stats9 - Monday October 11 POLS4150 RESEARCH METHODS IN...

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Monday, October 11 http://emwilk.myweb.uga.edu/POLS4150.html Course Webpage: POLS4150 – RESEARCH METHODS IN POLITICAL SCIENCE (90595) Hypothesis Testing
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Hypothesis Testing Null hypothesis : H 0 Suggests that difference in means of two samples is due to sampling error H 0 : µ 1 = µ 2 Where: µ 1 : first population mean µ 2 : second population mean Alternative hypothesis : H 1 : µ 1 ≠ µ 2 Testing differences between the means:
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Testing differences between the means: 2 Considerations: 1. Critical values for our level of significance Critical value for α = .05 is 1.96 if N > 120 2. Absolute value of observed / calculated t / Z Hypothesis Testing
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Means Testing If | t | or | Z | is > critical value, then we reject H 0 . This does not necessarily mean that H 0 is definitively false When testing differences in means, df = N 1 + N 2 – 2 If | t | or | Z | < critical value, then we fail to reject H 0 . This does NOT mean that H 0 is necessarily true N 1 = number of observations in first sample N 2 = number of observations in second sample
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Using Appendix B when means testing Critical Values Level of significance for Two-tailed test ( α ) df .10 6.314 2.920 2.353 2.132 .05 12.706 4.303 3.182 2.776 .02 31.821 6.965 4.541 3.747 .01 63.657 9.925 5.841 4.604 1 2 3 4 1.645 1.960 2.326 2.576 So if N 1 = 3 and N 2 = 3, df = 4. At the .05 level, the critical value is 2.776.
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Using Appendix B when means testing Critical Values Level of significance for Two-tailed test ( α ) df .10 6.314 2.920 2.353 2.132 .05 12.706 4.303 3.182 2.776 .02 31.821 6.965 4.541 3.747 .01 63.657 9.925 5.841 4.604 1 2 3 4 1.645 1.960 2.326 2.576 So to reject H 0 at the .05 level, the absolute value of the t we calculate must be > 2.776
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Where: Y 1 = mean of first sample Y 2 = mean of second sample Means Testing (Y 1 – Y 2 ) t = S Y1 – Y2 = standard error of the difference between sample means. S Y1 – Y2
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α is the threshold for assurance ( α = .05 or .01.) of not committing a Type 1 error Type 1 error : rejecting a H 0 that is in reality true. p-value : exact probability of committing a Type 1 error t-scores and exact p-values
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Hypothesis Testing Our decision based on sampling Reality H 0 is true H 0 is false Fail to reject H 0 reject H 0 Correct decision Correct decision Type II error Type I error
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Steps: 1. State the Null Hypothesis 2. Calculate z / t 3. Consider α (.05? .01?) 4. Find Critical value that corresponds to α and df
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