Question

In: Statistics and Probability

3 6 4 8 1 10 2 9 11 12 15 22 3 6 7 5...

3 6 4 8 1
10 2 9 11 12
15 22 3 6 7
5 8 1 12 14

Each column represents a different treatment given to sick rats. Each cell is a different rat. Use statistical analysis and use post hoc testing using contrasts to find the best treatment.

Treatment 1: vitamins

Treatment 2: prescription pills

Treatment 3: brain surgery

Treatment 4: shock therapy

Treatment 5: dietary changes

Solutions

Expert Solution

Anova: Single Factor
SUMMARY
Groups Count Sum Average Variance
Column 1 ( vitamins ) 4 33 8.25 28.91666667
Column 2 ( prescription pills ) 4 38 9.5 75.66666667
Column 3 ( brain surgery ) 4 17 4.25 11.58333333
Column 4 ( shock therapy ) 4 37 9.25 7.583333333
Column 5 ( dietary changes ) 4 34 8.5 33.66666667
ANOVA
Source of Variation SS df MS F P-value F crit
Between Groups 72.7 4 18.175 0.577289571 0.683540644 3.055568
Within Groups 472.25 15 31.4833333
Total 544.95 19

Since we see that P-value of ANOVA test>0.05 so there is insufficient evidence that the 5 treatments are not all equal. Hence we can conclude that these 5 treatments are equally effective. Therefore we do not need to perform post hoc test.


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