Question

"Three Sample ANOVA QB"

Researcher wants to compare test performance for tests printed on three different colors of paper; Red, Green, and the Standard White. The researcher selects a sample of 11 individuals and has each individual take one test on Red paper, another test on Green paper, and a third test on the Standard White paer. The data are listed below. The researcher wants to minimize the probability of making a Type I error.

   Red Green White   
90 88 86
89 87 85
88 86 84
87 85 83
86 84 82
85 83 81
84 82 80
83 81 76
82 80 78
81 79 77
    80 78 79   

Means 85 83 81 Grand Mean = 83

2)What is the correct observed test statistic value for this statistical test of the means (Round to two decimal places)?

3) What is the correct critical value for this statistical test of the means?

6) conduct post-hoc analysis using Tukey’s HSD. What is the critical value?

7)what is the value of Tukey’s HSD for comparing Red paper to Green paper (Round to two decimal places)?

8)what is the value of Tukey’s HSD for comparing Red paper to White paper (Round to two decimal places)?

9)what is the value of Tukey’s HSD for comparing Green paepr to White paper (Round to two decimal places)?

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’

Step.3 New window will-pop on screen. Refer following screen shot and enter information accordingly.

Minitab output:

One-way ANOVA: Red, Green, White

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 3 Red, Green, White

Analysis of Variance

Source DF Adj SS Adj MS F-Value P-Value
Factor 2 88.00 44.00 4.00 0.029
Error 30 330.00 11.00
Total 32 418.00

Model Summary

S R-sq R-sq(adj) R-sq(pred)
3.31662 21.05% 15.79% 4.47%

Means

Factor N Mean StDev 95% CI
Red 11 85.00 3.32 (82.96, 87.04)
Green 11 83.00 3.32 (80.96, 85.04)
White 11 81.00 3.32 (78.96, 83.04)

Pooled StDev = 3.31662

Tukey Pairwise Comparisons

Grouping Information Using the Tukey Method and 95% Confidence

Factor N Mean Grouping
Red 11 85.00 A
Green 11 83.00 A B
White 11 81.00 B

Means that do not share a letter are significantly different.

Que.2

Observed test statistic,

F = 4.00

Que.3

The correct critical value for this statistical test of the means is F_2,30 at 5% level of significance is 3.3158

[ This value is not given in the minitab output, this is find using F table ]

Que.6

Critical value for Tukey’s HSD is 3.49

[ This value is not given in the minitab output, this is find using critical table ]