Hypothesis Tests

Quick reference

• 00:05 Hi, I'm Ray Sheen.
• 00:05 I kept talking about hypothesis tests and you're probably starting to wonder,
• 00:10 what are these tests?
• 00:11 Well, let's take a look.
• 00:14 Well, in this lesson, we'll lay out a decision tree for
• 00:17 determining which test to use when.
• 00:19 Steps 3 and 4 of the hypothesis testing process are to gather data and
• 00:22 apply the appropriate test to the data in order to calculate the test statistic.
• 00:27 It should come as no surprise that different tests are used depending
• 00:30 upon the type of data that is available, and
• 00:32 that different tests calculate different test statistics.
• 00:36 Based upon the test results, we either accept or reject the null hypothesis.
• 00:41 When determining which test to use, there are a number of questions that we need to
• 00:45 ask about the data that's available and the hypothesis.
• 00:48 The answers will determine which test is best suited to give us a good statistic.
• 00:53 One question is whether or not special causes are present in the data.
• 00:57 Special causes will distort the data and invalidate the hypothesis test.
• 01:01 Another key question is, whether or not the data is normal.
• 01:04 We have different tests depending upon normality.
• 01:07 The nature of the data structure, whether it's discrete or continuous,
• 01:11 will also impact the hypothesis test selection.
• 01:13 And finally, the number of data samples in the investigation can impact which test we
• 01:18 should use.
• 01:20 So let me take you through a decision tree for how to select the hypothesis test.
• 01:24 This decision tree contains 20 different tests.
• 01:27 There are even more tests, but these are the most commonly used ones.
• 01:31 In some cases, several different tests could be used.
• 01:34 I've identified the one that I normally use, and
• 01:37 it provides an accurate test statistic for that condition.
• 01:40 If your business requires you to use a different test, then use it.
• 01:44 You will probably reach the same conclusion with respect to the hypothesis,
• 01:47 to either accept or reject the null.
• 01:50 So we start by determining if the process is stable, if not,
• 01:54 address the special causes.
• 01:56 If the process is stable, then we consider the type of data.
• 01:59 Is it discrete, continuous, or some of both?
• 02:02 When all the variables are continuous, we next ask the question of,
• 02:06 how many independent variables are being considered?
• 02:09 If there's only one independent variable, you can check for correlation, and
• 02:12 if it exists, create a simple linear regression equation.
• 02:16 If there are multiple variables, do a multiple regression analysis.
• 02:20 When both the dependent and independent variables are discrete, we need to ask
• 02:24 the question, again, how many samples are involved in the hypothesis?
• 02:28 If only one sample is involved, do a one-sample test of proportions.
• 02:32 If two samples, do two-sample test of proportions.
• 02:34 And if more than two samples, do a chi-square test.
• 02:37 Now consider the case where one of the variables is discrete and
• 02:41 one is continuous.
• 02:43 At this point, you need to determine if the data is normal or not.
• 02:46 If the data is normal,
• 02:47 we will ask our same question about the number of data samples in the analysis.
• 02:52 If it's just one sample, do a one-sample t-test, or a one-sample test for variance,
• 02:57 depending upon the effect you want to analyze.
• 02:59 If more than one sample, we need to do a variance test, either the F-test or
• 03:03 the Bartlett's test.
• 03:04 This is because the remaining tests are conducted differently,
• 03:07 depending upon the answer to the question of whether the variances are equal.
• 03:12 If there are two samples involved, either use a two-sample t-test or
• 03:15 a paired t-test, depending upon the structure of the data in the hypothesis.
• 03:19 If there's more than two samples, use the ANOVA test.
• 03:23 Now let's look at the case where the data is not normal.
• 03:27 Again, we ask the question to how many samples are involved?
• 03:31 If there's only one sample, use the one-sample sign or
• 03:34 the one-sample Wilcoxon depending upon the shape of the data.
• 03:37 If there are two samples, do a Levene's test for variance and
• 03:41 then the Mann-Whitney for the means.
