Question

Problem #1: Let’s examine how well people perform at task depending on how difficult they believe the task will be (“perceived difficulty” of the task). We randomly select three samples containing the un-powerful n of 5 participants each and provide them with the same 10 easy math problems. However, to influence their perceptions, we tell the participants in level 1 that the problems are easy, in level 2 that the problems are of medium difficulty, and in level 3 that the problems are difficult. The dependent measure is the number of problems that participants correctly solve within an allotted time.

Data form Perceived Difficulty Experiment

Facto A: perceived difficulty
Level :        easy	Level : medium	Level : difficult
9	4	1
12	6	3
4	8	4
8	2	5
7	10	2

1.    Compute this one-way ANOVA problem by hand using the definitional formula.

2.    What do you conclude about the differences related to the perceived difficulty

3.    Compute Tukey’s HSD

4.    Compute the confidence intervals

5.    Compute the effect size

Answer 1

Hypothesis:

Ho: All the mean are equal.

H1: Not all the mean are equal.

1)

One-way ANOVA: Y versus problem

Source	DF	SS	MS	F	P
problem	2	63.33	31.67	4.52	0.034
Error	12	84	7
Total	14	147.33

S = 2.646 R-Sq = 42.99% R-Sq(adj) = 33.48%

2) The estimated p-value is 0.034 and less than 0.05 level of significance. Hence, reject the null hypothesis and conclude that there has at least one-factor level which has the significant different mean for the number of problems that participants correctly solve within an allotted time at 0.05 level of significance.

3) Tukey’s HSD=q(0.05, 3, 12) = q(0.05, 3, 15-3) 3.77

4)

5.    Compute the effect size

ANS: Effect Size=Sum od Square Factor/Total sum of Square=  63.33 /147.33 = 0.4299