Question

Data is collected from a completed randomized design for comparing two treatments A and B:

A: 25, 24, 22
B: 27, 30, 29

The experimenter is interested in finding out if treatment B is better than treatment A. Find the p-values using both the randomization test and the t-test and then make a conclusion (alpha = 0.05)

Answer 1

I used MINITAB software to solve this question. Go through following steps:

Step.1 Enter data in minitab as shown in screen shot.

Step.2 Go to ‘Stat’ menu ---> ‘ANOVA’ ---> ‘One way ANOVA’. Select '' Comparison' option on that window. Select 'Tukey Test'.

Step.3 Refer following screen shot and enter information accordingly.

Minitab output:

Method

Null hypothesis All means are equal
Alternative hypothesis At least one mean is different
Significance level α = 0.05

Equal variances were assumed for the analysis.

Factor Information

Factor Levels Values
Factor 2 A, B

Analysis of Variance

Source DF Adj SS Adj MS F-Value P-Value
Factor 1 37.500 37.500 16.07 0.016
Error 4 9.333 2.333
Total 5 46.833

Model Summary

S R-sq R-sq(adj) R-sq(pred)
1.52753 80.07% 75.09% 55.16%

Means

Factor N Mean StDev 95% CI
A 3 23.667 1.528 (21.218, 26.115)
B 3 28.667 1.528 (26.218, 31.115)

Pooled StDev = 1.52753

Tukey Pairwise Comparisons

Grouping Information Using the Tukey Method and 95% Confidence

Factor N Mean Grouping
B 3 28.667 A
A 3 23.667 B

Means that do not share a letter are significantly different.

P-value for randomized test = 0.016

For performing t test, go to 'Stat' ---> 'Basic statistics' -----> Select 'Two sample t test'. New window pop-up on screen enter information according to following screen shot.

Minitab optput:

Two-Sample T-Test and CI: A, B

Two-sample T for A vs B

N Mean StDev SE Mean
A 3 23.67 1.53 0.88
B 3 28.67 1.53 0.88

Difference = μ (A) - μ (B)
Estimate for difference: -5.00
95% upper bound for difference: -2.34
T-Test of difference = 0 (vs <): T-Value = -4.01 P-Value = 0.008 DF = 4

P-value for t test is 0.008.

Since p-value is less than 0.05, we reject null hypothesis and conclude that treatment B is better than treatment A.