# P Value – Definition

### P-Value Definition

The P-value refers to a continuous measure of the evidence against a model to determine the tendency of occurrence of an event or not. It is also a method of examining the level of marginal significance within a statistical hypothesis representing the tendency of the occurrence of a given event. The p-value is an alternative to rejection points, it provides a level of significance in which the null hypothesis should be rejected or ignored. A smaller p-value is an indicator of strong evidence supporting the alternative hypothesis.

### A Little More on Calculating P-Value

Spreadsheets, p-value tables and other statistical software are used when calculating p-values. Often times, readers experience difficulties comparing different test results, this is due to the fact that researchers employ varying levels of significance in their research and question examination.

For instance, when two studies of returns from two specific assets are examined using two different levels of significance, a reader comparing the tendency of returns for the two assets will not find this easy and straightforward.

To aid easy comparison, the p-value is introduced by the researchers in the hypothesis test, this allows the reader to interpret the level of statistical significance. This is referred to as the p-value approach to hypothesis testing.

### P-Value Approach to Hypothesis Testing

To determine if there are reasons to reject the null hypothesis, the p-value approach to hypothesis uses the calculated probability. The null hypothesis is the initial claim about a population of statistics. The null hypothesis is also known as a conjecture.

The alternative hypothesis is used in hypothesis testing that is contrary to the null hypothesis. It states whether the population parameters are different from the value of the population parameter as stated in the conjecture or inference. The p-value or critical value is stated in advance to check how the required value rejects the null hypothesis. It is taken to be that the observations are the result of a real effect.

### Type I Error

A type I error is referred to as a false positive finding or conclusion. In other words, a type I error is the false refusal or rejection of the null hypothesis. The tendency of a type I error occurrence or rejection of the null hypothesis when it is true equals the critical value used. In a different view, the tendency of attesting that the null hypothesis is true is equivalent to 1 minus the critical value.

### KEY TAKEAWAYS

P-value examines the level of marginal significance following the tendency of an event’s occurrence or not. Spreadsheets, p-value tables and other statistical software are used when calculating p-values. When P-value is small, there is cogent evidence supporting the alternative hypothesis.

### Real World Example of P-Value

For example, an investor affirms that their investment performance equals that of the Standard  & Poor’s (S & P) 500 Index. To determine this, a two-tailed test is conducted. The null hypothesis declares that over a period of time or time frame, the portfolio’s returns will be equivalent to the S&P 500’s returns. The alternative hypothesis, on the other hand, states that the portfolio’s returns did not equal the S&P 500’s returns. If a one-tailed test had been conducted, the portfolio’s returns in an alternative hypothesis would have been either less or greater than the S&P 500’s returns.

The commonly used p-value is 0.05, if the investor drives at a conclusion that the p-value is less than 0.05, there is cogent evidence against the null hypothesis. With this, the investor would ignore the null hypothesis and accept the alternative hypothesis. If the p-value is greater than 0.05, there is an indication of weak evidence against the conjecture or assumption. Then, the null hypothesis will be accepted by the investor. In the scenario where the p-value is 0.001, there is strong evidence against the null hypothesis, and the portfolio’s returns did not equal the S&P 500’s returns.