Name:_____________________________ HP340: Statistical Methods, Fall 2016 Due Date: Nov 9, 2016 Homework #7 Instructions: Clearly circle the letter of the best answer for multiple-choice questions and show your work when calculations are required. Where necessary, please explain your reasoning for the approach you used. 1. In a one-factor between-subjects analysis of variance, the F statistic is defined as ________. (1 point) a. MSA / dfError b. MSTotal / MSError c. SSA / dfA d. MSA / MSError e. SSError / dfError 2. SSA and SSError are also called ___________ and ____________ sums of squares, respectively. (1 point) a. between groups; mean groups b. within groups; between groups c. between groups; within groups d. none of the above 3. If SStotal = 50, SSA = 30, SSError = 20, dftotal = 25, dfA = 15, and dfError = 10 in a one-factor between-subjects analysis of variance, then MSError=_____ (1 point) a. 1.43 b. 0.83 c. 2.08 d. 2.14 e. 2.00 4. For the data provided above, what are the values of Fobs and Fcrit (assume =0.05) (4 points: show your work) a. 1.0; 2.54 b. 2.0; 2.54 c. 1.0; 2.85 d. 2.0; 2.85 e. a or c 5. Fill in the missing cells (denoted with ?) in the following ANOVA table: (8 points: show your work) SS df MS F Between Groups 100 4 ? ? Within Groups 135 45 ? Total ? ? 6. For the completed table above: a. How many levels of factor A are there? b. How many subjects are there for each group? c. What is the total number of subjects in the study? d. Is Fobs significant for =0.05? 7. The napping times of preschool, kindergarten, and 1st grade students are shown in the table below (in minutes). (34 points total) Preschool 30 20 25 22 23 (5 points) 1st Grade 15 12 13 15 17 Kindergarten 15 19 17 17 20 a. (2 points) State the null and alternative hypotheses to determine if there is difference in the napping times of the students in the three levels of school. b. (20 points) Showing all of your work, construct an ANOVA table and find Fobs \"by hand\". SS df MS Between Groups Within Groups Total c. (4 points) What is your decision regarding the hypotheses stated in a. for =0.01? What is your conclusion from the test? d. (8 points) Calculate the Tukey CD and interpret the pairwise comparisons. The SPSS file posted on BlackBoard (HW7.data.sav) contains scores from an experiment examining the effects of different doses of a new drug on levels of depression in a patient population. The drug as has a side effect: it may increase anxiety. Thus, this experiment also tests the effects of the drug on levels of anxiety. In this experiment, there is one betweensubjects factor (drug dose), and two dependent variables. Because it has two dependent variables, you'll have to run two different ANOVAs. Use this data file to answer Questions 8- 11, and the extra credit. For each question, be sure to copy-and-paste the relevant SPSS output used to answer the question, and write an informative and complete conclusion statement. Use =.05 for both questions. 8. Is there a significant effect of drug on mean depression scores? 9. If there is a significant drug effect on depression, which doses are different than placebo? (15 points) 10. Is there a significant effect of drug on mean anxiety scores? (15 points) (15 points) 11. If there is a significant drug effect on anxiety, which doses are different than placebo? (15 points) Extra Credit: Based on the findings above, which dose (or doses) would you recommend to both decrease depression and not increase anxiety? Provide the rationale for your choice. (10 points) $FL2@(#) IBM SPSS STATISTICS 64-bit Macintosh 22.0.0.0 ################P#########Y@01 Nov 1612:27:20 ###########################PATIENTI########################DRUGDOSE############# ###########DEPRESSI########################ANXIETY #################Placebo######?#5 mg #######@#10 mg #######@#20 mg ######################################################################### ############ ####################################################### #######H###PATIENTI=PatientID DRUGDOSE=DrugDose DEPRESSI=Depression ANXIETY=Anxiety########################P###################Y###PatientID: $@Role('0' )/DrugDose:$@Role('0' )/Depression:$@Role('0' )/Anxiety:$@Role('0' ) #######edvfdu}gdthdvidtjdtkdxldvmdwndxodxpdtqdvrdtsdwtdv}udx}vdv~ wdxxdvyeszex{ev| et}ev~evewetexeuetev}erexeveuexeuerevfrftfs} frft{fpfqfqftfq{ftftfp~frfqfsfsftfrfqgqgngr gngpgpgqgpgqgngogqgqgqgogrgpgqgngn