Question

1. Neuroscience researchers examined the impact of environment on rat development. Rats were randomly assigned to be raised in one of the four following test conditions: Impoverished (wire mesh cage - housed alone), standard (cage with other rats), enriched (cage with other rats and toys), super enriched (cage with rats and toys changes on a periodic basis). After two months, the rats were tested on a variety of learning measures (including the number of trials to learn a maze to a three perfect trial criteria), and several neurological measure (overall cortical weight, degree of dendritic branching, etc.). The data for the maze task is below.

Impoverished	Standard	Enriched	Super Enriched
23	18	12	9
19	21	14	7
15	15	11	11
24	13	9	9
19	19	15	12
26	15	14	8
24	18	12	9

a. Carry out the appropriate statistical analysis using SPSS to test whether the levels are different. Please provide me an annotated copy of your output. Was the assumption of homogeneity of variance met? Explain.

2. What does the analysis tell you about the null hypothesis?

c. If relevant use one or more post hoc tests, which means were different to which? Explain.

Answer 1

Result:

1. Neuroscience researchers examined the impact of environment on rat development. Rats were randomly assigned to be raised in one of the four following test conditions: Impoverished (wire mesh cage - housed alone), standard (cage with other rats), enriched (cage with other rats and toys), super enriched (cage with rats and toys changes on a periodic basis). After two months, the rats were tested on a variety of learning measures (including the number of trials to learn a maze to a three perfect trial criteria), and several neurological measure (overall cortical weight, degree of dendritic branching, etc.). The data for the maze task is below.

Impoverished	Standard	Enriched	Super Enriched
23	18	12	9
19	21	14	7
15	15	11	11
24	13	9	9
19	19	15	12
26	15	14	8
24	18	12	9

a. Carry out the appropriate statistical analysis using SPSS to test whether the levels are different. Please provide me an annotated copy of your output. Was the assumption of homogeneity of variance met? Explain.

The Levenes test based on median, test value 1.298, P=0.298 which is > 0.05 level of significance. The assumption of homogeneity of variance is met.

1. What does the analysis tell you about the null hypothesis?

Calculated F=26.484, P=0.000 which is < 0.05 level of significance. Ho is rejected. we conclude that at least one mean is significantly different from others.

c. If relevant use one or more post hoc tests, which means were different to which? Explain.

Tukey test shows:

Impoverished is significant from other three groups Standard, Enriched and Super Enriched.

Standard is significant from groups Enriched and Super Enriched.

Enriched and Super Enriched are not significant.

SPSS output:

Descriptives
Score
	N	Mean	Std. Deviation	Std. Error	95% Confidence Interval for Mean	Minimum	Maximum
Lower Bound	Upper Bound
Impoverished	7	21.4286	3.86683	1.46152	17.8523	25.0048	15.00	26.00
Standard	7	17.0000	2.76887	1.04654	14.4392	19.5608	13.00	21.00
Enriched	7	12.4286	2.07020	0.78246	10.5140	14.3432	9.00	15.00
Super Enriched	7	9.2857	1.70434	0.64418	7.7095	10.8620	7.00	12.00
Total	28	15.0357	5.34362	1.00985	12.9637	17.1078	7.00	26.00

Test of Homogeneity of Variances
	Levene Statistic	df1	df2	Sig.
Score	Based on Mean	3.128	3	24	0.044
Based on Median	1.298	3	24	0.298
Based on Median and with adjusted df	1.298	3	16.417	0.309
Based on trimmed mean	3.037	3	24	0.049

ANOVA
Score
	Sum of Squares	df	Mean Square	F	Sig.
Between Groups	592.107	3	197.369	26.484	0.000
Within Groups	178.857	24	7.452
Total	770.964	27

Multiple Comparisons
Dependent Variable:   Score
	(I) Group	(J) Group	Mean Difference (I-J)	Std. Error	Sig.	95% Confidence Interval
	Lower Bound	Upper Bound
Tukey HSD	Impoverished	Standard	4.42857*	1.45920	0.027	0.4032	8.4539
Enriched	9.00000*	1.45920	0.000	4.9747	13.0253
Super Enriched	12.14286*	1.45920	0.000	8.1175	16.1682
Standard	Impoverished	-4.42857*	1.45920	0.027	-8.4539	-0.4032
Enriched	4.57143*	1.45920	0.022	0.5461	8.5968
Super Enriched	7.71429*	1.45920	0.000	3.6889	11.7396
Enriched	Impoverished	-9.00000*	1.45920	0.000	-13.0253	-4.9747
Standard	-4.57143*	1.45920	0.022	-8.5968	-0.5461
Super Enriched	3.14286	1.45920	0.165	-0.8825	7.1682
Super Enriched	Impoverished	-12.14286*	1.45920	0.000	-16.1682	-8.1175
Standard	-7.71429*	1.45920	0.000	-11.7396	-3.6889
Enriched	-3.14286	1.45920	0.165	-7.1682	0.8825
*. The mean difference is significant at the 0.05 level.