Question 535907: In hypothesis testing, as the α level gets smaller, the level of confidence increases. T or F, and why or why not?
Answer by oberobic(2304)   (Show Source):
You can put this solution on YOUR website! When you set the α level, you are setting the level of random chance that you are willing to accept.
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If you set α=.10, then you know that your results could be by chance 1/10 or 10% of the time.
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If you set α=.05, then you know that your results could be by chance 1/20 or 5% of the time.
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If you set α=.01, then you know that your results could be by chance 1/100 of 1% of the time.
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So, it is reasonable to say that your level of confidence in whether the obtained result is "real" or simply by chance increases as α is set lower and lower.
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Note that α itself does not "get smaller." As the statistician, you set the α level that you want to use. For an initial exploratory analysis you might use α=.10. For a highly stringent test, you might use α=.01. Using α=.05 is convention and strikes a balance between being too aggressive or too conservative.
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And you should remember that as you set α lower and lower, there is a complementary effect, perhaps better called a side-effect. The likelihood that you reject a real difference goes up.
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Read more in your textbook or online regarding Type I and Type II errors. See also β and 1-β (the Power of a test).
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Done.
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