ANOVA

Quick reference

• 00:05 Hello, I'm Ray Sheen.
• 00:06 We're now going to look at the ANOVA test.
• 00:08 This test becomes strongly linked to lean six sigma because it is used in so
• 00:13 many of the advanced lean six sigma techniques.
• 00:16 Again we start with hypothesis testing decision tree.
• 00:20 We have normal data discrete and continuous x and y and
• 00:24 multiple variables, that get us to the ANOVA.
• 00:28 So let's look at the one way ANOVA.
• 00:30 ANOVA stands for Analysis of Variance.
• 00:33 We compared the means from each of the samples in the analysis to determine if
• 00:37 one of the means is statistically different from the other.
• 00:41 In that regard, it is similar to the 2-Sample T-Test, but
• 00:44 instead of just two samples, it can have many samples.
• 00:48 It is often used to identify significant subsets of the data in large populations.
• 00:53 That is the feature that is used in both the gauge R&R analysis, and
• 00:57 the design of experiments analysis.
• 00:59 It can sort through the many different data points based upon the categories
• 01:03 being used.
• 01:03 And determine which if any provide a result that is statistically different
• 01:07 from the others.
• 01:09 You may be wondering why we would use ANOVA when we could do the same thing with
• 01:13 T-Tests.
• 01:15 Well, the problem is that you can't get the same fidelity in the answer
• 01:18 by using multiple T-Tests.
• 01:20 Keep in mind that with our normal Lean Six Sigma confidence level of 0.95,
• 01:25 there is still a 5% chance for a type I error of false positive.
• 01:29 Now if we have four samples, we would need to conduct six tests.
• 01:33 So the probability of a type I error is compounded.
• 01:37 That means that our chance of making a type I error is now 26.5%.
• 01:42 And keep in mind that the Type II error probabilities often even higher than
• 01:46 the Type I error.
• 01:47 So the chance of the Type II error is often even higher still.
• 01:51 The more T-Tests we run, the more likely we are to make a wrong decision,
• 01:55 either Type I or Type II.
• 01:58 However, with ANOVA is it only one test that needs to be run and
• 02:02 that will check all those relationships between the sample means.
• 02:06 In addition to that,
• 02:07 ANOVA is somewhat forgiving on the assumption of normal data.
• 02:11 It will tolerate a low level of non normal behavior and
• 02:14 still provide excellent results.
• 02:16 So let's look at how we do this test.
• 02:19 In Excel, select the data analysis menu from the data ribbon then
• 02:23 select ANOVA single factor.
• 02:25 Annotate whether the data is grouped by rows or columns and provide the range for
• 02:30 your data table.
• 02:31 The rows or columns must be next to each other and
• 02:34 there can not be any blank rows or columns in the data.
• 02:37 Excel will calculate a P-value.
• 02:39 In this example, the P-value of 0.22 is less than our 0.05,
• 02:44 so we eject the null hypothesis.
• 02:47 The mean values are statistically different.
• 02:49 Minitab will go one step further in testing using ANOVA.
• 02:53 Start in a similar manner, go to the Stat pull down menu and select ANOVA,
• 02:58 then select One Way.
• 02:59 Select the format of your data columns like you did on other test and
• 03:03 then select the data column for analysis.
• 03:06 Then go to the Option panel to select equal variances if you have that
• 03:10 condition.
• 03:11 Also, you can go to the Graphs panel to select the type of graphs you want.
• 03:16 I recommend the interval plot under data plots and the three in one residual plot.
• 03:20 Minitab will provide both plots and
• 03:23 a summary of the analysis in the session window.
• 03:26 As you can see,
• 03:27 one of the items it provides is a P-value which is still 0.022.
• 03:32 Let's take a minute to look at the graphs that we get from Minitab.
• 03:36 The Minitab and Excel P-value will tell us if there's a statistically
• 03:40 significant difference in the means.
• 03:42 But they don't tell you, which sample was the problem.
• 03:45 That is where the graphs add value.
• 03:47 A quick glance at the graphs will normally reveal the difference.
• 03:51 As I mentioned on the last slide, select the Graphs button,
• 03:54 then select both the data graph and residual graphs.
• 03:58 Personally, I like the interval plot, but if a different view works better for you,
• 04:02 then use it.
• 04:03 You can select individual residual plots or do the three in one or
• 04:07 four in one option, depending on the type of test.
• 04:10 So let's look at the interval plot, we have four different categories of data and
• 04:14 the mean was definitely changing between the different categories.
• 04:18 Time 1 and time 4 don't even overlap at the edges of their confidence interval.
• 04:23 So they are clearly not from the same population.
• 04:26 We'll probably need to look at other contextual information to understand
• 04:30 possible reasons for
• 04:31 these differences, that could include looking at the residual plot.
• 04:35 The normality line does not look normal and
• 04:38 we would expect that since there are different populations in the data.
• 04:41 This is a typical reason for non-normality and
• 04:45 we see that the histogram were heavily excude.
• 04:47 Again, an indication that the data is not normal.
• 04:50 It's interesting to see that the verses fit data shows that the range of
• 04:55 residuals was similar, except for that one outlier in the sample on the far right.
• 05:00 That point is up at the upper right hand corner of the plot.
• 05:03 But since the residuals versus fit is similar in other respects,
• 05:07 there is probably not a time-based pattern at work.
• 05:10 But rather, some other attribute that is not captured in the data that is affecting
• 05:15 each of these samples.
• 05:16 So far, we've been trying to evaluate one factor with multiple samples.
• 05:21 However, we can also have multiple factors when working with ANOVA.
• 05:25 Both Excel and Minitab can run an ANOVA with two response factors and
• 05:29 in fact Minitab can work with even more than two.
• 05:32 In Excel, select the Data Analysis menu on the data ribbon and
• 05:36 then select ANOVA Two Factor without replication.
• 05:40 We'll talk about replication when we do the class on the designer experiments.
• 05:45 Now enter the data range in the same way you would with one way ANOVA.
• 05:48 The Excel results will provide a P-value for both column analysis and row analysis.
• 05:54 In Minitab, start with the Stat pulldown menu,
• 05:57 select ANOVA, select General Linear Model, and
• 06:00 then select Fit General Linear Model, and you get this panel.
• 06:05 Now select your Response columns, then select your Factor columns.
• 06:09 You can even include interaction effects by selecting the model button.
• 06:13 And then on the panel that comes up deciding which categories of interactions
• 06:17 you want to conclude and selecting the Add button for that category.
• 06:21 ANOVA is an excellent test for many applications within Lean Six Sigma.
• 06:27 It does a great job of sorting out the complex situation.

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