Minitab v13 - Analysis of Variance - One-Way

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

Post-hoc comparisons are also covered.

Using the Unstacked Method

Use the "One-way (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: MTBanova-1w.MTW One-way 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   550.9                           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

Using the Stacked Method

This method is the only one that gives access to the post hoc comparisons (discussed below). Use the "One-way..." 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:

One-way 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                           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

Post Hoc Comparisons

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's pairwise comparisons Family error rate = 0.115 Individual error rate = 0.0500 Critical value = 2.201 Intervals for (column level mean) - (row level mean)                1           2      2   -14.011            0.311      3   -18.611     -11.351           -4.289       2.151

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.