ANOVA Analysis

Quick reference

• 00:04 Hi, I'm Ray Sheen.
• 00:05 Well, we've considered a bit of the theory behind ANOVA.
• 00:08 Now let's take a look at how we actually do the analysis.
• 00:12 There are actually several flavors to the ANOVA test.
• 00:15 One-way ANOVA compares the mean values of multiple data sets.
• 00:20 It seeks to determine if there is a significant difference.
• 00:23 Two-way ANOVA compares the means of independent factors within
• 00:28 the data sets to determine if there is a significant difference.
• 00:32 We can do the one-way ANOVA analysis in three different ways.
• 00:36 We can do it manually using the table on the next slide.
• 00:39 We can use Excel, or
• 00:41 we can use a statistical software package such as Minitab.
• 00:45 For two-way ANOVA, you have to use a statistical software.
• 00:49 Like many of our hypothesis tests,
• 00:52 the results of the ANOVA can be shown graphically or with a statistical value.
• 00:58 Let's look at the manual method with the F Distribution Table.
• 01:02 You may have a question on the IASSC Lean Six Sigma Black Belt exam that
• 01:05 will require the use of this table.
• 01:07 The table is based upon several data set parameters.
• 01:10 In this case, we're using an alpha of 0.05.
• 01:14 If different parameters are used, it'll require a different table.
• 01:18 We will do a quick exercise.
• 01:20 We have three samples, and each of these three samples is made up of 6 items.
• 01:27 The column entry is the degree of freedoms based upon the number of samples.
• 01:31 Well, that degree of freedom is calculated by subtracting 1 from the total number of
• 01:35 datasets.
• 01:36 In our case, that means 3-1, which is 2.
• 01:40 So we go to column number 2.
• 01:42 Now, the row entry is the sum of the degrees of freedom for
• 01:46 each of the unique samples.
• 01:48 Since each sample, in this case, had 6 items,
• 01:51 the degree of freedom for each sample is 1 less than that, or 5.
• 01:56 And since there are 3 of those, we add 3, 5 times and come up with a total of 15.
• 02:03 So we go in on row 15.
• 02:05 So looking at column 2 and row 15, the F value then is 3.68.
• 02:11 Now let's look at how we do the test in Excel or Minitab.
• 02:14 In Excel, select the data analysis menu from the data ribbon.
• 02:18 Then select ANOVA single factor.
• 02:21 Know whether the data is grouped by rows or columns and provide the range for
• 02:26 the data table.
• 02:27 The rows or columns must be next to each other,
• 02:30 there cannot be any blank rows or columns in the data.
• 02:34 Excel will calculate a P value.
• 02:37 In this example, the P value of 0.022 is less than 0.05,
• 02:42 so reject the null hypothesis.
• 02:44 The mean values are statistically different.
• 02:47 Minitab will go one step further in its analysis using ANOVA.
• 02:51 Start in a similar manner, so go to the Stat pulldown menu,
• 02:55 select ANOVA, then select One Way.
• 02:58 Select the format of your data columns like you did on other tests.
• 03:02 Then select the data columns for analysis.
• 03:05 Now, go to the Options panel and select Equal Variance if you have that condition.
• 03:10 Also, you can go to the Graphs panel to select the types of graphs that you want.
• 03:15 I recommend the interval plot under the data plots and
• 03:19 the Three in One residual plot.
• 03:21 Minitab will provide both plots and
• 03:23 a summary of the analysis in the session window.
• 03:27 As you can see, one of the items it provided is that the P value,
• 03:32 which is 0.022.
• 03:34 Let's take a minute to look at the graphs that we get from Minitab.
• 03:38 The Minitab and XLP values will tell you that there is a statistically significant
• 03:43 difference in the means.
• 03:44 But that doesn't tell you which sample was the problem.
• 03:48 This is where the graphs add value.
• 03:51 A quick glance at the graphs will normally reveal the difference.
• 03:54 As I mentioned in the last slide, select the graphs button and
• 03:58 then select both data graphs and residual graphs.
• 04:01 Personally, I like the interval plot, but if a different view works better for
• 04:06 you then use it.
• 04:06 You can select individual residual plots or
• 04:10 do the Three in One or Four in One option.
• 04:13 So let's look at the interval plot.
• 04:16 We have four different categories of data and
• 04:18 the mean was definitely changing between these different categories.
• 04:23 The mean for time 1 falls within the confidence interval for time 2, and
• 04:27 the mean for time 2 falls within the confidence interval for time 3.
• 04:32 The mean for time 3 falls within the confidence interval for
• 04:35 times 2 and times 4.
• 04:37 And the mean for time 4 falls within the confidence interval for time 3, but
• 04:41 the mean for time 4 does not fall within the confidence interval for time 1.
• 04:46 There's no overlap for those confidence intervals.
• 04:48 So they're clearly not from the same population.
• 04:52 We may need to look at other contextual information to
• 04:54 understand the possible reason for the difference.
• 04:58 That could include looking at the residual plots.
• 05:01 This line does not look normal, and
• 05:03 we would expect that since there are different populations in the data.
• 05:07 That is a typical reason for non-normality.
• 05:11 And we see that the histogram is heavily skewed,
• 05:14 again an indication that the data is not normal.
• 05:17 It's interesting to note that the versus fit data shows that the range of residuals
• 05:23 was similar except for that outlier point on the sample at the far right.
• 05:27 The point is in the upper right corner of that plot.
• 05:30 But since the residual versus fit is similar on the other plots,
• 05:34 this is probably not a time based pattern at work but rather there's some other
• 05:39 special cause attribute not reflected in this data that's affecting the samples.
• 05:44 So far, we've been trying to evaluate one factor with multiple samples.
• 05:49 However, we can also have multiple factors when working with ANOVA.
• 05:54 Both Excel and Minitab can run an ANOVA with two response factors, and
• 05:59 Minitab can even run it with more than two.
• 06:01 In Excel, select the Data Analysis menu on the data ribbon, and
• 06:06 then select ANOVA Two Factor without replication.
• 06:10 We'll talk about replication when we do the class on the design of experiments.
• 06:15 Now under the data range in the same way as you would with a one-way ANOVA,
• 06:20 the Excel results will provide a P value for both a column analysis and
• 06:24 a row analysis.
• 06:25 In Minitab, start with the stat pulldown menu,
• 06:29 select ANOVA, select General Linear Model,
• 06:32 then select Fit General Linear Model, and you get this panel.
• 06:36 Next, select your response columns and then select your factor columns.
• 06:41 You can even include interaction effects by selecting the Model button, and
• 06:45 then on the panel that comes up deciding which categories of interaction you want
• 06:49 to include, and selecting the Add button for that category.
• 06:54 Well, there are several ways to do the ANOVA analysis.
• 06:57 Take your pick based upon the tools available to you.

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