3.6 - One-way ANOVA Greenhouse Example in Minitab

Minitab 18

Minitab®  – One-Way ANOVA

  1. Import the data

    The data (Lesson1 Data) can be copied and pasted from a word processor into a worksheet in Minitab:

    Minitab worksheet

     

  2. Run the ANOVA

    To run the ANOVA, we use the sequence of tool-bar tabs: Stat > ANOVA > One-way... .

    minitab menu options

    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':

    minitab dialog box

    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’.

    one-way multiple=

    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:

    ANOVA Graphs dialog box

    You can now ‘back out’ by clicking on OK in each nested panel.

  3. Results

    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

    Method

    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 Information
    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:

diagnostics plots

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.