What is the 'P-Value'

The p-value is the level of marginal significance within a statistical hypothesis test representing the probability of the occurrence of a given event. The p-value 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 p-value means that there is stronger evidence in favor of the alternative hypothesis.

BREAKING DOWN 'P-Value'

P-values are calculated using p-value 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 p-value in the hypothesis test and allow the reader to interpret the statistical significance themselves. This is called a p-value approach to hypothesis testing.

P-Value Approach to Hypothesis Testing

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 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 p-value, 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 two-tailed 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 one-tailed 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 p-value is 0.05. If the investor concludes that the p-value 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 p-value 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 p-value 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.

RELATED TERMS
  1. Null Hypothesis

    A type of hypothesis used in statistics that proposes that no ...
  2. Hypothesis Testing

    A process by which an analyst tests a statistical hypothesis. ...
  3. Type II Error

    A statistical term used within the context of hypothesis testing ...
  4. Type I Error

    A type of error that occurs when a null hypothesis is rejected ...
  5. Alpha Risk

    The risk in a statistical test that a null hypothesis will be ...
  6. Statistically Significant

    The likelihood that a result or relationship is caused by something ...
Related Articles
  1. Investing

    Hypothesis Testing in Finance: Concept & Examples

    When you're indecisive about an investment, the best way to keep a cool head might be test various hypotheses using the most relevant statistics.
  2. Investing

    What is a Null Hypothesis?

    In statistics, a null hypothesis is assumed true until proven otherwise.
  3. Investing

    How Statistical Significance is Determined

    If something is statistically significant, it’s unlikely that it happened by chance.
  4. Investing

    What's a T-Test?

    T-Test is a term from statistics that allows for the comparison of two data populations and their means. The test is used to see if the two sets of data are significantly different from one another. ...
  5. Investing

    Efficient Market Hypothesis

    An investment theory that states it is impossible to "beat the market".
  6. Investing

    Efficient Market Hypothesis: Is The Stock Market Efficient?

    Deciding whether it's possible to attain above-average returns requires an understanding of EMH.
  7. Insights

    Investopedia Explains Fractal Markets Theory

    Fractal Market Hypothesis has emerged as an alternative to longstanding economic theories due to its ability to explain investor behavior during crises.
  8. Financial Advisor

    Are Low-Risk High-Yield Investments Real? (DIA)

    Risk and reward necessarily move in the same direction. Or do they? Is it possible to defy logic and earn great returns while putting little on the line?
  9. Financial Advisor

    Advisors: Watch Out for Confirmation Bias

    Here's how advisors can make sure that confirmation bias does not color their own perceptions as they manage clients’ portfolios.
  10. Investing

    Market Efficiency Basics

    Market efficiency theory states that a stock’s price will fully reflect all available and relevant information at any given time.
RELATED FAQS
  1. What does a strong null hypothesis mean?

    Find out what null hypothesis is and why it is important to the scientific method. See how statisticians and economists use ... Read Answer >>
  2. What is the relationship between confidence inferrals and a null hypothesis?

    Learn about the relationship between confidence intervals and the null hypothesis in scientific research and empirical experimentation. Read Answer >>
  3. Has the Efficient Market Hypothesis been proven correct or incorrect?

    Explore the efficient market hypothesis and understand the extent to which this theory and its conclusions are correct or ... Read Answer >>
  4. What are the differences between weak, strong and semi-strong versions of the Efficient ...

    Discover how the efficient market theory is broken down into three versions, the hallmarks of each and the anomalies that ... Read Answer >>
  5. What does the efficient market hypothesis assume about fair value?

    Found out what the efficient market hypothesis says about the fair value of securities, and learn why technical and fundamental ... Read Answer >>
  6. What are the primary assumptions of Efficient Market Hypothesis?

    Find out about the key assumptions behind the efficient market hypothesis (EMH), its implications for investing and whether ... Read Answer >>
Hot Definitions
  1. Graduate Management Admission Test - GMAT

    A standardized test intended to measure a test taker's aptitude in mathematics and the English language. The GMAT is most ...
  2. Magna Cum Laude

    An academic level of distinction used by educational institutions to signify an academic degree which was received "with ...
  3. Cover Letter

    A written document submitted with a job application explaining the applicant's credentials and interest in the open position. ...
  4. 403(b) Plan

    A retirement plan for certain employees of public schools, tax-exempt organizations and certain ministers. Generally, retirement ...
  5. Master Of Business Administration - MBA

    A graduate degree achieved at a university or college that provides theoretical and practical training to help graduates ...
  6. Liquidity Event

    An event that allows initial investors in a company to cash out some or all of their ownership shares and is considered an ...
Trading Center