Question

*More than 2 dependent samples*

A cognitive psychologist was interested in the ability to solve puzzles. He selected 24 college sophomores and matched them on the basis of IQ and assigned, in groups of four, to one of four puzzle conditions (six blocks of four). He wants to make sure that all the puzzles are equally difficult. The dependent variable was the amount of time it took for a subject to complete the puzzle. The data are presented below. Were there differences in puzzle difficulty at the .05 level?

	Puzzle
Block	1	2	3	4
1	23	34	31	40
2	25	38	36	37
3	27	33	30	32
4	28	32	41	38
5	25	36	39	46
6	22	34	40	39

Answer 1

Null Hypothesis: The mean time of all four puzzle are same

Alternative Hypothesis: At least one has significant mean time.

Two-way ANOVA: Time_1 versus Block, Puzzle

Source	DF	SS	MS	F	P
Block	5	88.333	17.667	1.51	0.245
Puzzle	3	642.167	214.056	18.31	0.000
Error	15	175.333	11.689
Total	23	905.833

S = 3.419 R-Sq = 80.64% R-Sq(adj) = 70.32%

Conclusion: The estimated p-value of the puzzle treatment is 0.000 and less than 0.05 level of significance. Hence, we reject the null hypothesis and conclude that there are differences in puzzle difficulty at the .05 level of significance.