Question

1.   The CEO of the firm you work for is reading some research about the market you firm is in. He keeps coming across this concept of p-value and is perplexed by what it means. He asks you to explain it to him in a way he can understand it. (He took stats 40 years ago at an inferior university). Write up an explanation of p-value and use an example that will clearly explain this concept to him.    Remember, he basically has no background in statistics.

Answer 1

The p value is used in hypothesis testing.

Hypothesis testing consists of two statements one is null hypothesis and the other one is called as alternative hypothesis. In null hypothesis we give a statement that is of null approach, suppose if we want to test the product of two companies (which company delivers better product), then our null hypothesis in this case will be- there is no difference between the product of two companies and the alternative hypothesis may be- the product of company 1 is better than product of company 2, or the the product of company 2 is better than company 1 or the product of two companies are different from each other.

So before performing the experiment, we make null hypothesis and decide upon the significance level alpha traditionally 5% or 1% . So when the p value is less than the given alpha we reject our null hypothesis and when it is greater than alpha we do not reject the null hypothesis.

Example

Assume than an investor claims that their investment portfolio's performance is equivalent to some index. To determine this, investor conducts a test. The null hypothesis will be portfolio's returns are equivalent to index returns over a specified period, while the alternative hypothesis states that portfolio's returns and index's returns are not equivalent.

The Commonly used value of alpha(level of significance) is 0.05 ( as mostly it is taken as 5%)

So if the investor finds that P value is less than 0.05 then there is a evidence against the null hypothesis. As a result, the investor would reject the null hypothesis and accept the alternative. The smaller the P value, the greater the evidence against the null hypothesis. Conversely if P value is greater than 0.05, it indicates that there is a weak evidence against null hypothesis so the investor would fail to reject the null hypothesis.

P values are calculated using P value tables or statistical softwares.