William H. Knapp III

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This homework was due on Monday, December 3 at 06:00 a.m. Turkish time. Late submissions receive half credit.

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1. Imagine you have a 3X7 Mixed design where the first factor varies between subjects. What is the minimum number of participants you need to conduct the corresponding ANOVA?
HINT: You need at least one degree of freedom for the error term for the between-subjects factor.
HINT: You need the same number of participants in each condition.

2. Imagine you have a 3X7 Mixed design where the first factor varies between subjects and you have 5 observations per condition. How many different error terms do you have?

3. Imagine you have a 3X7 Mixed design where the first factor varies between subjects and you have 5 observations per condition. How many degrees of freedom do you have for the effect of the between-subjects factor?

4. Imagine you have a 3X7 Mixed design where the first factor varies between subjects and you have 5 observations per condition. How many degrees of freedom do you have for the error term for the between-subjects factor?
HINT: How many participants do you have? How many degrees of freedom do you have for your participants in total?
HINT: How many of those degrees of freedom do you lose for the between-subjects factor of interest?

5. Imagine you have a 3X7 Mixed design where the first factor varies between subjects and you have 5 observations per condition. How many degrees of freedom do you have for the interaction between the two factors?

6. Imagine you have a 3X7 Mixed design where the first factor varies between subjects and you have 5 observations per condition. How many degrees of freedom do you have for the error term for the interaction between the two factors?
HINT: The error term comes from nesting subjects in the within-subjects factors only. Thus, the error term is the interaction between subjects and the within-subjects variable. HINT: The degrees of freedom for subjects has been reduced by the degrees of freedom for the between-subjects variables. In other words, the degrees of freedom for the 'subjects' is the degrees of freedom that you, hopefully, found for the error for the between-subjects factor.

7. Imagine you have a study with one dependent variable named DV and two independent variables named IV1 and IV2 from a group of subjects named SUB. If both of the independent variables varied betweeen subjects, what model should you specify for the ANOVA.
DV~IV1*IV2
DV~IV1*IV2+Error(SUB/IV1)
DV~IV1*IV2+Error(SUB/IV2)
DV~IV1*IV2+Error(SUB*IV1*IV2)
DV~IV1*IV2+Error(SUB/(IV1*IV2))

8. Imagine you have a study with one dependent variable named DV and two independent variables named IV1 and IV2 from a group of subjects named SUB. If both of the independent variables varied within subjects, what model should you specify for the ANOVA.
DV~IV1*IV2
DV~IV1*IV2+Error(SUB/IV1)
DV~IV1*IV2+Error(SUB/IV2)
DV~IV1*IV2+Error(SUB*IV1*IV2)
DV~IV1*IV2+Error(SUB/(IV1*IV2))

9. Imagine you have a study with one dependent variable named DV and two independent variables named IV1 and IV2 from a group of subjects named SUB. If only IV1 varied betweeen subjects, what model should you specify for the ANOVA.
DV~IV1*IV2
DV~IV1*IV2+Error(SUB/IV1)
DV~IV1*IV2+Error(SUB/IV2)
DV~IV1*IV2+Error(SUB*IV1*IV2)
DV~IV1*IV2+Error(SUB/(IV1*IV2))

10. Imagine you have a study with one dependent variable named DV and two independent variables named IV1 and IV2 from a group of subjects named SUB. If only IV2 varied betweeen subjects, what model should you specify for the ANOVA.
DV~IV1*IV2
DV~IV1*IV2+Error(SUB/IV1)
DV~IV1*IV2+Error(SUB/IV2)
DV~IV1*IV2+Error(SUB*IV1*IV2)
DV~IV1*IV2+Error(SUB/(IV1*IV2))

11. Imagine you have a study with one dependent variable named DV and four independent variables named IV1, IV2, IV3, and IV4 from a group of subjects named SUB. If all of the independent variables varied betweeen subjects, what model should you specify for the ANOVA.
DV~IV1*IV2*IV3*IV4
DV~IV1*IV2*IV3*IV4+Error(SUB/IV1)
DV~IV1*IV2*IV3*IV4+Error(SUB/IV2)
DV~IV1*IV2*IV3*IV4+Error(SUB/(IV1*IV2))
DV~IV1*IV2*IV3*IV4+Error(SUB/(IV3*IV4))
DV~IV1*IV2*IV3*IV4+Error(SUB/(IV1*IV3*IV4))
DV~IV1*IV2*IV3*IV4+Error(SUB/(IV2*IV3*IV4))
DV~IV1*IV2*IV3*IV4+Error(SUB/(IV1*IV2*IV3*IV4))