• 03:44 And finally, if there are two or more samples, you can use the Mood's median,
• 03:47 Kruskal-Wallis, or Friedman test depending upon the data characteristics.
• 03:52 We'll cover all of these tests in detail in the remaining lessons.
• 03:55 But let's first consider a few of the preliminary questions that are in
• 03:59 the front half of the decision tree.
• 04:01 I'll start with common cause and special cause.
• 04:04 We've discussed this in detail in other lessons and
• 04:07 other parts of the Lean Six Sigma program.
• 04:09 So here's a quick review.
• 04:11 Common cause is normal variation.
• 04:13 It's random in nature, but within normal bounds for the process.
• 04:17 Because of that, it is predictable.
• 04:19 Every process has some level of common cause variation that is inherent in
• 04:23 the process design.
• 04:25 You cannot change this type of variation without a fundamental change to
• 04:28 the process.
• 04:29 In contrast, special cause variation is unique.
• 04:32 It is unpredictable, non-random variation.
• 04:34 It's not due to the inherent design of the process.
• 04:37 Therefore, it is outside the control of the process.
• 04:40 But it impacts process performance.
• 04:43 Although it can't be predicted, it can be controlled by placing process controls on
• 04:47 the process or input that screens or filters out the special causes.
• 04:52 When you have special causes present in your Lean Six Sigma project,
• 04:55 you don't need to do further hypothesis testing.
• 04:58 You already have a clear root cause of the problem that you need to solve,
• 05:01 so, fix it.
• 05:03 Next, we ask whether the data is continuous or discrete?
• 05:06 Again, we've discussed these topics in detail in Lean Six Sigma courses, so
• 05:10 this is just a quick review.
• 05:12 Discrete data is data that can take on a set or predefined specific value.
• 05:17 There is a clear break between data values, and
• 05:20 no meaningful data information exists between these values.
• 05:23 For instance, a switch is either on or off, or
• 05:26 we are using material from supplier A or supplier B.
• 05:30 Most of these tests will require that the information be expressed as an integer
• 05:35 such as off is 0, and on is 1, or supplier A is 1 and supplier B is 2.
• 05:40 If you were to plot the data, it's a step function with a value for
• 05:43 each integer that represents a discrete value.
• 05:46 There is no fractional values between those levels.
• 05:49 In contrast, continuous data can take on any value.
• 05:52 Between any two continuous data values,
• 05:54 there is the ability to have another value.
• 05:57 Often, the data is represented in decimals or fractions rather than integers.
• 06:01 And a data plot will have a smooth curve rather than the stair-step effect with
• 06:05 discrete data.
• 06:07 Finally, let's review normal and non-normal.
• 06:10 Normal data has some very specific characteristics.
• 06:13 First, it's symmetric, there is many data points above the mean as below the mean.
• 06:17 Second, it is peaked in the center, there is a central tendency that has many
• 06:21 more data points at the center of the distribution than at the edges.
• 06:26 And third, while the edges are dropping to near zero, they theoretically
• 06:30 could extend to infinity, but practically they will reach zero.
• 06:35 This gives us the bell-shaped curve that is so
• 06:37 frequently discussed when looking at data.
• 06:40 Finally, the curve is smooth, or at least is becoming smooth based upon the number
• 06:45 of increments in the measurement system.
• 06:47 Non-normal data can be characterized by one or more of these effects.
• 06:52 First, it may not be symmetric.
• 06:54 The data is skewed to one side or the other.
• 06:57 Second, it may not have a peak center due to central tendency.
• 07:01 It could be uniform where the data is level across the distribution, or
• 07:05 even a bathtub shape where the edges are high but the center is low.
• 07:09 And third, the edges have a sharp limit,
• 07:11 often due to physical limitation in the system.
• 07:14 Finally, the curve is not smooth, but rather several big steps.
• 07:19 For our purposes, unless the data meets all of the criteria for normal data,
• 07:23 we will treat it like it is non-normal.
• 07:26 There are many different hypothesis tests.
• 07:30 You must choose the correct test, to get a meaningful answer to your question.

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