The graph and table below show how Type 1 and Type 2 errors are related to the actual situation and the decisions we make. Our sample mean may be drawn from the null distribution (indicating no effect) or from some alternative distribution (indicating an effect exists). We can never be sure what the actual alternative distribution may be, but we can use hypothesis testing procedures to determine the probability that we will be able to reject the null hypothesis if the actual mean is equal to any specific value of interest.
In the table below, each of four cells represent a decision outcome and its associated probability. The areas underneath each sampling distribution to the left and to the right of the critical value sum to 1.0 or 100%. These areas correspond to the probability for each outcome given the specified actual situation.
Notice that alpha, α, and the corresponding critical value (dotted red line) are defined in reference to the null distribution and not to the alternative distribution. To view how each decision outcome is related to the distributions in the graph, notice the color in the appropriate table cell.
Actual Situation: |
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Null is true; alternative is false (no effect) |
Null is false; alternative is true (effect exists) |
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Decision: |
Reject the null – Right of CV (effect supported) |
Type I Error (Probability = α) | Correction Decision (Probability = 1 – β) |
Fail to reject the null – Left of CV (effect not supported) |
Correct Decision (Probability = 1- α) | Type II Error (Probability = β) |
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