

Minitab  Analysis of Variance  OneWay
The minitab worksheet is available.
It contains the following data:
Data Format Column N Comments Unstacked 0 4 scores on the written papers 2 5 scores on the written papers 4 5 same data as for "Written" less 1 subject Stacked Code 14 dummy codes for groups (1="0", 2="2", 3="4") Scores 14 all of the "0", "2", & "4" data Posthoc comparisons are also covered.
Use the "Oneway (Unstacked)..." command off of the "Stat, ANOVA" menu. That is:
That will take you to the following dialog box:
Type in (or double click them from the left hand menu) the columns that have the different groups of data. The output will look like this:
Results for: MTBanova1w.MTW Oneway ANOVA: 0, 2, 4
Analysis of Variance
Source DF SS MS F P
Factor 2 292.1 146.1 6.21 0.016
Error 11 258.8 23.5
Total 13 550.9S = 4.850 RSq = 53.03% RSq(adj) = 44.49%
Individual 95% CIs For Mean
Based on Pooled StDev
Level N Mean StDev++++
0 4 26.750 5.377 (*)
2 5 33.600 4.506 (*)
4 5 38.200 4.764 (*)
++++
Pooled StDev = 4.850 24.0 30.0 36.0 42.0
This method is the only one that gives access to the post hoc comparisons (discussed below). Use the "Oneway..." command off of the "Stat, ANOVA" menu. That is:
That will take you to the following dialog box:
Type (or double click from the left hand menu) the "Response:" or dependent variable and the "Factor:" or the dummy codes for the levels of the IV. The output will look like this:
Oneway ANOVA: Seconds versus Code Analysis of Variance for Seconds
Source DF SS MS F P
Code 2 292.1 146.1 6.21 0.016
Error 11 258.8 23.5
Total 13 550.9
S = 4.850 RSq = 53.03% RSq(adj) = 44.49%
Individual 95% CIs For Mean
Based on Pooled StDev
Level N Mean StDev++++
1 4 26.750 5.377 (*)
2 5 33.600 4.506 (*)
3 5 38.200 4.764 (*)
++++
Pooled StDev = 4.850 24.0 30.0 36.0 42.0
If we get a significant omnibus F ratio as we did above, it is worthwhile to conduct comparisons to localize the effect. Thus, we need to rerun the analysis above and this time we will choose the "Comparisons..." button. This will lead us to the following dialog box:
Let's check "Fisher's" since it is essentially the same as the protected t we used in lecture. Leave the individual error rate at 5% (i.e., a=.05). The output from the above analysis will be repeated with the following portion appended:
Fisher 95% Individual Confidence Intervals
All Pairwise Comparisons among Levels of CodeSimultaneous confidence level = 88.50%
Code = 1 subtracted from:
Code Lower Center Upper ++++
2 0.311 6.850 14.011 (*)
3 4.289 11.450 18.611 (*)
++++
8.0 0.0 8.0 16.0
Code = 2 subtracted from:
Code Lower Center Upper ++++
3 2.151 4.600 11.351 (*)
++++
8.0 0.0 8.0 16.0
This is not exactly easy to interpret. In the Minitab help file, it notes: "The multiple comparisons are presented as a set of confidence intervals, rather than as a set of hypothesis tests...the null hypothesis of no difference between means is rejected if and only if zero is not contained in the confidence interval." Thus, of the three tests (1x2, 1x3, & 2x3), the only confidence interval that does not contain zero is the 1x3. In other words, the 1x3 comparison is significant which agrees with what we found with our manual calculations.