Statistical Analysis

Quick reference

• 00:05 Hi, I'm Ray Sheen.
• 00:06 Now, during the analyze stage of a Lean Six Sigma project,
• 00:10 we will often be conducting statistical analysis.
• 00:13 Let's cover a few of the principles involved in this analysis.
• 00:17 So how should we approach the use of statistical analysis for our problem?
• 00:22 We'll start with the basic problem-solving elements that we have already discussed.
• 00:26 Use inductive and deductive reasoning to create a null and alternative hypothesis.
• 00:32 We'll then use the statistical analysis to accept or reject the hypothesis.
• 00:38 Depending upon the structure of your hypothesis and
• 00:41 the characteristics of your data set, such as whether it is variable or
• 00:45 attribute and how many data sets you have.
• 00:48 There are a number of different statistical tests that can be used.
• 00:51 Different tests work with different types of data.
• 00:55 Unfortunately, there is no universal test that works with everything.
• 00:59 That's why we created a separate Hypothesis Testing course, and
• 01:04 allows us to focus in on the statistical tests used in Lean Six Sigma analysis.
• 01:09 While there is no universal test, there is a universal measure for
• 01:13 the statistical test analysis used with hypothesis testing.
• 01:17 The Universal measure is the P value, or the probability value.
• 01:22 This measure tells us the probability that your null hypothesis is true.
• 01:26 Based upon the size of the P value, you can either accept or
• 01:30 reject the null hypothesis.
• 01:32 Now, there's a caution here.
• 01:34 The reason we'll be picky about how to write a null and an alternative hypothesis
• 01:38 is that the P value tells you whether to reject the null hypothesis or not.
• 01:43 It does not specifically say that your alternative hypothesis is true.
• 01:48 A poorly constructed alternative hypothesis that is not truly the inverse
• 01:53 of the null hypothesis may not be true either, but
• 01:56 more about that in the hypothesis testing course.
• 01:59 For now it's enough to know that when I write good hypotheses,
• 02:03 there are statistical tests that will tell me whether to accept them or reject them.
• 02:07 Another important topic to discuss is inferential statistics.
• 02:12 This means answering the question,
• 02:14 is the data of your analysis similar to all of the problem data.
• 02:18 Inferential statistics allow us to draw conclusions about all
• 02:22 the data in a population, even though we only have access to a portion of the data.
• 02:27 Political pollsters do this all the time,
• 02:30 they do a poll of several hundred or thousand people and use the statistics
• 02:35 from that data sample to predict the outcome of a national election.
• 02:39 Occasionally, you'll be lucky enough to have all the data for your problem,
• 02:44 but most of the time we only have a portion of the data, and
• 02:48 that's when we need to do inferential statistics.
• 02:51 We can't go back in time and collect data that was not recorded.
• 02:55 We may not have access to all the products or all the customers or all the locations.
• 03:01 Now let's be clear, when we analyze a dataset,
• 03:04 that's only giving us information about the items that are in that dataset.
• 03:09 But with some additional analysis,
• 03:11 we can determine to what degree the analysis of that data set can be used to
• 03:16 infer the characteristics of the full population of all the instances.
• 03:21 This additional analysis is based upon sampling and confidence intervals.
• 03:26 The purpose of inferential statistics is to allow us to use the sample
• 03:30 statistics as a surrogate for the entire population statistics.
• 03:34 Now, the statistical value calculated the sample such as the mean is a point.
• 03:40 But there is some uncertainty as to how close
• 03:43 the sample point is to the real point for the entire population.
• 03:48 The uncertainty is described with a confidence interval.
• 03:52 Essentially, that is the range around the calculated point in
• 03:56 which the real point exists.
• 03:59 The size of that range is based upon characteristics of your sample data and
• 04:04 your desired confidence level, 90% confident, 95, 99% confident.
• 04:10 Although not precisely correct,
• 04:12 it's essentially correct to say that it is probable that the actual mean value
• 04:17 will be within the confidence interval around the sample mean point.
• 04:21 I won't go through all the calculations right now,
• 04:24 we do that in the hypothesis testing course.
• 04:26 But to use this confidence interval, we need the standard deviation
• 04:30 of the population, which we can derive from the size of the sample and
• 04:34 the standard deviation of the sample itself.
• 04:37 Then we need to decide what confidence interval to use.
• 04:40 Most Lean Six Sigma projects use 95%, or
• 04:43 we need to decide on an interval width with which we are comfortable.
• 04:48 If we start with the confidence level, we'll calculate the confidence interval.
• 04:52 If we start with the interval, we can determine the confidence level.
• 04:56 The confidence interval will ultimately be described with a point estimate and
• 05:01 a range around that point estimate.
• 05:04 The size of that range depends upon the confidence level, and
• 05:08 is essentially plus or minus the Z value that you see in the table.
• 05:13 Statistical analysis will allow us to move from guessing the problem to knowing
• 05:17 the problem.
• 05:18 And with inferential statistics,
• 05:20 we can even apply a confidence level to our knowledge of this situation.

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