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 homework is modelled off of a classic finding in cognitive psychology reported by Treisman and Gelade (1980). T&G had participants look perform a visual search task in which they were supposed to find a specific letter (i.e. a target) hidden amongst distracting letters. Sometimes the target would have a shape or color different from all of the distractors (i.e. it had a unique feature). Other times, the target would share the shape and colors of some of the distractors (i.e. there were common features). T&G were interested in how the number of letters in the display (i.e. display size) could influence the time it took participants to identify the target. They used 4 different display sizes: 1, 5, 15, and 30. Additionally, the targets only appeared on some of the trials.
Thus we have 3 factors: target features (unique or common), display size (1, 5, 15, or 30), and target presence (absent or present). Let's say there were 8 different people in each condition. If we wanted to summarize what type of ANVOA we were performing we could say factorial ANOVA or 3-way ANOVA. How else would many people who understand statistics describe the ANOVA we could use to analyze these data?
3 X 8
3 X 2 X 4 X 2
3 X 2 X 4
2 X 4 X 2
8 X 2 X 4 X 2
8

2. How many conditions were there?

3. How many people participated in the experiment?

4. How many degrees of freedom are there total?

5. How many degrees of freedom are there for the error?

6. How many degrees of freedom are there for the effect of target features?

7. How many degrees of freedom are there for the effect of display size?

8. How many degrees of freedom are there for the effect of target presence?

9. How many degrees of freedom are there for the interaction between target features and display size?

10. How many degrees of freedom are there for the interaction between target features and target presence?

11. How many degrees of freedom are there for the interaction between display size and target presence?

12. How many degrees of freedom are there for the interaction between target features, display size, and target presence?

13. How could you calculate the total sum of squares?
Subtract every score from the corresponding condition mean and sum the squared differences.
Subtract every score from the corresponding condition mean and square the summed differences.
Subtract every score from the grand mean and sum the squared differences.
Subtract every score from the grand mean and square the summed differences.
Subtract every condition mean from the grand mean and sum the squared differences.
Subtract every condition mean from the grand mean and square the summed differences.

14. How could you calculate the sum of squares for the error?
Subtract the corresponding condition mean from every score and sum the squared differences.
Subtract the corresponding condition mean from every score and square the summed differences.
Subtract the grand mean from every score and sum the squared differences.
Subtract the grand mean from every score and square the summed differences.
Subtract the grand mean from every condition mean and sum the squared differences.
Subtract the grand mean from every condition mean and square the summed differences.

15. How could you calculate the sum of squares for the main effect of target presence?
Subtract the grand mean mean from the mean of each level of the factor in question, and sum the squared differences.
Subtract the grand mean mean from the mean of each level of the factor in question, sum the squared differences, and multiply by 8.
Subtract the grand mean mean from the mean of each level of the factor in question, sum the squared differences, and multiply by 16.
Subtract the grand mean mean from the mean of each level of the factor in question, sum the squared differences, and multiply by 32.
Subtract the grand mean mean from the mean of each level of the factor in question, sum the squared differences, and multiply by 64.
Subtract the grand mean mean from the mean of each level of the factor in question, sum the squared differences, and multiply by 128.

16. How could you calculate the sum of squares for the main effect of display size?
Subtract the grand mean mean from the mean of each level of the factor in question, and sum the squared differences.
Subtract the grand mean mean from the mean of each level of the factor in question, sum the squared differences, and multiply by 8.
Subtract the grand mean mean from the mean of each level of the factor in question, sum the squared differences, and multiply by 16.
Subtract the grand mean mean from the mean of each level of the factor in question, sum the squared differences, and multiply by 32.
Subtract the grand mean mean from the mean of each level of the factor in question, sum the squared differences, and multiply by 64.
Subtract the grand mean mean from the mean of each level of the factor in question, sum the squared differences, and multiply by 128.

