P Value

For example, if we have a random variable A and the value x. The p-value of x is the probability that A takes the value x or any value that has the same or less chance to be observed.

Example

Hypothesis

Null Hypothesis: Drug has no effect. (Sample mean would also be 1.2 sec even with drug) Alternative Hypothesis: Drug has an effect. (Mean is not equal 1.2 sec when drug is given)

Given, $\sigma_{\overline{x}}=\frac{\sigma}{\sqrt{n}}=\frac{0.5}{10}=0.05$ [Best estimation of sample standard deviation] $z=\frac{1.2-1.05}{0.05}=3$ [Z score or how far we are away from the mean]

That means, the z-score is 3, its 3 SD away (i.e., beyond the probability of 99.7% of the normal distribution), which is 0.3% = 0.003 Therefore, the p-value is 0.003

The probability of getting a result more extreme than 1.05 seconds given the Null Hypothesis is True, is 0.3% and is called the p-value. This rejects the Null Hypothesis.

P-values have different threshold other than 0.05, based on different experimental scenarios! A large probability means that the H0 or default assumption is likely. A small value, such as below 5% (0.05) suggests that it is not likely and that we can reject H0 in favor of H1, or that something is likely to be different (e.g. a significant result).

In this example, we performed a Parametric Statistical Hypothesis Tests.

Sometimes, P is the probability that two variables are independent (i.e., Correlation Test). See More Use Cases​

T-value

The larger the absolute value of the t-value, the smaller the p-value, and the greater the evidence against the null hypothesis.

References

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