Question

Using SAS

An experiment was conducted to investigate the effects of environment and strain on the performance of rats in a maze test. Three strains of rats were studies under two environmental conditions. The error scores for the 24 rates were recorded. Test by the significant level a .10 Do the data provide sufficient evidence to indicate that the mean error scores lof the rats under free environment is significantly greater than the mean error scores of the rats under Restricted environment. 1) Perform one-way ANOVA comparing the mean error scores of the rats among the three types of strain. Perform a scheffe's multiple comparison. Create a contrast to compare the mean error scores of Dull against the mean of Bright and Mixed. 2) Perform two-way analysis of variance comparing the mean error scores of the rats among the three types of strain and two environmental conditions. Perform duncan's multiple comparisons. And make two-way interaction plots. 3) Strain Environment Bright Mixed Dul 28 33 101 22 38 33 541 122 36 2235 72 60 136 Free 35 38 Restricted46 25 83 64 71 9987

Answer 1

a)

Two-sample T for the score

Environment N Mean StDev SE Mean
Free 12 44.7 32.1 9.3
Restricted 12 68.0 31.0 9.0

Difference = mu (Free) - mu (Restricted)
Estimate for difference: -23.3
95% lower bound for difference: -45.5
T-Test of difference = 0 (vs >): T-Value = -1.81 P-Value = 0.958 DF = 22
Both use Pooled StDev = 31.5815

The estimated p-value is 0.958 and more than 0.10 level of significance. Hence, retain the null hypothesis and conclude that mean error score of the rate under free environment is not significantly greater the mean error score of rate under Restricted.

b)

Tests of Between-Subjects Effects
Dependent Variable:Score
Source	Type III Sum of Squares	df	Mean Square	F	Sig.
Corrected Model	5587.583a	2	2793.792	2.990	.072
Intercept	76162.667	1	76162.667	81.512	.000
Strain	5587.583	2	2793.792	2.990	.072
Error	19621.750	21	934.369
Total	101372.000	24
Corrected Total	25209.333	23

Comment: The estimated p-value of treatment Strain is 0.072. Hence, it has the significant effect at 0.10 level of significance and concludes that at least one mean error score strain has a significant difference from other error means at 0.10 level of significance.

From the above table, the estimated p-value of Dull and Bright is 0.081. Hence, the mean error score between the Dull and Bright have a significant difference at 0.10 level of significance. Whereas, the estimated p-value of Dull and Mixed is 0.267. Hence, the mean error score between the Dull and Bright have an insignificant difference at 0.10 level of significance.

c)

Comment: The p-values of Starin and environment are 0.053 and 0.059 respectively. Hence, both the treatments have the significant effect on the error score.

From the Duncan test, we can conclude that Bright and Dull has significant mean error scores at 0.10 level of significance.

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From this interaction plot, we can conclude that there is no interaction between the strain and the environment.