Alpha and Beta Risk

Quick reference

• 00:04 Hi, I'm Ray Sheen.
• 00:05 Even when you do everything right,
• 00:07 you can still get the wrong answer with a hypothesis test.
• 00:10 This is a nature of working with statistics.
• 00:14 When working with a hypothesis testing,
• 00:16 we call this the alpha risk and the beta risk.
• 00:20 So let's consider what could happen with a hypothesis test.
• 00:25 The hypothesis test will provide a statistic that we use to either reject
• 00:30 the null hypothesis, or fail to reject the null hypothesis.
• 00:35 But depending upon the statistical value,
• 00:37 it's possible to reach the wrong conclusion.
• 00:40 For instance, it's very possible that there is an overlap in the statistical
• 00:45 range between the dataset where the null is true and
• 00:49 the dataset where the alternative hypothesis is true.
• 00:53 If the calculated statistic for a specific test is in that area of overlap,
• 00:57 it's possible that the wrong conclusion could be reached.
• 01:02 A condition where we would reject the null hypothesis,
• 01:05 even though that is true, is known as the alpha risk.
• 01:09 And the condition when we fail to reject the null hypothesis,
• 01:13 even though it is not true, is the beta risk.
• 01:17 It's fairly obvious that these two risks are inversely related.
• 01:22 When you lower one type of risk, you are likely to increase the other type.
• 01:27 For instance, if we change the level of the statistic so
• 01:30 that we reduce the likelihood of the alpha risk, that is,
• 01:34 we reject the null hypothesis when it's true, it would be offset by an increase
• 01:39 in the risk that we fail to reject the null hypothesis when it is not true.
• 01:44 Now, we can get the fact of reducing both alpha risk and
• 01:48 beta risk if we increase the sample size.
• 01:52 This will decrease the confidence interval for both conditions,
• 01:56 which will reduce the amount of overlap and the likelihood of an error.
• 02:02 Let me show you what I mean about alpha risk and beta risk.
• 02:05 This truth table considers four conditions.
• 02:08 The top row is the case when the null hypothesis is actually true.
• 02:12 And the bottom row is the case when the alternative hypothesis is actually true.
• 02:18 Then the left column is the case when the statistic would say that we fail
• 02:23 to reject the null hypothesis.
• 02:26 And the right-hand column is the case where the statistic would reject the null
• 02:30 hypothesis.
• 02:32 So the upper left quadrant is a correct decision.
• 02:36 In that case, the null hypothesis is actually true and
• 02:39 we fail to reject the null hypothesis, meaning that we accept it as true.
• 02:44 And the lower right quadrant is a correct decision.
• 02:48 In that case, the alternative hypothesis is actually true and
• 02:52 we reject the null hypothesis.
• 02:54 But now, let's look at the upper right quadrant.
• 02:58 The null hypothesis was actually true, but we rejected the null hypothesis.
• 03:03 That is an alpha risk error, or sometimes called the type I error.
• 03:09 And the lower left corner is also a problem.
• 03:12 In that case, the alternative hypothesis is actually true, but
• 03:16 we failed to reject the null hypothesis.
• 03:18 So we will proceed as though the null hypothesis were true.
• 03:22 That is the beta risk, and is called a type II error.
• 03:27 Now, I think we can agree that we want to make the right decision.
• 03:31 But if there's going to be a mistake,
• 03:33 I'd rather that the mistake was that I didn't recognize the problem,
• 03:37 rather than I thought we found a problem and that was not there.
• 03:41 When that happens, I'm likely to spend a lot of time and
• 03:44 money fixing a problem that doesn't exist.
• 03:47 So the hypothesis test statistic will be based upon the magnitude of the alpha risk
• 03:51 I'm willing to accept.
• 03:53 And the alpha risk value is directly related to the confidence level that we
• 03:57 discussed in a previous lesson.
• 04:00 Alpha is 1 minus the confidence level.
• 04:04 But the overall accuracy is based upon more than just the alpha risk.
• 04:09 It's also dependent upon the precision of the descriptive statistic used in
• 04:13 the analysis.
• 04:15 When there are only a few data points in the dataset,
• 04:18 there is a high level of uncertainty in the mean value, and the standard deviation
• 04:23 can be quite high because it only takes one point to have a major effect on both.
• 04:29 However, with a large number of data points in the sample set, the uncertainty
• 04:33 of the mean is low, and the accuracy of the standard deviation is much better.
• 04:38 The result is that the accuracy of the hypothesis
• 04:41 test is much better as the number of points in the sample set goes up.
• 04:46 Okay, let's wrap up this discussion with a few comments about choosing your
• 04:50 confidence level and alpha value.
• 04:52 As we said, alpha and confidence interval are directly related.
• 04:56 Alpha is equal to 1 minus the confidence interval.
• 04:59 The alpha level is often chosen based upon the type of risk involved.
• 05:04 A risk that has a very severe impact will likely have a higher confidence level.
• 05:09 We don't want bad things to happen.
• 05:12 And, of course,
• 05:14 the higher confidence level will mean a smaller alpha risk on the test.
• 05:19 Most of the time Lean Six Sigma projects use a confidence level of 0.95 or 95%.
• 05:24 And that's a level I'll be using for all of our examples.
• 05:28 But if your project has a higher levels of risk,
• 05:31 you may want to change the confidence level.
• 05:35 This table represents some of the commonly used values,
• 05:38 depending upon the risk of getting the analysis wrong.
• 05:42 Alpha and beta risks help us understand the likelihood of a false positive or
• 05:46 a false negative when conducting an hypothesis test.

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