Minitab® – One-Way ANOVA
- Import the data
The data (Lesson1 Data) can be copied and pasted from a word processor into a worksheet in Minitab:
- Run the ANOVA
To run the ANOVA, we use the sequence of tool-bar tabs: Stat > ANOVA > One-way... .
You then get the pop-up box seen below. Be sure to select from the drop-down in the upper right 'Response data are in a separate column for each factor level':
Then we double-click from the left-hand list of factor levels to the input box labeled ‘Responses’, and then click on the box labeled ‘Comparisons’.
We check the box for Tukey and then exit by clicking on OK. To generate the Diagnostics, we then click on the box for Graphs and select the 'Three in one' option:
You can now ‘back out’ by clicking on OK in each nested panel.
Now in the Session Window we see the ANOVA table along with the results of the Tukey Mean Comparison:
One-Way ANOVA: Control, F1, F2, F3
Null Hypothesis: All means are equal
Alternative Hypothesis: Not all means are equal
Significance Level: \(\alpha=0.05\)
Equal variances were assumed for the analysis.
Factor Levels Values Factor 4 Control, F1, F2, F3
Analysis of Variance
Source DF Adj SS Adj MS F-Value P-Value Factor 3 251.44 83.813 27.46 0.000 Error 20 61.03 3.052 Total 23 312.47
(Extracted from the output that follows from above.)
Grouping Information Using Tukey Method
N Mean Grouping F3 6 29.200 A F1 6 28.600 A B F2 6 25.867 B Control 6 21.000 C
Means that do not share a letter are significantly different.
Now you can see why people love Minitab! The output requires no further work to get the lettering we need for our means bar chart. In SAS, we got the pair-wise comparison p-values from the table of Differences in LSmeans, but still have to work out the lettering. Here, Minitab has done it for us.
The diagnostic (residual) plots, as we asked for them, are in one figure:
Note that the Normal Probability plot is reversed (i.e, the axes are switched) compared to the SAS output. Assessing straight line adherence is the same, and the residual analysis provided is comparable to SAS output.