# What is 'P' value in any research study? How to determine/calculate it?

Is it really necessary that every study should have its own 'P' value to prove its significance?

Kindly share your expert opinion.

I am eagerly expecting some interesting replies especially from the respected statisticians on this website.

Kindly share your expert opinion.

I am eagerly expecting some interesting replies especially from the respected statisticians on this website.

## Popular Answers

Mauricio Abreu Pinto Peixoto· Núcleo de Tecnologia Educacional para a Saúde"...To understand both the original purpose of the p-value p and the reasons p is so often misinterpreted, it helps to know that p constitutes the main result of statistical significance testing (not to be confused with hypothesis testing), popularized by Ronald A. Fisher. Fisher promoted this testing as a method of statistical inference. To call this testing inferential is misleading, however, since inference makes statements about general hypotheses based on observed data, such as the post-experimental probability a hypothesis is true. As explained above, p is instead a statement about data assuming the null hypothesis; consequently, indiscriminately considering p as an inferential result can lead to confusion, including many of the misinterpretations noted in the next section.

On the other hand, Bayesian inference, the main alternative to significance testing, generates probabilistic statements about hypotheses based on data (and a priori estimates), and therefore truly constitutes inference. Bayesian methods can, for instance, calculate the probability that the null hypothesis H0 above is true assuming an a priori estimate of the probability that a coin is unfair. Since a priori we would be quite surprised that a coin could consistently give 75% heads, a Bayesian analysis would find the null hypothesis (that the coin is fair) quite probable even if a test gave 15 heads out of 20 tries (which as we saw above is considered a "significant" result at the 5% level according to its p-value).

Strictly speaking, then, p is a statement about data rather than about any hypothesis, and hence it is not inferential. This raises the question, though, of how science has been able to advance using significance testing. The reason is that, in many situations, p approximates some useful post-experimental probabilities about hypotheses, such as the post-experimental probability of the null hypothesis. When this approximation holds, it could help a researcher to judge the post-experimental plausibility of a hypothesis.[4][5][6][7] Even so, this approximation does not eliminate the need for caution in interpreting p inferentially, as shown in the Jeffreys–Lindley paradox mentioned below.

[edit]Misunderstandings

The data obtained by comparing the p-value to a significance level will yield one of two results: either the null hypothesis is rejected, or the null hypothesis cannot be rejected at that significance level (which however does not imply that the null hypothesis is true). A small p-value that indicates statistical significance does not indicate that an alternative hypothesis is ipso facto correct.

Despite the ubiquity of p-value tests, this particular test for statistical significance has come under heavy criticism due both to its inherent shortcomings and the potential for misinterpretation.

There are several common misunderstandings about p-values.[8][9]

The p-value is not the probability that the null hypothesis is true.

In fact, frequentist statistics does not, and cannot, attach probabilities to hypotheses. Comparison of Bayesian and classical approaches shows that a p-value can be very close to zero while the posterior probability of the null is very close to unity (if there is no alternative hypothesis with a large enough a priori probability and which would explain the results more easily). This is the Jeffreys–Lindley paradox.

The p-value is not the probability that a finding is "merely a fluke."

As the calculation of a p-value is based on the assumption that a finding is the product of chance alone, it patently cannot also be used to gauge the probability of that assumption being true. This is different from the real meaning which is that the p-value is the chance of obtaining such results if the null hypothesis is true.

The p-value is not the probability of falsely rejecting the null hypothesis. This error is a version of the so-called prosecutor's fallacy.

The p-value is not the probability that a replicating experiment would not yield the same conclusion.

1 − (p-value) is not the probability of the alternative hypothesis being true (see (1)).

The significance level of the test is not determined by the p-value.

The significance level of a test is a value that should be decided upon by the agent interpreting the data before the data are viewed, and is compared against the p-value or any other statistic calculated after the test has been performed. (However, reporting a p-value is more useful than simply saying that the results were or were not significant at a given level, and allows the reader to decide for himself whether to consider the results significant.)

The p-value does not indicate the size or importance of the observed effect (compare with effect size). The two do vary together however – the larger the effect, the smaller sample size will be required to get a significant p-value."