What is P-Value?

In terms of statistics, P-Value is the possibility of acquiring results of a statistical hypothesis test, presuming that the null hypothesis is faultless. The p-value is generally used as an alternative to different rejection points so as to offer the smallest level of substantialness whereat the null hypothesis might get rejected.

A smaller p-value signifies that there is a piece of robust evidence that is working in favour of the alternative hypothesis.

Understanding the Calculation of P-Value

Usually, P-values are found by using p-value tables or statistical / spreadsheets software. Such calculations are based on the known or assumed possible distribution of a certain statistic that is being tested. From the deviation between the selected referenced value and the observed value, P-values get calculated, only if there is a probable statistic’s distribution. Also, the massive difference between these two values signifies a lower P-value.

In terms of mathematics, the P-value gets calculated with an integral calculus from the area that is available under the probability distribution curve for all of the values of statistics that are far from the reference value. Overall, the bigger the difference between two observed values, the less possibility will be there of the difference being because of a random chance. And, this is precisely what a lower P-value reflects.

Example of P-Value

Suppose an investor has claimed that the performance of his investment Portfolio is equal to the Standard & Poor’s (S&P) 500 Index. To comprehend the same, the investor executes a two-tailed test.

The null hypothesis signifies that the returns of the portfolio are equal to the returns of the S&P 500 over a specific time period. On the other hand, the alternative hypothesis says that the returns of the portfolio are not equal to that of the returns of the S&P 500. It is not necessary for the P-value hypothesis to use a pre-selected level of confidence whereat the investor must reset the null hypothesis that the returns are equal. On the contrary, it offers a measure regarding how much proof is there to discard the null hypothesis.

The lesser the P-value, the higher will be the proof against the null hypothesis. Therefore, in case the investor discovers that 0.001 is the P-value, there will be a strong proof against the null hypothesis. And, the investor can be confident about his portfolio returns not to be equal to the returns of the S&P 500.