Question

Please note that for all problems in this course, the standard cut-off (alpha) for a test of significance will be .05, and you always report the exact power unless SPSS output states p=.000 (you’d report p<.001). Also, remember that we divide the p value in half when reporting one-tailed tests with 1 – 2 groups.

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

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

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

14. 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

General Linear Model: Response versus Time, Age Group

Method

Factor coding

(-1, 0, +1)

Factor Information

Factor	Type	Levels	Values
Time	Fixed	3	1, 2, 3
Age Group	Fixed	2	1, 2

Analysis of Variance

Source	DF	Adj SS	Adj MS	F-Value	P-Value
Time	2	42.87	21.433	17.86	0.000
Age Group	1	22.53	22.533	18.78	0.000
Time*Age Group	2	31.67	15.833	13.19	0.000
Error	24	28.80	1.200
Total	29	125.87

since we p-value for each factor and also for interaction effects are 0.00 which is less than level of significance 0.05 hence we reject null hypothesis in all the cases and conclude that there are significant differences between Times and Age groups and also the interaction effect is significant.