One-Sample Sign

Quick reference

• 00:04 Hi I'm Ray Sheen.
• 00:06 So far we've been focusing on what to do when the data is normal.
• 00:10 But often the data is not normal.
• 00:13 So now, let's see how we would approach that situation with
• 00:18 the one-sample sign test or the one-sample Wilcoxon test.
• 00:22 So we are moving to a different section of the hypothesis testing decision tree.
• 00:27 We're still working with data that is continuous and discrete, but
• 00:31 now we take the path for non-normal data and move toward the bottom of the tree.
• 00:36 When there is one data sample set involved, the decision is to use either
• 00:40 the one-sample sign test or the one-ample Wilcoxon.
• 00:44 We'll look at both of those tests in this lesson.
• 00:47 But let's take a few moments to first discuss non-normal tests.
• 00:52 Recently, we've been focused on tests with normal data, but
• 00:55 many real world situations are not normal.
• 00:58 That doesn't mean that there are special causes present.
• 01:01 It could just mean that the physical attributes being studied don't act with
• 01:05 a bell-shaped Gaussian distribution.
• 01:08 Don't become so focused on normality that you fail to do appropriate testing.
• 01:13 There are plenty of non-normal hypothesis tests that are very effective.
• 01:17 With the aid of the computer, we're not overwhelmed by the math.
• 01:21 Many of the tests with normal data are somewhat forgiving for
• 01:24 small amounts of non-normality.
• 01:26 We mentioned this when discussing the ANOVA.
• 01:28 So if it is a minor non-normality, you may still be okay.
• 01:33 But even if it is a major one, you can still transform the data into normal
• 01:36 data if you believe that, that is necessary.
• 01:40 One legitimate concern with respect to non-normal data is that Excel does not
• 01:44 have any non-normal tests in the analysis toolkit that was accessed through the data
• 01:49 analysis menu on the data ribbon.
• 01:51 So you will likely need a statistical analysis application like Minitab to
• 01:56 do these tests.
• 01:58 Fortunately, Minitab has all these tests and even some
• 02:01 additional ones that we won't discuss that could be used for hypothesis testing.
• 02:06 Let's talk for a moment about non-normal test selection.
• 02:09 The hypothesis decision tree will include several options for non-normal tests.
• 02:14 This is due to the fact that non-normal tests are often optimized for
• 02:18 particular types of non-normality.
• 02:20 Non-normal tests or as they're referred to in Minitab as non-parametric tests,
• 02:25 do not work with the mean and standard deviation of a distribution.
• 02:29 Because those statistical parameters are often a little bit whacked out by
• 02:33 the nature of the non-normal.
• 02:35 Instead, they're optimized for data descriptions that are not bell-shaped.
• 02:39 One advantage of these tests is that they generally can be used with either
• 02:42 attribute or ordinal data.
• 02:44 Again, the shape of the curve is more important than the smoothness of
• 02:47 the distribution curve, which of course means that they will work with both
• 02:51 discrete and continuous data types.
• 02:54 Let's look at this table for a moment.
• 02:56 It helps to draw a comparison between some of the common hypothesis tests used
• 03:01 with normal data and those used with non-normal data.
• 03:05 When there is one set of sample data being compared to a target,
• 03:08 we use the one sample T-test on normal data.
• 03:11 And either one-sample sign or one-sample Wilcoxon with non-normal data,
• 03:15 more about both of those in just a few slides.
• 03:19 With two samples that are normal, we use the F-test, and the 2-sample t-test.
• 03:25 When they are not normal, we use the Levene's test and the Mann-Whitney test.
• 03:29 And finally, for multiple sample sets that are normal, we use ANOVA.
• 03:34 With non-normal data, we can use Mood's median,
• 03:37 Kruskal-Wallis, and Friedman, depending upon the shape of the data.
• 03:42 More about all of those in another lesson.
• 03:45 So let's consider the one-sample sign test first.
• 03:48 This test is similar to the one sample T-test for normal data, but this is used
• 03:53 when the data is not normal such as when it is skewed, truncated,or non-symmetric.
• 03:59 Since the data is not normal, the median is used instead of the mean.
• 04:04 The median is a better measure of central tendency for non-normal data.
• 04:08 The hypothesis is normally structured such that the null hypothesis is that
• 04:13 the sample median equals the target median.
• 04:16 The alternative hypothesis is normally stating
• 04:19 that the sample median will either be above or
• 04:21 below the target medium, depending upon the underlying question of the hypothesis.
• 04:28 Conducting this test in Minitab is very simple.
• 04:31 Start with the stat pull down menu, select Nonparametric,
• 04:34 which is near the bottom of that menu, and then select one-sampled sign test,
• 04:38 which is at the top of the next menu.
• 04:41 Select your Data column in the same way you have done with other tests.
• 04:44 And then entered the target median in the field that is labeled Test Median.
• 04:49 Finally, set the operator for
• 04:51 your alternative hypothesis at less than greater than or not equal to.
• 04:55 The P-value result will show in the session window.
• 04:58 The one-sample Wilcoxon works almost exactly the same as the one-sample
• 05:02 sign test.
• 05:03 It is also similar to the one-sample T-test for normal data.
• 05:07 However, a difference between this test and the one-sample sign test is that
• 05:12 the one-sample Wilcoxon requires the data to be symmetric.
• 05:16 It can be uniform or even bath-tub shaped, but it should be symmetric.
• 05:21 Since the data is non-normal,
• 05:23 the median is used instead of the mean as a better measure of central tendency.
• 05:27 The null and alternative hypotheses are the same as on the one-sample sign test.
• 05:32 The null is that the median equals the target.
• 05:34 And the alternative is that the median is greater than or less than the target.
• 05:39 The Minitab actions are the same as one-sample sign,
• 05:42 except that one sample Wilcoxon is selected from the non-parametric menu.
• 05:47 The data column selection, entering the target, and
• 05:50 setting the operator are done in the same manner as the one-sample sign test.
• 05:55 One-sample sign and one-sample Wilcoxon are great tests to use when
• 06:00 checking to see if your solution is able to meet the desired standard.

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