12SampleSizeCalc

12SampleSizeCalc - Statistical Techniques I EXST7005 Sample...

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Statistical Techniques I EXST7005 Sample Size Calculation
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The sample size formula The Z-test and t-test use a similar formula. Z Y n = - μ σ 0 2
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The sample size formula (continued) Lets suppose we know everything in the formul except n. Do we really? Maybe not, but we ca get some pretty good estimates. Call the numerator ( f8e5 Y - μ 0) a difference, f8e5 d. It is some mean difference we want to be able to detect, so f8e5 d = f8e5 Y - μ 0. The value σ 2 is a variance, the variance of the data that we will be sampling. We need this variance, or an estimate, S2.
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The sample size formula (continued) So we alter the formula to read. Z d n = σ 2
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The sample size formula (continued) What other values do we know? Do we know Z? No, but we know what Z we need to obtain significance. If we are doing a 2-tailed test, and we set α = 0.05, then Z will be 1.96. Any calculated value larger will be "more significant", any value smaller will not be significant. So, if we want to detect significance at the 5% level, we can state that . ..
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The sample size formula (continued) Z d n α σ 2 2 We will get a significant difference if
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The sample size formula (continued) We square both sides and solve for n. Then we will also get a significant difference if n Z d α σ 2 2 2 2
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The sample size formula (continued) Then, if we have an idea of values for f8e5 d, σ 2, and Z, we can solve the formula for n. If we are going to use a Z distribution we should
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12SampleSizeCalc - Statistical Techniques I EXST7005 Sample...

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