Quant #16: What is the Meaning of the P-Value?

In quantitative research, especially in hypothesis testing, the p-value is a measure of the probability of obtaining the observed results, given that the null hypothesis is true. For example, if we assume that it is true that x has no effect on y (null hypothesis assumed to be true), the probability of detecting an effect (x on y) – given the above assumption – is what is called the p-value. The lower the p-value, the more unlikely it is for that result (detected effect) to have occurred, given the assumption that no effect exists. Another example would the comparison of two groups on a given characteristic (e.g., average salary between two companies). If you assume that there is no difference between the two groups, the probability that you'll detect a difference (under the assumption of no difference) is the p-value.

The p-value is used to quantify the statistical significance of a given result. A result is said to have statistical significance if it is very unlikely to have happened or arisen assuming the null hypothesis. A low p-value implies a statistically significant result (in general, a p-value of 0.05 or lower is judged to be statistically significant). More informally, the p-value of a test result can be understood as the probability that the result happened by chance. A statistically significant result implies that the null hypothesis can be rejected (in favor of the alternative hypothesis). Put another way, a low p-value indicates that sufficient evidence against the null hypothesis exists.