What is P-Value?
P-Value or the probability value is the determining factor on a null hypothesis for the probability of an assumed result to be true and being accepted or rejected, and acceptance of the alternate result in case of rejection of the assumed result.
Explanation
- In case of a null hypothesis made on a scenario, there is always a probability of the occurrence of a required result. There is also an alternate result which is existent and which holds equivalent probability, however, it would be inferred only if the assumed/required result fails to be proved. 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 rejection of this assumed result and acceptance of the alternate result.
- For example, in a hypothetical situation, we make a survey on a new appliance in the market and results are assumed 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 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.
Formula
It can be calculated using z analysis (z test) where:
where,
- P1 = sample proportion of the whole population
- P0 = Assumed proportion for the result to occur
- n = size of the population
The z value is predicted from previous calculations, and 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.
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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 wishes to invest in a portfolio ABC, however, he feels that there is a probability of 25% that this portfolio will earn the desired rate of interest, while there is another portfolio MNO which is his alternate choice. He samples from 150 stocks and finds out that 40 stocks in portfolio ABC earn the required rate of interest. Calculate the p-value, and assuming that 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 followed that:
- P1 = 40/150 = 0.267
- P0 = 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, which is away from the calculation above, and hence the portfolio ABC gets rejected (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 very low chances of its occurrence. This 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 in cases where making a decision is difficult 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 the probability analysis. In finance, investment decisions are mostly dependent on the probability of profits and losses. Hence, even after the calculation of probability, if the p-value is calculated then it kind of 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 then this calculation is done, then results can be forecasted. Hence, it helps in calculating future cash flows and going 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 in general they are used interchangeably. The probability of occurrence of such a result may be directly calculated, however, p-value calculation also includes a probability of other results’ occurrence. However, statisticians refer to this value for more appropriate results. In most cases, it lies within a range of 0 – 0.05 (5%) has a negative result which means the alternate result would be considered, and a value higher than 0.05 signifies that the desired result will be accepted. However, this will not be hard and fast for all cases and will depend upon the conditions and product.
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This has been a guide to what is P-Value in Statistics and its definition. Here we discuss p-value examples to calculate probability value along with interpretation and uses. You may learn more about financing from the following articles –
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