What is P-Value?

Explanation

  • Always a probability of the occurrence of a required result when in a scenario made a null hypothesisNull HypothesisNull hypothesis presumes that the sampled data and the population data have no difference or in simple words, it presumes that the claim made by the person on the data or population is the absolute truth and is always right. So, even if a sample is taken from the population, the result received from the study of the sample will come the same as the assumption.read more.There is also an alternate result that is existent and holds an equivalent probability. However, it would infer if the assumed/required result fails to prove. The P-Value calculation determines whether the assumed result will hold “True” or the alternate result. A higher value determines the acceptance of the assumed result, while a lower signifies the rejection of this assumed result and acceptance of the alternate result.For example, in a hypothetical situation, we survey a new appliance in the market, and results assume that 60% of females will accept the appliance, with an alternate result expected that 60% of males will accept the appliance. With the help of the P-Value, we try to determine the results. A higher value will signify that the assumed expected result is “True,” which means 60% of females accept the appliance. Consequently, a lower would imply acceptance of the alternate results, which means 60% of males accept the appliance.Hence, it determines the acceptance or rejection of an assumed result.

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Formula

It can be calculated using z analysis (z test) where:

where,

  • P1 = sample proportion of the whole populationP0 = Assumed proportion for the result to occurn = size of the population

The z-value is predicted from previous calculations. If the P-value is equal to or less than the calculated z value, then the sample can be approved for the desired result (null hypothesis). Else gets rejected, and the alternate result gets approved.

The z-values are previously calculated values in line with P-values in the form of tables. With the help of z-values, the corresponding values are derived from the below table.

Source: https://www.chegg.com/

Example

Let us understand with an example.

Consider Mr. X’s wishes to invest in a portfolio ABC. However, he feels there is a probability of 25% that this portfolio will earn the desired interest rate, while another portfolio MNO is his alternate choice. He samples from 150 stocks and finds that 40 stocks in portfolio ABC earn the required interest rate. Calculate the P-Value, and assuming that the z-value is 1.72, find out if the portfolio ABC is suitable for investment or should be rejected.

Solution

From the z-test, it is as follows that:

  • P1 = 40/150 = 0.267P0 = 0.25 (the assumed proportion for the result to occur)n = 150

Hence p-value should be as follows:

  • = (0.26667 – 0.25)/SQRT((0.25*(1-0.25))/150)= 0.4714

As per the expected z-value, the P-Value from the above table should be 0.0427, away from the above calculation. Hence, the portfolio ABC gets rejected (the null hypothesis gets rejected).

Interpretation

  • A higher P-Value denotes that the probability of occurrence of the assumed result is very likely. It suggests that the probability ascertained on the occurrence of that result is true, and the outcome will be in favor of the required result. On the contrary, a low value signifies that the required or assumed result has a very low chance of occurrence. It also denotes that the alternate result is more probable to occur. A low value on the assumed or required result automatically rejects this result, and the alternate result is automatically accepted.

Usage and Relevance

  • It is used when making a difficult decision and may lead to serious losses. Finding out a p-value makes it easier to determine between 2 different options.It serves as a double-check on probability analysis. In finance, investment decisions depend mostly on the probability of profits and losses. Hence, even after calculating probability, if the P-Value is calculated, it ensures that the decision taken will be in favor or not.Calculation of returns using a P-Value is a good way of forecasting results. In reality, the futuristic returns cannot be seen today. However, if all constraints are properly measured, and this calculation is done, one can forecast results. Hence, it helps calculate future cash flows and go a little further ahead. It will also help in making future financial-related decisions.

Conclusion

P-Value is similar to the probability of occurrence of the desired result. However, there is a minute difference between the two, as per statistical calculation, although they are generally used interchangeably. One may directly calculate the probability of occurrence of such a result. However, P-Value calculation also includes a probability of other results’ occurrence. However, statisticians refer to this value for more relevant results. In most cases, it lies within a range of 0 – 0.05 (5%) and has a negative result, which means the alternate result would be considered, and a value higher than 0.05 signifies that it will accept the desired result. However, this will not be hard and fast for all cases and will depend upon the conditions and product.

This article is a guide to what P-Value is in Statistics and its definition. Here, we discuss P-Value examples to calculate probability value, interpretation, and uses. You may learn more about financing from the following articles: –

  • P-Value in ExcelT-TestChi Square Test ExcelHypothesis TestingPresent Value vs Future Value