Question

A cognitive psychologist is interested in examining how well people performed a task in relation to their perception of its difficulty. Three random samples are selected and are told they will be asked to solve some math problems. However, to influence their perceptions, the psychologist tells one of the samples that the problems are easy, in another that the problems are of medium difficulty, and another that the problems are difficult. Afterwards, all participants are asked to complete math problems that are actually easy and the number correctly solved is recorded. Below are the data. What can the psychologist conclude with ? = 0.05?

Easy	Medium	Difficult
4 12 4 9 10 8 7	4 6 8 2 9 6 5	1 3 4 2 2 3 2

b) Compute the appropriate test statistic(s) to make a decision about H₀.
critical value =  ; test statistic =  
Decision:  ---Select--- Reject H0 Fail to reject H0

c) Compute the corresponding effect size(s) and indicate magnitude(s).
?² =  ;  ---Select--- na trivial effect small effect medium effect large effect


e) Conduct Tukey's Post Hoc Test for the following comparisons:
2 vs. 3: difference =  ; significant:  ---Select--- Yes No
1 vs. 3: difference =  ; significant:  ---Select--- Yes No

Answer 1

critical value =3.5546 ; test statistic = 9.6944

Decision : Reject NULL HYPOTHESIS H0 .

SINCE CRITICAL VALUE IS SMALLER THAN CALCULATED VALUE OF F.

The overall effect size f = 0.9600 (LARGE EFFECT)
The effect size for EASY vs MEDIUM is f = 0.3601 small
The effect size for EASY vs DIFFICULT is f = 0.9508 large
The effect size for MEDIUM vs DIFFICULT is f = 0.5906 medium

e)

1 vs. 2: difference =2 .00 ; significant: No

2 vs. 3: difference = 3.2857 ; significant: Yes

1 vs. 3: difference = 5.2857 ; significant: Yes

NOTE: I USED SPSS AND EXCEL.