are constructed so that all three treatments have exactly the same mean.Treatment1 2 30 2 36 6 24 4 56 4 6a) Before you begin any calculations, predict what value should be obtained for SSB. (Hint:how big are the differences between treatments?)b) Calculate SSTand SSW. You should find that all of the variability in the data is within-treatments variability (SST= SSW).c) Complete the analysis of variance with α = 0.05 to determine whether there are any significantdifferences among the three treatments. (Does your answer agree with your prediction in parta?)(5) There is some evidence that high school students justify cheating in class on the basis of poorteacher skills or low levels of teacher caring (Murdock, Miller & Kohlhardt, 2004). Students appearto rationalize their illicit behavior based on perceptions of how their teachers view cheating. Poorteachers are thought not to know or care whether students cheat, so cheating in their classes isokay. Good teachers, on the other hand, do care and are alert to cheating, so students tend not tocheat in their classes. Following are hypothetical data similar to the actual research results. Thescores represent judgments of the acceptability of cheating for the students in each sample. Use anANOVA with α = 0.05 to determine whether there are significant differences in student judgmentsdepending on how they see their teachers.Poor teacher Average teacher Good teachernk6 8 10Xk6 2 2PiX2ik246 65 82(6) A developmental psychologist is examining the development of language skills from age 2 toage 5. Four different groups of children are obtained, one for each age, with n = 15 children ineach group. Each child is given a language skills assessment test. The resulting data were analyzedwith an ANOVA to test for mean differences between age groups. The results of the ANOVA arepresented in the following table. Fill in all the missing values (marked by “–”).Source SS df MS FBetween 81 – – –Within – – –Total 249 –PSY 201 3(7) The following data represent the results from an independent-measures study comparing twotreatment conditions.Treatment1 28 27 36 35 59 2nk5 5Xk7 3s2k2.5 1.5PiX2ik255 51a) Use an independent t test with α = 0.05 to determine whether there is a significant meandifference between the two treatments.b) Use an ANOVA with α = 0.05 to determine whether there is a significant mean differencebetween the two treatments.c) Compare the F statistic with the t2statistic.(8) A published report of a repeated measures research study includes the following description ofthe statistical analysis. “The results show significant differences among the treatment conditionsF (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 cancorrect the physical problem, people who have lived with hearing impairment often develop poorcommunication strategies and social skills. To address this problem, a home education programhas been developed to help people who are receiving hearing aids for the first time. The programemphasizes communication skills. To evaluate the program, overall quality of life and satisfactionwere measured before treatment and again at the end of the training program, and once more ata 6-month follow-up (Kramer et al., 2005). Data similar to the results obtained in the study areshown below. Do the data indicate a significant improvement in quality of life following the trainingprogram? Test with α = 0.05.Quality of Life ScoresPerson Before After 6-MonthsA 3 7 8B 0 5 7C 4 9 5D 1 7 4Tk8 28 24PiX2ik26 204 154PSY 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 gavebirth. The data showed an increase in pain thresholds as the pregnancy progressed. The changewas gradual until 1 or 2 days before birth, at which point there was an abrupt increase in painthreshold. Apparently a natural painkilling mechanism was preparing the animals for the stress ofgiving birth. The following data represent pain-threshold scores similar to the results obtained byGintzler. Do these data indicate a significant change in pain threshold? Use a repeated-measuresANOVA with α = 0.05.Days Before Giving BirthSubject 9 7 5 3 1A 35 39 41 49 52B 33 38 40 44 55C 39 41 44 47 57D 37 40 45 46 56E 36 37 40 44