Solution to Exercise 10.42.

  I entered the data by hand into Minitab. Here is the data as it appears in the worksheet:

IColor cff

1 26.8

1 27.9

1 23.7

1 25.0

1 26.3

1 24.8

1 25.7

1 24.5

2 26.4

2 24.2

2 28.0

2 26.9

2 29.1

3 25.7

3 27.2

3 29.9

3 28.5

3 29.4

3 28.3

The results of ANOVA:

One-way Analysis of Variance

Analysis of Variance for cff     
Source     DF        SS        MS        F        P
IColor      2     23.00     11.50     4.80    0.023
Error      16     38.31      2.39
Total      18     61.31
                                   Individual 95% CIs For Mean
                                   Based on Pooled StDev
Level N     Mean   StDev  --------+---------+---------+--------
1     8   25.587   1.365   (-------*------) 
2     5   26.920   1.843          (--------*---------) 
3     6   28.167   1.528                   (--------*--------) 
                          --------+---------+---------+--------
Pooled StDev =    1.547          25.5      27.0      28.5

Tukey's pairwise comparisons

    Family error rate = 0.0500
Individual error rate = 0.0201

Critical value = 3.65

Intervals for (column level mean) - (row level mean)

                 1           2

       2      -3.609
               0.944

       3      -4.736      -3.665
              -0.422       1.172

The plots appear here:

(1)

Boxplots.

(2)

Dotplots.

(3)

Residual plot.

The dotplots and residual plots suggest that the variances within the eye color groups are about the same. The within group standard deviations range from 1.365 to 1.843, and so are about the same. The normal probability plot of the residuals looks pretty good. There is not enough information to know if the most important assumption is valid: independent random samples within groups. Could it be that there are individuals who are related (e.g. siblings)? We'll just have to assume it's OK.

The p-value of 0.023 is significant: we reject the null hypothesis of no difference between the groups. The Tukey intervals tell us that $\mu_1 - \mu_2$ = cannot be rejected ( is in the Tukey CI), and that $\mu_2 - \mu_3$ = cannot be rejected, but we do have significance for $\mu_1 - \mu_3$ < since that CI ((-4.736,-0.422)) is all negative values. In other words, the Critical Flicker Frequency in the blue eyed group is significantly higher than the brown eyed group, but there is not a significant difference between the green eyed group and either of the others.