p-Value approach

The p-value approach avoids the use of significance level; instead, it reports how significant the sample evidence is. The p value of a sample is:

• The probability of seeing a sample with at least as much evidence in favour of the alternative hypothesis as the sample actually observed.
• The smaller the p-value, there is more evidence in favor of the alternative hypothesis.

Let’s understand the concept of p-value with a simple example.

Suppose that a bakery owner wants to know about the satisfaction level of his customers. He takes feedback from his customers on a ‘-5 to +5’ scale, -5 representing highly dissatisfied, +5 representing fully satisfied, and 0 being neutral.

The hypothesis he will frame are as follows:

• $H_0: μ \geq 0$; the customers are satisfied.
• $H_1: μ < 0$; the customers are not satisfied.

He performs hypothesis testing for 100 samples and gets the p-value as 0.04.

What does this p-value of .04 mean?

This means that if the entire customer population is neutral in terms of satisfaction, only 4 random samples out of a 100 will provide evidence that they are satisfied with the services of the bakery.

So, what should he conclude from this result? Should he reject the null hypothesis, or not?

There is no exact statistical answer to this question; it depends on how convinced the researcher is about the satisfaction level of the customers.

Generally, smaller p-values indicate more evidence in support of the alternative hypothesis.

But at what p-values must you not reject the null hypothesis?

A p-value greater than 0.1 is interpreted as weak evidence in support of the alternative hypothesis.

The advantage of the p-value approach is that you do not need to state the confidence level before solving the hypothesis, as it is difficult to determine the confidence level in any particular situation. It is also evident from our discussion that a p-value can never be negative.