Statistical Analysis

Quick reference

• 00:05 Hi, I'm Ray Sheen.
• 00:06 During the Analyze stage of a Lean Six Sigma project,
• 00:09 we will often be conducting statistical analysis.
• 00:13 Let's cover a few of the principles involved in this analysis.
• 00:18 Let me start by saying you need to understand your statistics so
• 00:22 that you don't fool yourself into thinking something is good or bad when it isn't.
• 00:27 I'll illustrate this point by using a simple statistical measure, the mean or
• 00:32 average value.
• 00:33 No one statistics provide everything you need to know about the data set.
• 00:36 So while the mean is a very important number, and we use it often,
• 00:40 it still does not tell the whole story.
• 00:43 That's because statistical analysis works with the data set, not an individual
• 00:48 data point, but your customer feels their individual data point.
• 00:52 Their instance is what matters to them, so
• 00:54 while the average value in a data set may be a problem for most customers.
• 00:59 You may still have some customers with perfectly acceptable instances and
• 01:03 vice versa.
• 01:04 The average may be fine, but
• 01:06 there're isolated customers who are not satisfied with the process performance.
• 01:11 Let me illustrate with an example,
• 01:13 we have two call centers that are answering customers questions.
• 01:17 The customer calls an stays on hold until a customer service rep speaks with them.
• 01:21 The average hold time in both call centers is the same, seven minutes.
• 01:26 Now, that level itself may be unacceptable for some industries or customer groups but
• 01:30 maybe considered normal performance for others.
• 01:33 However, let's look in a little more detail at the data.
• 01:36 In the first call center, customers waited between five and
• 01:40 eight minutes with an average of seven minutes.
• 01:42 Depending upon the industry that might mean four angry customers or
• 01:45 four customers who are enjoying the sound of that beautiful telephone hold music.
• 01:50 In the second call center, three of the four customers only waited for
• 01:54 1 minute, but one customer waited for 25 minutes.
• 01:58 So in that case, there are three customers who are pleased with
• 02:01 the responsiveness and one customer who is contemplating how to
• 02:04 create a viral YouTube post complaining about the awful service.
• 02:08 Average in both cases are the same, but
• 02:10 the customer experiences are very different.
• 02:14 So be careful just throwing around statistics,
• 02:16 make sure you understand what they mean.
• 02:19 So how should we approach the use of statistical analysis in our problem?
• 02:23 Well, start with the basic problem-solving elements that we've already discussed.
• 02:28 Use inductive and deductive reasoning to create a null and alternative hypothesis.
• 02:33 We will then use statistical analysis to accept or reject the hypothesis.
• 02:37 Depending upon the structure of your hypothesis and the characteristics of your
• 02:41 data set, such as whether it is variable or attribute data.
• 02:44 And how many data sets you have to work with,
• 02:46 there are a number of statistical tests that you can use.
• 02:50 Different tests work with different types of data, unfortunately,
• 02:54 there's no universal test that works with everything.
• 02:57 That is why we create a separate hypothesis testing course.
• 03:01 It allows us to focus on each of the statistical tests used
• 03:04 in Lean Six Sigma analysis.
• 03:06 And while there's no universal test, there is a universal measure for
• 03:11 the statistical test analysis used when doing hypothesis testing,
• 03:16 that universal measure is the P value or probability value.
• 03:21 This measure tells you the probability that your null hypothesis is true.
• 03:26 Based upon the size of the P value, you can either accept or
• 03:29 reject the null hypothesis.
• 03:32 Now there's a caution here,
• 03:34 the reason we will be picky about how to write the null and alternative hypothesis,
• 03:38 is that the P value tells you whether you can reject the null hypothesis or not.
• 03:43 It does not specifically say that your alternative hypothesis is true.
• 03:47 A poorly constructed alternative hypothesis
• 03:50 that is not a true inverse of the null hypothesis may or may not be true.
• 03:55 But more about all that in the hypothesis testing course.
• 03:58 For now, it's enough to know that when I write a good hypothesis,
• 04:02 there're statistical tests that will tell me how to accept or reject them.
• 04:07 Another important topic to discuss is inferential statistics.
• 04:12 That means answering the question,
• 04:14 is the data in your analysis similar to all the problem data?
• 04:18 Inferential statistics allows us to draw conclusions about all the data in
• 04:22 a population, even though we only have access to a portion of that data.
• 04:26 Political posters do this all the time, they do a poll of several hundred or
• 04:30 thousand people, and use the statistics from that
• 04:33 data sample to predict the outcome of a national election.
• 04:37 Occasionally, you'll be lucky enough to have all the data for your problem.
• 04:41 But most of the time, we only have a portion of a data set,
• 04:44 and that is why we need to do inferential statistics.
• 04:48 We can't go back in time and collect data that was never recorded.
• 04:52 And we may not have access to all the products or customers or locations.
• 04:56 Now let's be clear, when we analyze a data set,
• 04:59 that is only getting information about the items represented by that data set.
• 05:04 But with some additional analysis,
• 05:06 we can determine to what degree the analysis of that data set can be used
• 05:11 to infer the characteristics of the full population of instances.
• 05:17 This additional analysis is based upon sampling rules and confidence intervals.
• 05:22 The purpose of inferential statistics is to allow us to use sample statistics
• 05:27 as a surrogate for the entire population statistics.
• 05:31 Now the statistical value calculated such as a mean is a point, but
• 05:36 there's some uncertainty is to how close the sample point is to the real point for
• 05:41 the entire population.
• 05:42 That uncertainty is described with a confidence Interval.
• 05:46 Essentially, that is the range around the calculated point in which
• 05:50 the real point actually exists.
• 05:53 The size of this range is based upon the characteristics of your sample data,
• 05:58 and the desired confidence level 90%, 95, 99.
• 06:02 Although not precisely correct,
• 06:03 it is essentially correct to say that it is a probability that the actual mean will
• 06:07 be within the confidence interval around the sample mean.
• 06:10 I won't go through all the calculations right now we'll do better
• 06:14 the hypothesis test in course.
• 06:17 But to use this confidence interval, we need to have the standard deviation
• 06:21 of the population, which we can derive from the size of the sample and
• 06:25 the standard deviation of the sample.
• 06:27 Then we either need to decide what confidence interval to use, most
• 06:32 people use 95%, or we need to decide what interval width we are comfortable with.
• 06:37 If we start with a confidence level, we will calculate the confidence interval
• 06:41 if we start with the interval, we will determine the confidence level.
• 06:45 The confidence interval will ultimately be described with a point estimate and
• 06:49 a range around that point estimate.
• 06:51 The size of the range depends upon the confidence level, and
• 06:55 is essentially plus or minus the Z value that you see in this table.
• 07:00 Statistical analysis will allow us to move from guessing the problem to knowing
• 07:05 the problem.
• 07:06 And with inferential statistics,
• 07:08 we can even apply a confidence level to our knowledge of this situation.

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