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The p value (also sometimes called alpha or probability level) is the percentage chance that the results of a statistical test are due to random error. So a p value of .01, for example, would mean that there is a 1% chance that the results are an error.
p is also the cut-off where a test is considered statistically significant. In Social Sciences, significance is assumed (and therefore the hypothesis supported) when p < .05. Other fields have different cut-offs, and there are times when a researcher may argue for a higher or lower p value.
It is important to note that p is only relevant to statistical significance. It has no bearing on the size or practical importance of results. As a common criticism of statistics is that a p value of .049 is "significant" while .051 is not, most researchers rely as much if not more on measures of effect size and practical application than on statistical significance. However, p remains the accepted convention for hypothesis testing.
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