Hypothesis Tests

Quick reference

• 00:04 Hi, I'm Ray Sheen.
• 00:05 You know, I kept talking about Hypothesis Tests.
• 00:09 And you're probably starting to wonder, 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
• 00:23 apply the appropriate test to the data, in order to to calculate the test statistic.
• 00:28 It should come as no surprise that different test are used depending upon
• 00:31 the type of data that is available, and
• 00:33 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,
• 01:10 will also impact the hypothesis test selection.
• 01:13 And finally, the number of data samples in the investigation
• 01:17 can impact which test we should use.
• 01:20 So let me take you through a decision tree, for
• 01:22 how to select the hypothesis test.
• 01:24 This decision tree contains twenty different tests, there even more tests,
• 01:29 but these are the most commonly used, once in some cases
• 01:32 several different tests could be used I've identified the one that I normally use.
• 01:37 And 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'll probably reach the same conclusion with respect to the hypothesis,
• 01:48 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 discreet, 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 multiple regression analysis.
• 02:20 When both the dependent and independent variables are discreet,
• 02:23 we need to ask the question, 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.
• 02:35 And if more than two samples do a Chi-Square test.
• 02:38 Now consider the case where one of the variables is discreet, and
• 02:42 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'll ask our same question about the number of data samples in the analysis.
• 02:52 If it's just one sample, d a one-sample T-test, or a one-sample test for
• 02:56 variance 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.
• 03:05 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 and the hypothesis.
• 03:20 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, again,
• 03:27 we ask the question to how many samples are involved.
• 03:30 If there is 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 Levene's test for variance,
• 03:41 and 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 Krusical-Walls, or Friedman test depending upon the data characteristics.
• 03:52 We'll cover all these tests in detail in the remaining lessons, but
• 03:56 let's first consider a few of the preliminary questions
• 03:59 that are in the front half of the decisions tree.
• 04:02 I'll start with common cause and special cause.
• 04:04 We've discussed this in detail in other lessons,
• 04:07 in other parts of the Lean Six Sigma program.
• 04:09 So here's a quick review, common cause is normal variation.
• 04:13 It's random in nature, but within normal bounds for
• 04:16 the process, because of that, it is predictable.
• 04:19 Every process has some level of common cause variation,
• 04:22 that is inherent in the process design.
• 04:25 You cannot change this type of variation,
• 04:26 without a fundamental change to the process.
• 04:29 In contrast, special cause variation is unique.
• 04:32 It is unpredictable, non-random variation,
• 04:34 it is not due to inherent design of the process.
• 04:37 Therefore, it is outside the control of the process, but
• 04:40 it impacts process performance.
• 04:43 Although it can't be predicted, it can be controlled by placing process controls
• 04:47 on 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 exists between these values.
• 05:24 For instance the switch is either on or off.
• 05:26 Or we are using material from supplier A or from supplier B.
• 05:30 Most of these tests will require that the information be expressed as an integer,
• 05:34 such as off is zero and on is one.
• 05:37 Or supplier A is one and supplier B is two.
• 05:40 If you were to plot the data, it's a step function with the 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 state of 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,
• 06:04 rather than the stair-step effect with 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,
• 06:14 there are as many data points above the mean as below the mean.
• 06:17 Second, it is peaked in the center, there is a central tendency.
• 06:21 That has many more data points at the center of the distribution,
• 06:24 than at the edges.
• 06:26 And third, while the edges are dropping to near zero,
• 06:29 they theoretically could extend to infinity.
• 06:32 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,
• 06:44 based upon the number 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, 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,
• 07:10 the edges have a sharp limit, 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
• 07:23 normal data, we will treat it like it is not normal.
• 07:28 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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