Thus, if the investor finds that the p-value is 0.001, there is strong evidence against the null hypothesis, and the investor can confidently conclude the portfolios returns and the SP 500s returns are not be equivalent.

He specializes in using statistics in investing, technical analysis, and trading.

In statistics, the p-value is the probability of obtaining results at least as extreme as the observed results of a statistical hypothesis test, assuming that the null hypothesis is correct.

A smaller p-value means that there is stronger evidence in favor of the alternative hypothesis.

P-values are usually found using p-value tables or spreadsheetsstatistical software.

These calculations are based on the assumed or known probability distribution of the specific statistic being tested.

P-values are calculated from the deviation between the observed value and a chosen reference value, given the probability distribution of the statistic, with a greater difference between the two values corresponding to a lower p-value.

The p-value approach to hypothesis testing uses the calculated probability to determine whether there is evidence to reject the null hypothesis.

The null hypothesis, also known as the conjecture, is the initial claim about a population (or data generating process).

The alternative hypothesis states whether the population parameter differs from the value of the population parameter stated in the conjecture.

In practice, the significance level is stated in advance to determine how small the p-value must be in order to reject the null hypothesis.

Because different researchers use different levels of significance when examining a question, a reader may sometimes have difficulty comparing results from two different tests.

For example, suppose a study comparing returns from two particular assets were undertaken by different researchers who used the same data but different significance levels.

The researchers might come to opposite conclusions regarding whether the assets differ.

If one researcher used a confidence level of 90 and the other required a confidence level of 95 to reject the null hypothesis and the p-value of the observed difference between the two returns was 0.08 (corresponding to a confidence level of 92), then the first researcher would find that the two assets have a difference that is statistically significant, while the second would find no statistically significant difference between the returns.

To avoid this problem, the researchers could report the p-value of the hypothesis test and allow the reader to interpret the statistical significance themselves.

An independent observer could note the p-value, and decide for herself whether that represents a statistically significant difference or not.

Assume an investor claims that their investment portfolios performance is equivalent to that of the Standard Poors (SP) 500 Index.

The null hypothesis states that the portfolios returns are equivalent to the SP 500s returns over a specified period, while the alternative hypothesis states that the portfolios returns and the SP 500s returns are not equivalent.

If the investor conducted a one-tailed test, the alternative hypothesis would state that the portfolios returns are either less than or greater than the SP 500s returns.).

P-value hypothesis test does not necessarily make use of a pre-selected confidence level at which the investor should reset the null hypothesis that the returns are equivalent.

Instead, it provides a measure of how much evidence there is to reject the null hypothesis.

The smaller the p-value, the greater the evidence against the null hypothesis.

How To Calculate P Value