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Ch8.part2

# Ch8.part2 - Statistical Significance levels • Alpha level...

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(1) One-tailed vs. Two-tailed testing (2) Type I and Type II Error (3) alpha level vs. probability (or “significance” level) Additional Hypothesis Testing Concepts Wednesday, June 1, 2011

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Two-tailed , a.k.a., non-directional test; places .025 at each end of the distribution +1.96 and - 1.96 for a z-test Wednesday, June 1, 2011
One-tailed , a.k.a., directional, test; places all .05 at one end of the distribution z crit in Table C.1 +1.645 or - 1.645 Changes Alternative Hypothesis: Wednesday, June 1, 2011

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Errors in Hypothesis Testing Reality in the Population Decision from Statistical Analysis H 0 is true Reject H 0 H 0 is false Fail to Reject H 0 (test statistic is not in rejection region) (test statistic is in rejection region) Wednesday, June 1, 2011
Null Hypothesis True Null false/Alternative Hypothesis True vs. Reject H0 Fail to Reject H0 Critical Value Where is the alpha Region (.05)? Where is the Type I Error? Where is the Type II Error? Where is Power? Where is Beta? Shown for a one-tailed test: Wednesday, June 1, 2011

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Statistical Significance levels

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Unformatted text preview: Statistical Significance levels • Alpha level: – The selected maximum risk of Type I Error that is acceptable • Probability value (p-value): – The smallest probability of a Type I Error you could have adopted and still rejected the null hypothesis. Wednesday, June 1, 2011 One-Sample Statistics N Mean Std. Deviation Std. Error Mean bloodsugar 10-2.0000 8.21922 2.59915 One-Sample Test-.769 9 .461-2.00000-7.8797 3.8797 bloodsugar t df Sig. (2-tailed) Mean Difference Lower Upper 95% Confidence Interval of the Difference Test Value = 0 Wednesday, June 1, 2011 • Suppose df=9, and observed t = .769, and you have a more thorough table of critical values for the t-test. df .50 .40 .30 .20 .10 .05 1 2 … 9 .70-ish .80-ish 1.0-ish 1.383 1.833 2.262 An observed t-test statistic: .769 If you had adopted alpha = ~.47, you would have rejected your null hypothesis, but with a .47 risk of a false alarm/Type I error. Alpha levels Wednesday, June 1, 2011...
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Ch8.part2 - Statistical Significance levels • Alpha level...

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