The P Value

Quick reference

• 00:04 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 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
• 00:34 based 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
• 00:50 not due to the alternative hypothesis.
• 00:53 In other words, the P Value tells us whether the statistics
• 00:56 are supporting the Null Hypothesis.
• 00:59 Is there a statistics significant relationship between the data sets?
• 01:03 And the way the P value is calculated, a high P value says that the null hypothesis
• 01:07 should be accepted but a low P value says that the null must be rejected.
• 01:15 So let's look at the P value and the level it can take on.
• 01:18 The P Value is based upon the statistical analysis
• 01:21 of the data sets that are being analyzed as part of the hypothesis test.
• 01:25 Different test 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
• 01:34 the variance, 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
• 01:48 that the difference is statistically significant.
• 01:51 Of course, there are always differences between the data sets.
• 01:54 There's always some level of inherent common cause variation that's occurring.
• 01:58 This P Value represents the probability that this difference is due to random
• 02:02 chance variation, as compared to it being due to a fundamental difference
• 02:07 in the processes that the data sets represent.
• 02:10 The P value is a probability number, so that value is always between zero and one.
• 02:16 Essentially, between 0% and 100%.
• 02:20 The P value is also related to our confidence interval.
• 02:23 Since we normally use the .95 confidence interval and Lean Six Sigma projects, a P
• 02:29 value of .05 is our threshold for whether to accept or reject the Null Hypothesis.
• 02:35 Another way of saying this is that the P value threshold
• 02:38 is the alpha value in the confidence level equation.
• 02:42 While this next statement is not precisely true, it is essentially true.
• 02:47 A P value of 0.05 says that there is less than a 5% chance
• 02:51 that if I reject 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 the 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.
• 03:08 And 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
• 03:16 is not normally distributed.
• 03:18 Now, to check for these hypotheses is to look at the median values of income across
• 03:23 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-lower level.
• 03:38 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,
• 03:45 it this case Minitab, that is a value of 0.016.
• 03:50 This is less than our threshold of 0.05, so reject the null hypothesis that
• 03:54 said the median income in Florida was randomly distributed.
• 03:59 Now let's look at another example.
• 04:01 In this case I wanna compare the median income between Florida and
• 04:05 Louisiana to see if they are the same.
• 04:07 So my null hypothesis is that there's 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've been even more specific and
• 04:20 said that the median income of Florida is higher than Louisiana.
• 04:23 Now, 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, and
• 04:36 the Louisiana median income was only $39,823.
• 04:42 Well that sounds like a lot.
• 04:43 But when we check the P Value,
• 04:45 it turns out that the difference is not statistically significant.
• 04:49 The P value is 0.099, which is greater than 0.05,
• 04:54 so we do not reject the null hypothesis.
• 04:57 For our purposes, we can consider the median income between these two states
• 05:02 to be in the same data set.
• 05:05 The P Value is a convenient metric to use
• 05:08 to determine whether the observed differences are statistically significant.
• 05:12 It is with the P value that we either reject the null hypothesis or
• 05:16 fail to reject it.

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