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About this lesson

This lesson reviews the different types of graphical and tabular results for a DOE study that are generated by Minitab. Each of these types of results provides a different perspective on the analysis of the design that is being studied.

Quick reference

DOE Analysis in Minitab

Minitab will analyse the results of a DOE and calculate the design space equation and identify significant factors that should be studied in a refining study.  

When to use

The math and statistics behind the DOE or not technically difficult, but when there are many factors, the effort to calculate manually becomes very time consuming and is prone to error.  Use Minitab, or an equivalent statistical application, to do the analysis of your DOE data.

Instructions

To do data analysis of a DOE study in Minitab, first create the study in Minitab as discussed in an earlier lesson.  Then record your test run data in the Response variable column of Minitab.  You are now ready to start the analysis.

Equation

The design space equation has a term for all the factors and all the interaction effects when doing a full factorial analysis.  This can be a very complex equation.  Many of those terms are not significant and removing them would not impact the accuracy and validity of the equation.   An important element of the analysis will be to determine significance of the factors and their interaction so that the insignificant ones can be removed and simplify the equation. 

Select the STAT pull down menu, then select DOE, Select Factorial, and finally Analyse Factorial Design.  The design must be analysed before any of the other options for analysis are available.

You will need to select the Response variable and I recommend selecting the Graphs button and choosing Standardized option.  When you click OK at the graphs panel and the main panel, Minitab will analyse the data.  In the session window, Minitab will provide the design space equation with all the factors. 

Significance

Minitab will also list the coefficients for all the terms and their P Value.  If the P value is below 0.05, the factor is significant.  This can also be seen in the significance graph.  All factors or interactions that extend beyond the dashed line are significant.  If the study was a screening study, the significant factors should be included in the refining study.  If the study was a refining study, the insignificant factors are removed and the analysis repeated. 

To do this, select STAT, DOE, Factorial and Analyse Factor Design.  On the panel that pops up, select the “Terms” button.  This brings us a panel with two windows.  The window on the right is all the available terms and the window on the left is the selected terms.  In the Selected Terms window, highlight each insignificant factor and click on the left arrow to remove it from that window.  If you accidentally remove a term, you can highlight it in the Available Terms window and use the right facing arrow.  If you need to include an interaction effect, be sure all the main effect terms that make up that effect are included, even if they are not significant by themselves.  Once the terms have been selected, click on OK and complete the analysis.  The R2 value should be virtually the same between the two analyses, but the second design space equation will be much simpler.

