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.
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, [Best estimation of sample standard deviation] [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
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
The larger the absolute value of the t-value, the smaller the p-value, and the greater the evidence against the null hypothesis.