17. How could you calculate the sum of squares for the interaction between target presence and display size?
Subtract the grand mean mean from the mean of each combination of levels of the factors in question, and sum the squared differences.
Subtract the grand mean mean from the mean of each combination of levels of the factors in question, sum the squared differences, and subtract the sum of squares for each factor in the interaction.
Subtract the grand mean mean from the mean of each combination of levels of the factors in question, sum the squared differences, and multiply by 8.
Subtract the grand mean mean from the mean of each combination of levels of the factors in question, sum the squared differences, multiply by 8, and subtract the sum of squares for each factor in the interaction.
Subtract the grand mean mean from the mean of each combination of levels of the factors in question, sum the squared differences, and multiply by 16.
Subtract the grand mean mean from the mean of each combination of levels of the factors in question, sum the squared differences, multiply by 16, and subtract the sum of squares for each factor in the interaction.
Subtract the grand mean mean from the mean of each combination of levels of the factors in question, sum the squared differences, and multiply by 32.
Subtract the grand mean mean from the mean of each combination of levels of the factors in question, sum the squared differences, multiply by 32, and subtract the sum of squares for each factor in the interaction.
Subtract the grand mean mean from the mean of each combination of levels of the factors in question, sum the squared differences, and multiply by 64.
Subtract the grand mean mean from the mean of each combination of levels of the factors in question, sum the squared differences, multiply by 64, and subtract the sum of squares for each factor in the interaction.
Subtract the grand mean mean from the mean of each combination of levels of the factors in question, sum the squared differences, and multiply by 128.
Subtract the grand mean mean from the mean of each combination of levels of the factors in question, sum the squared differences, multiply by 128, and subtract the sum of squares for each factor in the interaction.

18. How could you calculate the sum of squares for the interaction between target presence and target feature?
Subtract the grand mean mean from the mean of each combination of levels of the factors in question, and sum the squared differences.
Subtract the grand mean mean from the mean of each combination of levels of the factors in question, sum the squared differences, and subtract the sum of squares for each factor in the interaction.
Subtract the grand mean mean from the mean of each combination of levels of the factors in question, sum the squared differences, and multiply by 8.
Subtract the grand mean mean from the mean of each combination of levels of the factors in question, sum the squared differences, multiply by 8, and subtract the sum of squares for each factor in the interaction.
Subtract the grand mean mean from the mean of each combination of levels of the factors in question, sum the squared differences, and multiply by 16.
Subtract the grand mean mean from the mean of each combination of levels of the factors in question, sum the squared differences, multiply by 16, and subtract the sum of squares for each factor in the interaction.
Subtract the grand mean mean from the mean of each combination of levels of the factors in question, sum the squared differences, and multiply by 32.
Subtract the grand mean mean from the mean of each combination of levels of the factors in question, sum the squared differences, multiply by 32, and subtract the sum of squares for each factor in the interaction.
Subtract the grand mean mean from the mean of each combination of levels of the factors in question, sum the squared differences, and multiply by 64.
Subtract the grand mean mean from the mean of each combination of levels of the factors in question, sum the squared differences, multiply by 64, and subtract the sum of squares for each factor in the interaction.
Subtract the grand mean mean from the mean of each combination of levels of the factors in question, sum the squared differences, and multiply by 128.
Subtract the grand mean mean from the mean of each combination of levels of the factors in question, sum the squared differences, multiply by 128, and subtract the sum of squares for each factor in the interaction.

19. How could you calculate the sum of squares for the interaction between target presence, display size, and target feature?
Subtract the grand mean mean from each condition mean, and sum the squared differences.
Subtract the grand mean mean from each condition mean, sum the squared differences and multiply by 8.
Subtract the grand mean mean from each condition mean, sum the squared differences, multiply by 8, and subtract the sum of squares for the main effects of each factor in the interaction.
Subtract the grand mean mean from each condition mean, sum the squared differences, multiply by 8, subtract the sum of squares for the main effects of each factor in the interaction, and subtract the sum of squares for each two-way interaction.
Subtract the grand mean mean from the mean of each level of each factor, and sum the squared differences.
Subtract the grand mean mean from the mean of each level of each factor, sum the squared differences and multiply by 8.
Subtract the grand mean mean from the mean of each level of each factor, sum the squared differences, multiply by 8, and subtract the sum of squares for the main effects of each factor in the interaction.
Subtract the grand mean mean from the mean of each level of each factor, sum the squared differences, multiply by 8, subtract the sum of squares for the main effects of each factor in the interaction, and subtract the sum of squares for each two-way interaction.

20. If the mean squares for the effect of display size was 12 and the mean squares for the error was 24, what would the observed F be?