Hypothesis Tests: p-value

00:00 Now we know how to test hypotheses and how to reject them.

00:05 Actually, we rejected the null hypothesis at various levels of significance, but we couldn't find the level of significance for which we can no longer do it.

00:14 This is the right moment to introduce a measure called the P value.

00:20 This is the most common way to test hypotheses.

00:23 Instead of testing at pre assign levels of significance, we can find the smallest level of significance at which we can still reject the null hypothesis.

00:31 Given the observed sample statistic.

00:35 So how do we do that? Recall the tests with the data scientist salary.

00:40 We had a standard error of 2739 known population, standard deviation of 15,000 normally distributed population and a sample size of 30. The corresponding Z score was -4.67.

00:55 We rejected the null hypothesis, has significance levels of 0.05 and 0.01. But we wanted to know how much lower we could go.

01:05 We can check the Z table for plus 4.67, which gives us the same result as -4.67.

01:14 In most sea tables, you would not even find this value as it is so large.

01:18 Thus, we round up to the closest value available and get 0.0001. Wait.

01:26 But how do we actually test the hypothesis? Well, after choosing a significance level of alpha, you compare the p value to it. You should reject the null hypothesis if the p value is lower than the significance level.

01:42 Therefore, we can safely say that such a result is extremely significant by any measurement of significance.

01:51 Let's see another example.

01:53 If our Z score was 2.12, we would reject the null hypothesis at 5%, but would not reject it at 1% significance.

02:02 Now it becomes more interesting.

02:04 At this point, we can actually look at the table and then find the p value.

02:09 We look for the value that corresponds to 2.12 and find that it is 0.983.

02:17 The P value for a one sided test is one minus the number we see in the table.

02:22 So the corresponding p value is equal to 0.017.

02:29 The P value for a two sided test is equal to the number we see in the table multiplied by two. Therefore, the p value would be 0.03 for.

02:40 This is also the answer to our question.

02:45 All right. So where are P values used? Most statistical software packages, run tests and then provide us with a series of results. One of them is P value.

02:57 It is then up to the researcher to decide whether the variable is statistically significant or not.

03:04 Generally, software is designed to calculate the p value to the third digit after the separator. The point is, when you start conducting your own research, you would love to be able to see the three zeroes after the dot.

03:18 The closer to zero your p value is, the more significant is the result you've obtained. The final consideration is that the P value is an extremely powerful measure, as it works for all distributions.

03:32 No matter if we are dealing with the normal student's t binomial or uniform distribution, whatever the test, the p value rationale holds. If the p value is lower than the level of significance, you reject the null hypothesis.

03:48 Having said that, you would normally use the p value in the presence of a digital medium.

03:53 Throughout this course, I recommend that you use online p value calculators to support your studies and double check your answers when doing exercises.

04:03 Please download the PDF that comes with this lesson, as it will include detailed instructions for how to use online p value calculators.

04:12 Thanks for watching.