p is the Probability of an Alpha (False Positive) Error. Alpha (α) is the Level of Significance; its value is selected by the person performing the statistical test. If p < α (some say if p < α) then we Reject the Null Hypothesis. That is, we conclude that any difference, change, or effect observed in the Sample data is Statistically Significant. The p-value contains the same information as the Test Statistic Value, say z. That is because the value of z is used to determine the p-value. As shown in the following concept flow diagram,- Sample data is used to calculate a value for a Test Statistic, say,
*z.* - This value of
*z*forms the boundary for the area under the curve which represents the Cumulative Probability,*p*. - From this, tables or calculations give us the value of
*p*.
Similarly α contains the same information as the Critical Value. So comparing
p and the Critical Value is the same as comparing Alpha and the Test Statistic value. But the comparison symbols ( ">" and "<") point in the opposite direction. That's because p and Test Statistic have an inverse relation. A smaller value for p means that the Test Statistic value must be larger.
1 Comment
Great article, Jim Frost! Thank you for explaining the relationship between p-value and test statistic value, and how they contain the same information. It's crucial to understand that the comparison of p and critical value is the same as comparing alpha and test statistic value, as they point in opposite directions. This information is essential to ensure accurate and reliable statistical analysis.
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## AuthorAndrew A. (Andy) Jawlik is the author of the book, Statistics from A to Z -- Confusing Concepts Clarified, published by Wiley. ## Archives
March 2021
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