Original subtitles

Narrator: Now we know how to test hypotheses

and how to reject them.

Actually, we rejected a null hypothesis at various levels

of significance, but we couldn't find a level

of significance for which we can no longer do it.

This is the right moment to introduce a measure

called the P value.

This is the most common way to test hypotheses.

Instead of testing at preassigned levels of significance

we can find the smallest level of significance

at which we can still reject the null hypothesis

given the observed sample statistic.

So how do we do that?

Recall the test with the data scientist salary.

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 minus 4.67.

We rejected the null hypothesis

as significance levels of 0.05 and 0.01

but we wanted to know how much lower we could go.

We could check the Z table for plus 4.67

which gives us the same result as minus 4.67.

In most Z tables,

you would not even find this value as it is so large.

Thus, we round up

to the closest value available and get 0.0001.

Wait, 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.

Therefore, we can safely say

that such a result is extremely significant

by any measurement of significance.

Let's see another example.

If our Z score was 2.12, we would reject the null hypothesis

at 5%, but would not reject it at 1% significance.

Now it becomes more interesting.

At this point, we can actually look at the table

and then find the P value.

We look for the value that corresponds to 2.12

and find that it is 0.983.

The P value for a one-sided test is one minus the number

we see in the table.

So the corresponding P value is equal to 0.017.

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 0.034.

This is also the answer to our question.

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.

It is then up to the researcher to decide

whether the variable is statistically significant or not.

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 zeros after the dot.

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.

No matter if we are dealing with the normal,

students 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.

Having said that, you would normally use the P value

in the presence of a digital medium.

Throughout this course, I recommend that you

use online P value calculators to support your studies

and double check your answers when doing exercises.

Please download the PDF that comes

with this lesson as it will include detailed instructions

for how to use online P value calculators.

Thanks for watching.