09Power - Statistical Techniques I EXST7005 Power and Types...

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Statistical Techniques I EXST7005 Lets go Power and Types of Errors
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Logic of Test of Hypothesis is based on the selected probability, (significance level) for the test statistic (Z) which determines the range of what would be expected due to chance alone assuming H0 is true . Significance level notation, commonly used leve and terminology "Significant" = 0.05 "Highly significant" = 0.01 Hypothesis testing Concepts
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Errors! Is it possible, when we do a test of hypothesis that we are wrong? Yes, unfortunately. It is always possible that we are wrong. Furthermore, there are two types of error that we could make!
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Data indicates: H0 is true Data indicates: H0 is false True result: H0 is true NO ERROR Type I Error: Reject TRUE H0 True result: H0 is false Type II Error: Fail to Reject FALSE H0 NO ERROR Types of error
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Type I Error Type I error is the REJECTION of a true Null Hypothesis. This type of error is also called α (alpha) error. This is the value we choose as the "level of significance" So we actually set the probability of making this type of error. The probability of a type I error = α
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Type II Error Type II error is the FAILURE TO REJECT of a Null Hypothesis that is false. This type of error is also called β (beta) error. We do not set this value, but we call the probability of a type II error = β Furthermore, in practice we will never know this value. This is another reason we cannot "accept the null hypothesis, because it is possible that we are wrong and we cannot state the probability of this type of error.
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So what can we do? The good news, it is only possible to make one error at a time. If you reject H0, then maybe you made a type I error, but you have not made a type II error. If you fail to reject H0, then maybe you made a type II error, but you have not made a type I erro
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The probability of Type II Error This is a probability that we will not know. This probability is called β However, we can do several things to make the error smaller. So this will be our objective. First, let's look at how these errors occur.
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Type II Error 10 12 14 16 18 20 22 24 26 -4 -3 -2 -1 0 1 2 3 4 Examine an hypothesized distribution (below) that we believe to have a mean of 18.
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We are going to do a 2 tailed test with an α valu of 0.05. Our critical limits will be ±1.96. 10
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This note was uploaded on 12/29/2011 for the course EXST 7087 taught by Professor Wang,j during the Fall '08 term at LSU.

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09Power - Statistical Techniques I EXST7005 Power and Types...

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