Question

1. A cognitive psychologist was interested in the ability to solve puzzles. They selected 24 college sophomores and matched them on the basis of IQ and assigned them, in groups of four, to one of four puzzle conditions (six blocks of four). The psychologist 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? Make sure to complete a 6-step hypothesis test. Puzzle Block 1 2 3 4 1 23 34 31 40 2 2538 36 37 3 2733 30 32 4 28 32 41 38 5 25 36 39 46 6 22 34 40 39

Answer 1

Result:

To test the puzzle conditions effect,

Ho: µ1= µ2= µ3= µ4

H1: At least one of the mean is different from the others

Critical value F(3,15) = 3.29

Calculated F=18.31 which is > critical F value 3.29.

Ho is rejected.

We conclude that there is differences in puzzle difficulty at 0.05 level of significance.

To test the block effect,

Ho: µ1= µ2= µ3= µ4= µ5= µ6

H1: At least one of the mean is different from the others

Critical value F(5,15) = 2.90

Calculated F=1.51 which is < critical F value 2.90.

Ho is not rejected.

We conclude that there is no block effect.

Excel used for calculations.

Randomized Block Design (ANOVA: Two-Factor Without Replication)
SUMMARY	Count	Sum	Average	Variance
B1	4	128	32.0000	50.0000
B2	4	136	34.0000	36.6667
B3	4	122	30.5000	7.0000
B4	4	139	34.7500	34.2500
B5	4	146	36.5000	76.3333
B6	4	135	33.7500	68.2500
Puzzle1	6	150	25.0000	5.2000
Puzzle2	6	207	34.5000	4.7000
Puzzle3	6	217	36.1667	22.1667
Puzzle4	6	232	38.6667	20.6667
ANOVA
Source of Variation	SS	df	MS	F	P-value	F crit
Rows ( Block)	88.3333	5	17.6667	1.5114	0.2448	2.9013
Columns( Puzzle)	642.1667	3	214.0556	18.3127	0.0000	3.2874
Error	175.3333	15	11.6889
Total	905.8333	23
				Level of significance	0.05