Hints & tips

  • Minitab has many more analytical plots and tools.  I have only showed you the ones that I have found most useful.  Feel free to play with the application and look for other analyses.
  • You may want to use different analyses for different phases of a Fractional Factorial DOE.  For instance the significance plots are very useful in a screening study and the design equation is very useful in a refining study.
  • Make sure you have correctly entered the data results and recorded the values with the correct test configuration in the worksheet.
  • A factor that was barely significant in the full analysis, may no longer be significant after the other insignificant factors are removed.  If that is the case, you should remove it also.
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  • 00:04 Hi I'm Ray Sheen.
  • 00:06 Yeah, we already discussed how to set up a DOE in Minitab.
  • 00:09 Now let's look at how to use Minitab to analyze our results.
  • 00:14 The good news is that Minitab has lots of ways to look at the results.
  • 00:18 And in fact, that can be the bad news if you get overwhelmed.
  • 00:23 So let me take you through some of the analysis that I use.
  • 00:26 First, Minitab will do a statistical analysis of the results recorded on your
  • 00:30 DOE worksheet that Minitab created when you did the setup.
  • 00:34 Minitab will calculate what we call descriptive statistics such as the mean or
  • 00:38 average, and the standard deviation.
  • 00:41 But to do the more advanced analysis, Minitab will use the ANOVA technique, or
  • 00:45 analysis of variations.
  • 00:47 We don't have time in this lesson to explain how ANOVA works, but
  • 00:51 it's one of the most widely used statistical techniques in the design and
  • 00:54 quality world today.
  • 00:55 And we will discuss it more in a later lesson.
  • 00:58 I mentioned this a moment ago, but let me re-emphasize.
  • 01:01 You must record the results of the response variable for
  • 01:04 each test run in the worksheet that Minitab created.
  • 01:08 Without that data, Minitab will not give you any results.
  • 01:11 You can have multiple response variables in that table, and
  • 01:14 we'll show you how to analyze with that on a later lesson.
  • 01:18 As I mentioned, Minitab provides lots of different ways to look at the data.
  • 01:22 In the top example here,
  • 01:23 I'm showing you the design space equation that would show up in the session window.
  • 01:28 In the middle are the main effects plots.
  • 01:31 Below them are the interaction plots and significance graphs.
  • 01:34 And in another lesson, I'll show you what I think is the most powerful of Minitab's
  • 01:38 data analysis formats, and that is the optimizer.
  • 01:42 We'll discuss some of these in this lesson, and the rest in the next lesson.
  • 01:46 One of the most important results from a DOE is factor significance.
  • 01:51 Significant factors are the control factors that have a significant effect
  • 01:55 on the response variable.
  • 01:57 These are the factors that you need to keep in your design space equation or
  • 02:01 use in the refining iteration of a fractional factorial study.
  • 02:06 Minitab will calculate which factors are significant.
  • 02:09 The P value is one way of showing significance.
  • 02:12 If the P value is below 0.05, the factor is significant.
  • 02:17 Also, Minitab will create a graph with a line showing which factors
  • 02:21 are significant and which are not.
  • 02:23 You do not need to use the insignificant factors in further studies.
  • 02:28 In fact,
  • 02:28 you can rerun the DOE results in Minitab with the insignificant factors removed.
  • 02:33 You should have virtually the same result.
  • 02:35 In particular, check the R squared value which should be almost identical
  • 02:40 to the previous run, which had all the factors in it.
  • 02:43 If an interaction effect is significant, but one or
  • 02:46 more of the factors in the interaction was not significant, you will need to still
  • 02:51 include that factor in further analysis so that the interaction will be included.
  • 02:57 So let's see how we do this.
  • 02:58 I'll start by looking at how Minitab will give us the design space equation and
  • 03:03 show the significance of the factors.
  • 03:05 To do this, you must analyze the DOE.
  • 03:07 Go to the stat pulldown menu and select DOE.
  • 03:10 Then select Factorial.
  • 03:12 And about halfway down the menu is Analyze Factorial Design.
  • 03:16 In the panel that comes up, highlight the variable from the list, that is your Y or
  • 03:20 response variable, and select it.
  • 03:22 I recommend that at this panel, you also select graphs.
  • 03:26 If you do that, you will bring up this panel.
  • 03:28 I prefer to use the standardized graphs, but it's really just a preference.
  • 03:33 And I definitely want the individual plots.
  • 03:36 When you do that, Minitab will determine the design space coefficients and
  • 03:40 the factor significance.
  • 03:43 Let's look at an example.
  • 03:44 The coefficients are listed in the session window along with their P value.
  • 03:49 Also further down the session window will be the full design space equation.
  • 03:53 In this example, there were four main coefficients and six two-way coefficients.
  • 03:59 Without getting into the weeds, if the P value, which is in the far right column,
  • 04:03 is less than 0.05, the coefficient is significant.
  • 04:08 We talk a lot about this in the hypothesis testing course.
  • 04:11 So if you want to know more about ANOVA and
  • 04:13 P value, I encourage you to take that course.
  • 04:16 As you can see, all the main factors are significant.
  • 04:19 And two of the interaction factors are significant, material and
  • 04:23 cooling temperature, and injection pressure and cooling temperature.
  • 04:27 We see the same thing in the graph.
  • 04:29 The horizontal bars show which factors are most significant.
  • 04:33 And the dashed red line is the significance threshold.
  • 04:37 Any bar that extends past that line is a significant factor or interaction.
  • 04:42 By the way, if this is a screening study,
  • 04:44 use the significant factors in the following refining study.
  • 04:49 Now let's look at how we use the significant factors.
  • 04:52 We can redo the analysis with your current data, but remove the insignificant so
  • 04:57 only the significant factors are left.
  • 04:59 Once again, go to Stat > DOE > Factorial > Analyze Factorial Design.
  • 05:05 Select the Terms button, and that should give you a panel that looks like this.
  • 05:09 In the Selected the Terms window, highlight the insignificant terms and
  • 05:14 then click on the left-facing arrow.
  • 05:16 That will remove the term from the analysis.
  • 05:19 Do this for all the insignificant terms.
  • 05:22 Once all the insignificant terms have been removed from the selected terms list,
  • 05:26 click on OK, and run the analysis.
  • 05:29 This will give you a much simpler design space equation.
  • 05:33 So we can eliminate the insignificant terms and simplify our analysis.
  • 05:37 Next, we'll look at how to use Minitab to optimize the results.

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