Many students are unsure about the interpretation of $P$-values and other concepts related to tests of significance. These ideas are used repeatedly in various applications so it is important that they be understood.
For testing a statistical hypothesis we can use one of the methods like Rejection region method or $P$-value testing method. $P$-value is the probability that our null hypothesis is actually correct.
The probability that the value of test statistic is at least as extreme as its computed value on the basis of the sample data under $H_{0}$ is known as the $P$-value.

## How to Calculate P-value

The $P$-value can be interpreted in terms of a hypothetical repetition of the study. Based on the given tests P- value is calculated as explained below :

Right Tailed Test :
$P$-value is the area to the right of the computed value of the test statistic under $H_{0}$.

Left Tailed Test :
$P$-value is the area to the left of the computed value of the test statistic under $H_{0}$.

Two Tailed Test:
$P$ value is twice the area to the left of the computed value of test statistic under $H_{0}$, if it is negative.

$P$ value is twice the area to the right of the computed value of test statistic under $H_{0}$, if it is positive.

Thus $P$-value for two tailed test is twice the area on either tail (left or right) of the computed value of test statistic under $H_{0}$.

## Method

Given below are some simple steps used in calculating P-value:

1)
Identify and set up the null hypothesis and alternative hypothesis.

2)
Before drawing the sample level of significance $\alpha$ is fixed, choose the appropriate one according to the problem.

3)
Identify and calculate the test criterion under $H_{0}$.

4)
Find the $P$-value of the computed test statistic under H$_{0}$.

5)
If $P$-value < $\alpha$, we reject $H_{0}$ at $\alpha$ level of significance.
If $P$-value > $\alpha$, we fail to reject $H_{0}$ at $\alpha$ level of significance.

6)
Conclude whether to accept or reject the null hypothesis for the given problem.

## Significance

When a $p$ value is reported to persons unfamiliar with statistics it becomes necessary to indicate the strength of the evidence.

The cut off are arbitrary and other persons might use a different language. Have a look at the table to clearly understand which can be helpful while making decisions based on the hypothesis. one should keep in mind the difference between statistical significance and practical significance

 $P$-Value Statement $P$ > 0.10 There will be no evidence against the null hypothesis and appears to be consistent with the null hypothesis. 0.05 < $P$ < 0.10 Weak evidence against the null hypothesis in favor of the alternative. 0.01 < $P$ < 0.05 Moderate evidence against the null hypothesis in favor of the alternative. 0.001< $P$ < 0.01 Strong evidence against the null hypothesis in favor of the alternative. $P$ < 0.001 Very strong evidence against the null hypothesis in favor of the alternative.