Question

QUESTION 3

1. 1. A researcher wanted to study the effects of caffeine on ability to memorize a list of 16 non-related words. Additionally, the researcher was curious if extroverts or introverts would be better on the memory task and if caffeine would affect their performance differently. Given four equal conditions with 10 people in each condition, participants were either given a cup of coffee or not (depending on their condition). All participants had a 16-word list presented five times and their recall after a 3-minute delay was assessed. Given the following data summary, answer the following:

   		Factor A: Caffeinated
   		No Caffeine	Caffeine
   Factor B: Extroversion	Extrovert	n = 10 M = 13 T = 130 SS = 18	n = 10 M = 11 T = 110 SS = 36	TExtrovert =240 MExtrovert = 12
   	Introvert	n = 10 M = 14 T = 140 SS =18	n = 10 M = 9 T = 90 SS = 28	TIntrovert =230 MExtrovert=11.5
   		T No Caffeine =270	T Caffeine =200

   ∑X² = 5770, G = 470, N = 40

   1. What are all of the hypothesis for the above problem?
   2. What are all of the potential main effects for the above problem?
   3. List a potential interaction effect for the above problem?
   4. Using an α = 0.01 to evaluate the main effects and interaction (include all relevant steps and the critical value used for comparisons)
   5. Calculate the effect sizes for the main effects and the interaction
   6. Report the results using APA format. (Should include Means when describing each of the Main effects in the text.

Answer 1

Sol:

	SS	df	MS	F	P value	Fcrit
A	2.500	1	2.500	0.900	0.3490	4.113
B	122.500	1	122.500	44.096	0.0000	4.113
AB	22.500	1	22.500	8.099	0.0070	4.113
Error	100.000	36	2.778
Total	247.500	39

(d) The Hypothesis:

FACTOR A

H0: There is no difference in the means of Factor A

Ha: At least one of the means differs from the others.

FACTOR B

H0: There is no difference in the means of Factor B.

Ha: At least one of the means differs from the others.

INTERACTION

H0: There is no interaction between the two factors. They are independent.

Ha: There is an interaction between the two factors. They are not independent.

The Decision Rule:

The Critical Value Method: If F test is > F critical, Then Reject H0

P Value Method: If p value is < , Then Reject H0.

The Decision:

For Factor A

F test (0.009) is < F Critical (4.113), We Fail to Reject H0

P value (0.349) is > (0.01). We Fail to Reject H0

The Conclusion: There isn't sufficient evidence to conclude that at least one mean differs from the others.

For Factor B

F test (44.096) is > F Critical (4.113), We Reject H0

P value (0.000) is < (0.01). We Reject H0

The Conclusion: There is sufficient evidence to conclude that at least one mean differs from the others.

For Interaction

F test (8.099) is > F Critical (4.113), We Reject H0

P value (0.007) is < (0.01). We Reject H0

The Conclusion: There is sufficient evidence to conclude there is an interaction between the 2 factors.

The Effect Sizes:

= SS effect / SS Total - SS Other 2 effects

= SS A / SS Total - SS B - SS AB = 2.5 / (972.55 - 122.5- 22.5) = 0.003 (Small effect)

= SS B / SS Total - SS A - SS AB = 122.5 - (972.55 - 2.5 - 22.5) = 0.13 (Small Effect)

= SS AB / SS Total - SS A - SS B = 84.05 / (972.55 - 2.5 - 832.05 ) = 0.61 (Medium effect)

Conclusion:

Extroversion and caffeine might contribute to ability to memorize, but that effect may vary across different levels of extroversion or amount of caffeine. A two way ANOVA tested reaction time for 40 people with No Caffeine and Some caffeine and with Introverts and Extroverts..

Different levels of caffeine did not show a difference in memory power F(1,39) = 0.9, p = 0.349, = 0.003 which a small effect, Different levels of extroversion showed a significant difference in memory power F(1,36) = 44.096, p = 0.0000, = 0.13 which had a small effect. The interaction between Extroversion and Caffeine was also significant F(1,36) = 8.099, p = 0.007, = 0.61, the effect being medium at the most.