What is the 'PValue'
The pvalue is the level of marginal significance within a statistical hypothesis test representing the probability of the occurrence of a given event. The pvalue is used as an alternative to rejection points to provide the smallest level of significance at which the null hypothesis would be rejected. A smaller pvalue means that there is stronger evidence in favor of the alternative hypothesis.
BREAKING DOWN 'PValue'
Pvalues are calculated using pvalue tables or spreadsheet/statistical software. 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, if two studies of returns from two particular assets were undertaken using two different significance levels, a reader could not compare the probability of returns for the two assets easily.For ease of comparison, researchers often feature the pvalue in the hypothesis test and allow the reader to interpret the statistical significance themselves. This is called a pvalue approach to hypothesis testing.
PValue Approach to Hypothesis Testing
The pvalue 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 of statistics. The alternative hypothesis states whether the population parameter differs from the value of the population parameter stated in the conjecture. In practice, the pvalue, or critical value, is stated in advance to determine how the required value to reject the null hypothesis.
Type I Error
A type I error is the false rejection of the null hypothesis. The probability of a type I error occurring, or rejecting the null hypothesis when it is true, is equivalent to the critical value used. Conversely, the probability of accepting the null hypothesis when it is true is equivalent to 1 minus the critical value.
Example
Assume an investor claims that her investment portfolio's performance is equivalent to that of the Standard & Poor's (S&P) 500 Index. The investor conducts a twotailed test. The null hypothesis states that the portfolio's returns are equivalent to the S&P 500's returns over a specified period, while the alternative hypothesis states that the portfolio's returns and the S&P 500's returns are not equivalent. If the investor conducted a onetailed test, the alternative hypothesis would state that the portfolio's returns are either less than or greater than the S&P 500's returns.
One commonly used pvalue is 0.05. If the investor concludes that the pvalue is less than 0.05, there is strong evidence against the null hypothesis. Consequently, the investor would reject the null hypothesis and accept the alternative hypothesis. Conversely, if the pvalue is greater than 0.05, there is weak evidence against the conjecture, so she would fail to reject the null hypothesis. If the investor finds that the pvalue is 0.001, there is strong evidence against the null hypothesis, and the portfolio's returns and the S&P 500's returns may not be equivalent.

Null Hypothesis
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Beta Risk
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Adaptive Expectations Hypothesis
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