William H. Knapp III

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This homework was due on Monday, November 26 at 06:00 a.m. Turkish time. Late submissions receive half credit.

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1. This is the first homework that involves real data from a real experiment. Get the data, save it, set your working directory and load the data into R. Use str(data) to get a look at the data. Like the hypothetical data discussed in class today, these data come from a visual search task. Participants are looking for different objects (i.e. targets) and indicate whether the target was present or not. RT represents response times (i.e. the time it took to respond whether or not the target appeared). Targets were identified with either a pictorial or verbal cue. The type of cue for each observation is represented by QQ. DS represents display sizes (i.e. the number of objects that participants had to look through) and was one of three values: 6, 12, or 18. ET stands for encoding time (i.e. how much time they had to interpret the cue before the objects appeared). Participants could have 50, 100 , 200, 400, 800, 1600, or 3200 milleseconds to encode the cues. SS represents the 24 subjects that successfully completed the experiment. We won't use the SS factor for this homework, but we will see it again on Monday. Finally, MF represents sex (i.e. male or female). Although this last factor is made up, the rest of the data is real.
If you did a one-way ANOVA to see if there was an effect of sex, what would the sum of squares for that effect be?

2. What is the mean squares for the error term?

3. According to Tukey's HSDs, which mean sex performed searches more slowly (i.e. had greater RTs)?
Females.
Males.
The difference was not significant according to our Tukey test.

4. Unless I say otherwise, any factorial ANOVAs you run should contain the main effects and interactions between the variables of interest. For the two-way ANOVA involving cue type (i.e. factor QQ) and encoding time (i.e. factor ET), what was the value of the observed F-statistic for the effect of cue type?

5. What was the critical value of F to deem this effect significant at the alpha=.01 level?

6. Looking at the interaction between cue type and encoding time for an alpha of .01, what should you do?
Fail to reject the null.
Reject the null.
Not enough information to tell.

7. According to Tukey's HSDs, what is the adjusted p-value for the difference between pictorially cued trials for 50 and 100 milliseconds of encoding time?

8. What's the lower limit for the 99% confidence interval of the difference between verbally and pictorially cued trials with 50 milliseconds of encoding time when computed using Tukey's HSD?

9. What's the upper limit for the same confidence interval?

10. Use a factorial ANOVA to determine if any of the main effects or interactions involving cue type, target presence, and encoding time were significant. What is the value of F for the cue type by encoding time interaction?

11. What was the critical value of F to deem this effect significant at the alpha=.05 level?

12. What is the probability of observing an event as or more extreme as the observed 3-way interaction involving all three factors?

13. Since the three-way interaction was not significant, are we justified in using Tukey's HSD to investigate differences in means for different combinations of all three factors?
Yes.
No.
Not enough information to tell.

14. Since the two-way interaction was significant, are we justified in using Tukey's HSD to investigate differences in means for different combinations of the cue type and encoding time factors?
Yes.
No.
Not enough information to tell.

15. Use a factorial ANOVA to determine if any of the main effects or interactions involving cue type, target presence, encoding time, and display size were significant. What is the Mean of Squares for the 4-way interaction?

16. According to Tukey's HSD for the four way interaction you just looked at, what is the difference between verbally and pictorially cued trials when participants have 3200 milleseconds to encode the cues?
HINT: If you just say TukeyHSD(av), the information you want will probably disappear off your screen because so many means are being compared. I recommend you do something like the following thsd=TukeyHSD(av). You can use str(thsd) if you're interested in seeing how thsd is structured. If you specified QQ before ET in your model, you can get all the means for that interaction like this: thsd$'QQ:ET' . If you don't include the quotes, R will give you an error. If you specified ET first, then use thsd$'ET:QQ' . Of course, if you named your variables differently, you'll have to use your variable names instead.

17. What was the associated p-value for the observed difference?

18. What was the lower limit for the 95% confidence interval for the above difference?

19. What was the upper limit for the 95% confidence interval for the above difference?

20. Since 0 falls within the confidence interval, what should you do?
Fail to reject the null.
Reject the null.
Not enough information to tell.