Difference between a two-way amova and a three-way anova

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Reference no: EM13251073

Q 1. How many independent variables are in a 4 x 6 factorial design? How many conditions (cells) are in this design?

Q 2. What is the difference between a cell (condition) mean and the means used to interpret a main effect?

Q 3. What is the deference between a complete factorial design and an incomplete factorial design?

Q 4. Explain the difference between a two-way AMOVA and a three-way ANOVA.

Q 5. Complete each of the following ANOVA summary tables.  In addition, answer the following questions for each of the ANOVA summary

a. What is the factorial notion?

b. How many conditions were in the study

c. How many subjects were in the study?

d. Identify the significant main effects and interactions effects

Source                         df                     SS                    MS                   F

A                                 1                      60

B                                 2                      40

A x B                          2                      90

Error                            30

Total                            35                    390

 

Source                         df                     SS                    MS                   F

A                                 2                      40

B                                 3                      60

A x B                          6                      150

Error                            72

Total                            83                    400

 

Source                         df                     SS                    MS                   F

A                                 1                      10

B                                 1                      60

A x B                          1                      20

Error                            36

Total                            39                    150

Q 6. A researcher is attempting to determine the effects of practice and gender on a timed task.  Participants in and experiment are given a computerized search task.  They search computer screen of various characters and attempt to find a particular character on each trail.  When they find the designated character they press a button to stop a timer.  Their reaction time (in seconds) on each trail is recorded.  Subjects practice for 2, 4, or 6 hours and are either female of male.  The reaction time data for the 30 subjects appear here.

                        Women            Men

2 Hours           12                    11

                        13                    12

                        12                    13

                        11                    12

                        11                    11

4 Hours           10                    8

                        10                    8

                        10                    10

                        8                      10

                        7                      9

6 Hours           7                      5

                        5                      6

                        7                      8

                        6                      6

                        7                      8                     

Source                         df                     SS                    MS                   F

Gender                                                            0.027

Practice                                               140.60

Gender x Practice                               0.073

Error                                                    28.00

Total                                                    168.70

a. Complete the ANOVA summary Table.

b. Are the values of Fobt significant at a = 05?

At a = .01?

c. What conclusions can be drawn from the F-ratios?

d. What is the effect size, and what does this mean?

e. Graph the means.

Q 7. A 4 x 6 factorial design has to two independent variables. Thus, there is the possibility of two main effects (one for each independent variable) and one interaction effect (the interaction between the two independent variables)

a. This is 2 x 3 design.

Gender                                                Raw Means

Practice           Female                        Male                (Practice)                   

1 hour              1,778.125        1,763.375        1,770.75

2 hour              1,512.375        1,764.25          1,638.31

3 hours                        1,182.75          1,662               1,422.38

Column           1,491.08          1,729.88

means

(gender)

b. Two-way ANOVA Summary Table

Source                         df                     SS                    MS                   F

Factor A                      1                      684,264           684,264           9.68

(gender)

Factor B                      2                      989,504           494,752           7.00

(practice)

A x B                          2                      489,104           244, 552          3.46

Error                            42                    2,967,768        70,661.143

Total                            47                    5,130,640

c. Gender: F(1, 42) = 9.68,  p < .01

Practice: F(2,42) = 7.00, p < .01

Interaction: F(2, 42) = 3.46, p < .05

d. The significant main effect of gender indicates that females preformed more quickly than males.  The significant main effect of the practices that of practice indicates that as the amount of time spent practicing increased, reaction time decreased. The significant interaction effect indicates that practice affected only females; the more females increased practiced, the more quickly they responded.  However, practice did not affect males; reactions times, for males were consistent across the various practice conditions.

e. Eta-squared was .13 for gender, .19 for practice, and .095 for the interaction.  Thus, overall the proportion of variance in the dependent variable accounted for by the independent variables is .415 or 41.5%.

Q 8. Explain the difference between multiple independent variables and multiple levels of  independent variables. Which is better?

Q 9. What is blocking and how does it reduce "noise"? What is a disadvantage of blocking?

Q 10. What is a factor? How can the use of factors benefit a design?

Q 11. Explain main effects and interaction effects.

Q 12. How does a covariate reduce noise?

Q 13. Describe and explain three trade-offs present in experiments.

Reference no: EM13251073

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