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Statistics Tip of the Week: p < Alpha is the same as Test Statistic > Critical Value

5/3/2017

1 Comment

 
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 Reje​ct 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,
  1. Sample data is used to calculate a value for a Test Statistic, say, z.
  2. This value of z forms the boundary for the area under the curve which represents the Cumulative Probability, p.
  3. From this, tables or calculations give us the value of p.
Picture
Similarly α contains the same information as the Critical Value. 
Picture
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. (See the blog post for March 30 of this year.)
Picture
See also the videos for
  • p, the p-value​
  • Alpha (α), the Significance Level
  • Null Hypothesis
  • Reject the Null Hypothesis
  • Critical Value
  • Test Statistic
1 Comment
mahmoudi
6/1/2018 01:45:36 pm

je peut faire un stage de spss

Reply



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    Author

    Andrew A. (Andy) Jawlik is the author of the book, Statistics from A to Z -- Confusing Concepts Clarified, published by Wiley.

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  • Home
    • Why This Book Is Needed
    • Articles List, Additional Concepts
    • Examples: 1-Page Summaries
    • Examples: Concept Flow Diagram
    • Examples: Compare and Contrast Tables
    • Examples: Cartoons
    • Example: Which to Use When Article
  • Buy
  • Blog
  • Sample Articles
  • Videos
  • Author
  • Communicate
  • Files
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