T-Tests

Quick reference

• 00:04 Hi, I'm Ray Sheen the next set of tests are probably the most commonly used
• 00:09 hypothesis tests on Lean Six Sigma projects.
• 00:13 These T-tests are a simple way for
• 00:15 determining if there is a difference between two data sets.
• 00:20 >> I'll start again with the hypothesis test decision tree.
• 00:23 We are working with normal, discrete and continuous data.
• 00:27 There are two T-tests to discuss the two sample T-test and the paired T-test.
• 00:32 I'll start with the most widely used T-test that is the Two Sample T-test.
• 00:37 This test is used to determine if the mean from two samples
• 00:40 are statistically different.
• 00:42 If not, the sample sets can be combined and treated as one population, but
• 00:46 if different, the difference may lead to an understanding of the root cause or
• 00:51 causes of the problem under investigation.
• 00:54 It's also used to demonstrate whether a change has been effective.
• 00:58 So the null hypothesis for
• 00:59 this test is that the mean of one sample equals the mean of the other sample.
• 01:04 And the alternative hypothesis is that they are different.
• 01:07 As with some of the other tests, you could choose to write the alternative
• 01:11 hypothesis so that one was greater than or less than the other.
• 01:16 The actual mathematics of the test will change depending upon whether the two
• 01:21 samples have equal variance.
• 01:23 So the F-test will need to have been done first in order to make the correct
• 01:27 selection.
• 01:28 If you don't do the F-test, assume unequal variance.
• 01:32 The p-value may not be quite as precise, but it will err on the safe side.
• 01:37 In Excel, go to the data analysis menu on the data ribbon.
• 01:40 Then select either t-Test Two Sample Assuming Equal Variance or
• 01:45 t-Test Two Sample Assuming Unequal Variance.
• 01:49 The data entry is the same that we have done on most of the other tests.
• 01:54 In Minitab, select the pull-down menu, Stat, then Basic Statistics,
• 01:58 and then 2-Sample t.
• 02:01 Enter the data in the same manner as which you've entered other test data.
• 02:05 You can select the Options button and then select the item for equal variances.
• 02:10 Otherwise, Minitab will assume unequal variances.
• 02:13 With both Excel and Minitab you get results with a p-value that you can use to
• 02:18 either reject the null hypothesis or fail to reject the null hypothesis.
• 02:23 Next, I would like to discuss the Paired T-Tes.
• 02:26 The Paired T-Test is a special case test.
• 02:29 Determines if two samples that are linked or paired together have similar means.
• 02:34 Pairing requires that every data item in one set is paired with
• 02:38 a unique data item in the other set, a one to one pairing.
• 02:43 In Lean Six Sigma program, this is often done as before and after tests.
• 02:48 So, an obvious characteristic of the paired data samples,
• 02:52 is that they must have exactly the same number of items in each sample.
• 02:55 Also, when recorded in the sample,
• 02:58 the paired item must be in the same order to ensure that the pairing is correct.
• 03:03 The hypothesis is similar to the Two Sample t-Test.
• 03:06 The null hypothesis is that the means from the two samples are the same, and
• 03:11 the alternative hypothesis is that they are not the same.
• 03:15 In Excel, this test is done by selecting the Data Analysis menu from the Data
• 03:19 ribbon, and then selecting t-Test Paired Two-Samples for Mean.
• 03:24 Then enter the data ranges as we have with other Excel tests.
• 03:27 In Minitab select the Stat pull down menu,
• 03:30 then select Basic Statistics and select Paired t-Test.
• 03:35 Again enter data columns in the same way as you have with other tests.
• 03:39 And you can select greater than or less than comparison from the option panel in
• 03:43 the same manner in which you've done it on the other tests.
• 03:47 Let's spend a moment and consider why we would use pairing.
• 03:51 One condition that I've already mentioned is the before after test.
• 03:55 In this case, items in a data set are tested to establish a baseline value,
• 04:00 then the improvement or other changes are made.
• 04:04 Now all the items are tested again to determine if the mean value has changed in
• 04:09 a statistically significant manner.
• 04:12 An example could be an average time for each operator to complete a unit of
• 04:16 production before and after the new inspection equipment was installed.
• 04:22 Another condition is the controlled test.
• 04:25 In this case, some items in the dataset are the control and
• 04:28 some are exposed to the improvement.
• 04:31 All items go through the same process at the same time.
• 04:34 The performance of the control items is compared to the improved items.
• 04:39 An example of this would be,
• 04:40 to use two different cleaning processes on different portions of the same carpet.
• 04:46 A third condition is matched subjects.
• 04:48 In this case, items under investigation is already a pair,
• 04:52 such as a package and label.
• 04:55 Although the items may be different in some important characteristic,
• 04:58 they both go through the same conditions or process.
• 05:01 And the results are then compared.
• 05:03 This is often used in behavioral testing with husbands and wives.
• 05:07 If for some reason you need to do this test by hand, and not with Excel or
• 05:12 Minitab functions, let's look at what would be needed.
• 05:16 Like the Z test the T test converts the sample means into standard
• 05:19 deviation units.
• 05:21 Whether it's a Z or T test, you take the test statistic and use the lookup table to
• 05:25 determine whether the statistic is greater than or less than the table value.
• 05:30 If the sample size is less than 30, use the T table and
• 05:34 if the sample size is greater than 30, use the Z table.
• 05:38 To find the value in the table, use the alpha value for your analysis and
• 05:42 your degrees of freedom.
• 05:44 The degrees of freedom is the number of items in the sample- 1.
• 05:49 The t statistic for two samples is the mean of one minus the mean of the other
• 05:53 divided by the square root of the variance of one over the sample size
• 05:58 plus the variance of the other over its sample size.
• 06:02 The t statistic for the paired two sample T test is the mean of the differences
• 06:07 between the pairs divided by the standard deviation of the differences over
• 06:11 the square root of the number of items in the sample.
• 06:16 >> Whether it's a Two Sample T-Test or the Paired T-test, you'll likely find
• 06:21 that these tests are the ones that you most frequently use in the analyze phase.

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