Question

Problem Set 2: Two-way mixed design ANOVA (8 pts) Research Scenario: A researcher is attempting to determine the effects of age and sleep deprivation on a reaction time task. Participants (5 “old”; 5 “young”) in an experiment are given a computerized search task. They search a computer screen of various characters and attempt to find a particular character on each trial. When they find the designated character, they press a button to stop a timer. Their reaction time (in ms) on each trial is recorded (note, so the lower the number, the faster the time). Participants each underwent all three sleep conditions across three days - after having 0, 4, or 8 hours of sleep (times were counterbalanced). The reaction time data for the 10 participants appear below. Using this table, enter the data into a new SPSS data file and run the appropriate test to assess whether sleep deprivation and/or age affect performance on reaction time. Remember that between subjects variables such as “Age” will be represented using a single column in SPSS. Within subjects variables such as sleep would be represented in multiple columns – one per level. Hint: for this data entry, you will end up for a total of four columns in SPSS. Young Old 0 hours 12 11 13 12 12 10 11 12 11 11 4 hours 10 11 10 12 10 10 8 10 7 9 8 hours 7 10 5 9 7 12 6 12 7 11

9. Paste the relevant SPSS output, including post hocs if necessary. (2 pts)

10. Create the most appropriate graph for this data given the results. (2 pts)

11. Write an APA-style Results section based on your analysis. All homework “Results sections” should follow the examples provided in the presentations and textbooks. They should include the statistical statement within a complete sentence that mentions the type of test conducted, whether the test was significant, and if relevant, effect size and/or post hoc analyses. Don’t forget to include a decision about the null hypothesis. (4 pts)

Answer 1

Between-Subjects Factors 15 age old young 10 hours hour 0 hour 4 10 hour 8 Tests of Between-Subjects Effects Dependent Variable: time Type Ill Sum Sig df Mean Square Source of Squares 97.067 16.178 Corrected Model 19.413 Intercept 2960.133 2960.133 2466.778 22.533 22.533 18.778 age 21.433 17.861 hours 42.867 13.194 age* hours 31.667 15.833 Error 28.800 24 1.200 Total 30 3086.000 Corrected Total 125.867 29 a. R Squared771 (Adjusted R Squared.724)

All factors age , number of hours and interaction are signiificant
as their p-value = 0 < alpha

hence we reject the null hypothesis in each case

Post Hoc Tests hours Multiple Comparisons Dependent Variable: time LSD Mean Difference (l- J) 95% Confidence Interval Lower Bound Upper Bouno Std. Error Sig ( hours (J) hours 1.8000 001 2.8111 hour 0 hour 4 48990 7889 2.9000 48990 1.8889 3.9111 hour 8 1.8000 001 2.8111 hour 0 48990 .7889 hour 4 1.1000 034 0889 48990 hour 8 2.9000 hour 8 hour 0 48990 3.9111 1.8889 1.1000 0889 48990 034 hour 4 Based on observed means The error term is Mean Square(Error) = 1.200 . The mean difference is significant at the 0.05 level