The P Value

Quick reference

• 00:02 Hi, I'm Ray Sheen.
• 00:06 In this session, I'll introduce the P value.
• 00:09 This is the most universally used statistic in hypothesis testing.
• 00:13 It will be the P value, which will tell us whether or
• 00:16 not we should reject the null hypothesis, or fail to reject it.
• 00:20 >> So let's start with some background on the p-value.
• 00:24 The P Value statistic is used with inferential statistics.
• 00:28 Remember that with inferential statistics,
• 00:30 we are inferring a statistical conclusion about an entire population of data based
• 00:35 upon the analysis of only a subset of that data.
• 00:38 The P Value tests that assumption.
• 00:41 The P Value is the probability that any difference we see between the data sets
• 00:46 that are being analyzed is due to strictly random events and
• 00:49 not due to the alternative hypothesis.
• 00:53 In other words, the P Value tells us whether the statistics are supporting
• 00:57 the null hypothesis.
• 00:58 Is there a statistically significant relationship between the datasets.
• 01:02 And the way the p value is calculated,
• 01:05 a high P Value says that the null hypothesis should be accepted,
• 01:09 but a low P Value says that the null hypothesis must be rejected.
• 01:15 So let's look at the P Value and the level that it can take on.
• 01:18 The P Value is based upon a statistical analysis of the data sets that are being
• 01:22 analyzed as part of the hypothesis test.
• 01:25 Different tests will analyze different aspects of the data set.
• 01:29 The test may be focused on the mean, or the median of the data.
• 01:32 The test may be using the standard deviation or the variance,
• 01:35 which is just the standard deviation squared.
• 01:38 And the test will often take into consideration the number of data points in
• 01:41 the sample.
• 01:42 Whatever the nature of the statistical value,
• 01:44 the P Value is calculated by comparing the data sets to determine if the difference
• 01:48 is statistically significant.
• 01:50 Of course, there are always differences between the data sets.
• 01:54 There is always some level of inherent common cause variation that is occurring.
• 01:58 This P Value represents the probability that this difference is due to random
• 02:03 chance variation as compared to it being due to a fundamental difference in
• 02:07 the processes that the data sets represent.
• 02:10 The P Value is a probability number, so that value is always between 0 and
• 02:15 1.0, essentially between 0% and 100%.
• 02:18 The P Value is also related to our confidence interval,
• 02:22 since we normally use the 0.95 confidence interval in Lean Six Sigma projects,
• 02:28 a P Value of 0.05 is our threshold for
• 02:31 whether to accept or reject the null hypothesis.
• 02:35 Another way of saying this is that the P Value threshold is the alpha value in
• 02:39 the confidence level equation.
• 02:42 Well, this next statement is not precisely true, it is essentially true.
• 02:46 A P value of 0.05 says that there is less than a 5% chance that if I reject
• 02:51 the null hypothesis I made the wrong decision.
• 02:55 Let's run through a few examples to illustrate how the P value works.
• 02:59 We'll start with a null hypothesis that says that the difference in the median
• 03:03 household income in the different counties of Florida is due to random chance, and
• 03:08 the alternative hypothesis is that the differences are not due to random chance.
• 03:13 And therefore the median household income across the counties of Florida is not
• 03:17 normally distributed.
• 03:18 Now the check for these hypotheses is to look at the median values of income across
• 03:22 Florida and determine if the resulting distribution is normal.
• 03:26 So that is what I did, and you can see the plot of that distribution on this graph.
• 03:31 A normal curve should have a high peak in the center and
• 03:34 be reducing down to a very low value at the upper and lower level.
• 03:37 That is not what the distribution shows.
• 03:40 And in fact there's a P value metric that was calculated by my statistical software,
• 03:46 in this case Minitab, that is a value of 0.016.
• 03:49 This is less than a threshold of 0.05.
• 03:52 So reject the null hypothesis that said the medium income in Florida was randomly
• 03:57 distributed.
• 03:59 Now let's look at another example.
• 04:00 In this case, I want to compare the median income between Florida and
• 04:04 Louisiana to see if they are the same.
• 04:07 So my null hypothesis is that there is no statistical difference between the median
• 04:11 income in Florida and Louisiana.
• 04:14 My alternative hypothesis is that the median incomes are not the same.
• 04:18 I could have been even more specific and
• 04:20 said that the median income of Florida is higher than Louisiana.
• 04:22 And if I find that there is a difference, I will check to see which one is higher.
• 04:28 You can see in the results that Florida is definitely higher than Louisiana.
• 04:32 The Florida median income in 2000 was $42,047,
• 04:36 and the Louisiana median income was only $39,823.
• 04:41 Well, that sounds like a lot, but when we check the P value,
• 04:44 it turns out that the difference is not statistically significant.
• 04:49 The P value is 0.099 which is greater than 0.05.
• 04:53 So we do not reject the null hypothesis.
• 04:57 For our purposes, we can consider the median income between these
• 05:02 two states to be in the same data set.
• 05:05 >> The P Value is a convenient metric to use to determine whether the observed
• 05:09 differences are statistically significant.
• 05:12 It is with the P value that we either reject
• 05:17 the null hypothesis, or fail to reject it.

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