12. Imagine you have a study with one dependent variable named DV and four independent variables named IV1, IV2, IV3, and IV4 from a group of subjects named SUB. If all of the independent variables varied within subjects, what model should you specify for the ANOVA.
DV~IV1*IV2*IV3*IV4
DV~IV1*IV2*IV3*IV4+Error(SUB/IV1)
DV~IV1*IV2*IV3*IV4+Error(SUB/IV2)
DV~IV1*IV2*IV3*IV4+Error(SUB/(IV1*IV2))
DV~IV1*IV2*IV3*IV4+Error(SUB/(IV3*IV4))
DV~IV1*IV2*IV3*IV4+Error(SUB/(IV1*IV3*IV4))
DV~IV1*IV2*IV3*IV4+Error(SUB/(IV2*IV3*IV4))
DV~IV1*IV2*IV3*IV4+Error(SUB/(IV1*IV2*IV3*IV4))

13. Imagine you have a study with one dependent variable named DV and four independent variables named IV1, IV2, IV3, and IV4 from a group of subjects named SUB. If only IV1 varied between subjects, what model should you specify for the ANOVA.
DV~IV1*IV2*IV3*IV4
DV~IV1*IV2*IV3*IV4+Error(SUB/IV1)
DV~IV1*IV2*IV3*IV4+Error(SUB/IV2)
DV~IV1*IV2*IV3*IV4+Error(SUB/(IV1*IV2))
DV~IV1*IV2*IV3*IV4+Error(SUB/(IV3*IV4))
DV~IV1*IV2*IV3*IV4+Error(SUB/(IV1*IV3*IV4))
DV~IV1*IV2*IV3*IV4+Error(SUB/(IV2*IV3*IV4))
DV~IV1*IV2*IV3*IV4+Error(SUB/(IV1*IV2*IV3*IV4))

14. Imagine you have a study with one dependent variable named DV and four independent variables named IV1, IV2, IV3, and IV4 from a group of subjects named SUB. If only IV1 varied within subjects, what model should you specify for the ANOVA.
DV~IV1*IV2*IV3*IV4
DV~IV1*IV2*IV3*IV4+Error(SUB/IV1)
DV~IV1*IV2*IV3*IV4+Error(SUB/IV2)
DV~IV1*IV2*IV3*IV4+Error(SUB/(IV1*IV2))
DV~IV1*IV2*IV3*IV4+Error(SUB/(IV3*IV4))
DV~IV1*IV2*IV3*IV4+Error(SUB/(IV1*IV3*IV4))
DV~IV1*IV2*IV3*IV4+Error(SUB/(IV2*IV3*IV4))
DV~IV1*IV2*IV3*IV4+Error(SUB/(IV1*IV2*IV3*IV4))

15. Imagine you have a study with one dependent variable named DV and four independent variables named IV1, IV2, IV3, and IV4 from a group of subjects named SUB. If only IV1 and IV2 varied between subjects, what model should you specify for the ANOVA.
DV~IV1*IV2*IV3*IV4
DV~IV1*IV2*IV3*IV4+Error(SUB/IV1)
DV~IV1*IV2*IV3*IV4+Error(SUB/IV2)
DV~IV1*IV2*IV3*IV4+Error(SUB/(IV1*IV2))
DV~IV1*IV2*IV3*IV4+Error(SUB/(IV3*IV4))
DV~IV1*IV2*IV3*IV4+Error(SUB/(IV1*IV3*IV4))
DV~IV1*IV2*IV3*IV4+Error(SUB/(IV2*IV3*IV4))
DV~IV1*IV2*IV3*IV4+Error(SUB/(IV1*IV2*IV3*IV4))

16. Imagine you have a study with one dependent variable named DV and four independent variables named IV1, IV2, IV3, and IV4 from a group of subjects named SUB. If only IV1 and IV2 varied within subjects, what model should you specify for the ANOVA.
DV~IV1*IV2*IV3*IV4
DV~IV1*IV2*IV3*IV4+Error(SUB/IV1)
DV~IV1*IV2*IV3*IV4+Error(SUB/IV2)
DV~IV1*IV2*IV3*IV4+Error(SUB/(IV1*IV2))
DV~IV1*IV2*IV3*IV4+Error(SUB/(IV3*IV4))
DV~IV1*IV2*IV3*IV4+Error(SUB/(IV1*IV3*IV4))
DV~IV1*IV2*IV3*IV4+Error(SUB/(IV2*IV3*IV4))
DV~IV1*IV2*IV3*IV4+Error(SUB/(IV1*IV2*IV3*IV4))

17. This is the third homework that involves real data from a real experiment. Get the data, save it, set your working directory and load the data into R. Feel free to look back at the last homework if you want more information about the different factors. Here' is a quick summary of the data we'll be dealing with today.
RT: Response Times, the dependent variable.
TP: Target Presence
DS: Display Size
ET: Encoding Time
QQ: Cue type
SS: Subject
MF: Sex (a between-subjects factor that did not occur in the original experiment)
Perform a Mixed ANOVA investigating all of the factors and their interactions. What's the value of the F statistic for the interaction of all the factors?

18. Looking at the interaction of all the factors with an alpha of .05, what should you do?
Fail to reject the null.
Reject the null.
Not enough information to tell.

19. What's the value of the F-statistic for the interaction between sex, target presence, and cue type?

20. What's the value of the F-statistic for the main effect of sex?