Question

Ad Lib Cntrol	Two per Day Control	Food Deprived	Water Deprived	Food and Water Deprived
18	20	6	15	12
20	25	9	10	11
21	27	8	9	8
16	23	6	12	13
15	25	11	14	11
90	120	40	60	55

Data represent the effects of food and/or water deprivation on behavior. Treatments 1 and 2 represent control conditions; animal received ad lib food and water (1) or else food and water twice per day (2). In treatment 3 animals were food deprived, in treatment 4 they were water deprived, and in treatment 5 they were deprived of both food and water. The dependent variable is the number of trials to reach a predetermined criterion. Assume we compared the combined control groups (treatments 1 and 2) with the combined experimental groups, the control groups with each other, the singly deprived treatments with the doubly deprived treatment, and the singly deprived treatments with each other

1. Fill out the table below based on the comparisons (linear contrasts)

Groups	Ad Lib Cntrol	Two per Day Control	Food Deprived	Water Deprived	Food and Water Deprived	Sum aj	Sum a^2j	Omega= Sum(ajX-barj)
Sample Means
aj
bj
cj
dj

2. Compute:

Sum ajbj

Sum ajcj

Sum ajdj

Sum bjcj

Sum bjdj

Sum cjdj

Are the four contrasts orthogonal? Explain.

3. Use the results of your computations for part a) to complete the following table.

Source	df	SS	MS	F	Sig (Y or N)
Treatments
Contrast 1
Contrast 2
Contrast 3
Contrast 4
Error
Total

4. Interpret the results for Contrast 1.
5. Taking into account all four contrasts, what do the results tell us about the effect of food/ water deprivation on the learning task?

Answer 1

• If two groups of equal size are to be compared, assign coefficients of +1 to the members of one group and -1 to those of the other group. It does not matter which group is assigned the positive coefficient.
• In comparing groups containing different numbers of treatments, assign to the first group, coefficients equal to the number of treatments in the second group, and to the second group, coefficients of the opposite sign equal to the number of treatments in the first group.

Table

Groups	Ad Lib Cntrol	Two per Day Control	Food Deprived	Water Deprived	Food and Water Deprived	Sum aj	Sum a^2j	Omega= Sum(ajX-barj)
Sample Means	30	40	13.3333	20	18.3333
aj	3	3	-2	-2	-2	0	30	106.6668
bj	1	-1	0	0	0	0	2	-10
cj	0	0	1	1	-2	0	6	-3.3333
dj	0	0	1	-1	0	0	2	-6.6667
aj^2	9	9	4	4	4		30
bj^2	1	1	0	0	0		2
cj^2	0	0	1	1	4		6
dj^2	0	0	1	1	0		2

Contrast 1	the combined control groups (treatments 1 and 2) with the combined experimental groups
Contrast 2	the control groups with each other
Contrast 3	the singly deprived treatments with the doubly deprived treatment
Contrast 4	the singly deprived treatments with each other

Sum ajbj	0
Sum ajcj	0
Sum ajdj	0
Sum bjcj	0
Sum bjdj	0
Sum cjdj	0

All summations equal to zero. Therefore, all contrasts are orthogonal to each other.

18	20	6	15	12	144	400	53.772889	25	40.11069
20	25	9	10	11	100	225	18.774889	100	53.77729
21	27	8	9	8	81	169	28.440889	121	106.7771
16	23	6	12	13	196	289	53.772889	64	28.44409
15	25	11	14	11	225	225	5.442889	36	53.77729
90	120	40	60	55	3600	6400	711.12889	1600	1344.447
					4346	7708	871.33333	1946	1627.333
Source	df	SS	MS	F	Sig (Y or N)
Treatments							qf(0.025,1,25)
Contrast 1	1	75.85204	75.85204	0.114937	Yes		0.0010019
Contrast 2	1	150	150	0.227291	Yes		0.0010019
Contrast 3	1	1.851815	1.851815	0.002806	Yes		0.0010019
Contrast 4	1	66.66733	66.66733	0.101019	Yes		0.0010019
Error	25	16498.67	659.9467
Total	29

All contrasts are significant.