# P-Value

Written By:
Paul Tracy
Updated August 5, 2020

## What is P Value?

The p-value is used in hypothesis testing to determine whether to accept or reject the null hypothesis. It is the smallest level of significance where the null hypothesis can be rejected.

The p-value reflects the strength of the evidence against the null hypothesis. A smaller p-value means that there is stronger evidence in favor of the alternative hypothesis.

## P-Value Table and Significance

Statisticians and analysts may use the p-value to measure the strength of the significant difference, and thus find out if the null hypothesis may be rejected.

(Note: The p-value is a probability. Computing the p-value and its cumulative distribution function is almost always done with statistical software.)

The appropriate level of significance is chosen by the hypothesis tester, and then compared to the p-value. If the p-value is smaller than the level of significance, then there is more evidence in favor of the alternative hypothesis.

Take a look at the table below to see a quick rundown of how to measure p-value significance:

P-Value Table
P-ValueP- Value
Size
Evidence Strength
Against Null Hypothesis
Reject or Accept
Null Hypothesis?
<=0.05SmallStrongReject
0.05Marginal-Could Go Either Way
>0.05LargeWeakAccept

For example, let's say 5% (0.05) is considered the level of significance (this is a typical benchmark). A p-value of 0.0175 would indicate there is a 0.0175 probability -- or very small chance -- that you'd be wrong to reject the null hypothesis. Put another way, there is more evidence in favor of the alternative hypothesis.

If the hypothesis tester decided that 1% would indicate a level of significance, however, a p-value of 0.0175 would indicate acceptance of the null hypothesis.

## Related Terms to P-Value

Null Hypothesis

Altman Z-Score (how statistics is used in stock investing)