what is p value 
in statistics a p value is defined as a number that indicates how likely you are to obtain a value that is at least equal to or more than the actual observation if the null hypothesis is correct the p value serves 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 stronger evidence in favor of the alternative hypothesis p value is often used to promote credibility for studies or reports by government agencies for example the u s census bureau stipulates that any analysis with a p value greater than 0 10 must be accompanied by a statement that the difference is not statistically different from zero the census bureau also has standards in place stipulating which p values are acceptable for various publications 1jessica olah investopediaunderstanding p valuep values are usually found using p value tables or spreadsheets statistical software these calculations are based on the assumed or known probability distribution of the specific statistic tested the sample size which determines the reliability of the observed data directly influences the accuracy of the p value calculation he p value approach to hypothesis testing uses the calculated he p value approach to hypothesis testing uses the calculated 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 mathematically the p value is calculated using integral calculus from the area under the probability distribution curve for all values of statistics that are at least as far from the reference value as the observed value is relative to the total area under the probability distribution curve standard deviations which quantify the dispersion of data points from the mean are instrumental in this calculation the calculation for a p value varies based on the type of test performed the three test types describe the location on the probability distribution curve lower tailed test upper tailed test or two tailed test in each case the degrees of freedom play a crucial role in determining the shape of the distribution and thus the calculation of the p value in a nutshell the greater the difference between two observed values the less likely it is that the difference is due to simple random chance and this is reflected by a lower p value the p value approach to hypothesis testingthe p value approach to hypothesis testing uses the calculated probability to determine whether there is evidence to reject the null hypothesis this determination relies heavily on the test statistic which summarizes the information from the sample relevant to the hypothesis being tested 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 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 p values provide a solution to this problem even a low p value is not necessarily proof of statistical significance since there is still a possibility that the observed data are the result of chance only repeated experiments or studies can confirm if a relationship is statistically significant for example suppose a study comparing returns from two particular assets was 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 if 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 readers to interpret the statistical significance themselves this is called a p value approach to hypothesis testing independent observers could note the p value and decide for themselves whether that represents a statistically significant difference or not example of p valuean investor claims that their investment portfolio s performance is equivalent to that of the standard poor s s p 500 index to determine this 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 the p value hypothesis test does not necessarily make use of a preselected 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 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 that the portfolio s returns and the s p 500 s returns are not equivalent although this does not provide an exact threshold as to when the investor should accept or reject the null hypothesis it does have another very practical advantage p value hypothesis testing offers a direct way to compare the relative confidence that the investor can have when choosing among multiple different types of investments or portfolios relative to a benchmark such as the s p 500 for example for two portfolios a and b whose performance differs from the s p 500 with p values of 0 10 and 0 01 respectively the investor can be much more confident that portfolio b with a lower p value will actually show consistently different results 