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Hypothesis Testing.docx

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PSYC 3000
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Hypothesis Testing 11/12/2012 5:47:00 AM With hypothesis testing: we can answer questions about our model - Null: = original value: no change - Alternative: the equation; if we reject the null. > < or does not equal (two tailed) - before doing tests: we check independence condition, random condition, success/failure condition - once we solve: we then ask how likely the data we observed would be were the null hypothesis a true model of the world - we look at probability: (p) - p high: fail to reject/accept null hypothesis - p low: reject; what we have observed is unlikely if our null was true The breakdown: 1) Hypotheses. One tailed/one sided alternative. Or Is it two tailed: increase/decrease/has it changed 2) Model; are the conditions satisfied (page 379. independence, random, success/failure: p(n) q(n) > 10 each) 3) Mechanics 4) Conclusion - sometimes we follow up with confidence interval: (page 383)  ^p +- ME  SE(^p) = Sqrt (p^q^/n) - we can not find the standard deviation from the null proportion (* if we rejected it, we can not use) - More about Tests. Chapter 21 11/12/2012 5:47:00 AM Example from class: 1) Descriptive 2) Analyze 3) Bring to DV 4)Statistics 5) Make 99 - made 99 percent confident interval; 99 percent confident between 17 and 23 - we can reject if do not see value in our interval - 0.136 not a part - Example two: - generate statistic: 0.38 - interval: 0.35 – 0.42 - 55 not in it therefore reject null - P value: conditional probability - probability of getting results unusual as seen given the null is true p(0.03): given the null there’s a 3% chance of observing the statistic value observed - big P values: (taken from z) results are inline with null assumption How Small is small? - we set a point: Alpha level: if p falls below; we reject - a: 0.1, 0.05, 0.01 - use alpha dependent on situation; safety of airbags; 0.01 - alpha level: significance level - if p > alpha level: fail to reject the null A 1 sided 2 sided 0.05 1.645 1.96 0.01 2.33 2.576 0.001 3.09 3.29 page 406: - compare the observed z score with the critical value. If z is less than z critical. Then we do not reject - you can also approximate hypothesis test by examining confidence interval - ask if null (Po) is contained in the interval confidence interval: two sided: correspond to two tailed - if falls outside; reject Errors in hypothesis testing: - null hypothesis is true; but we reject it (Type 1) - null hypotheses is false, but we accept (type II) - type I: make innocent person guilty type II: Make guilty person innocent - when you choose alpha level; your setting the probability of a type I error to a - - A tests ability to detect false null hypothesis: power of the test - Power: probability that test correctly rejects false null hypothesis (program -> course software -> spss -> spss sample power -> sample power -> 3) type 1 error: alpha type II error: B 1-B: power: probability that the test does reject Effect size: difference between null value and alternative value To increase the power: - increase the significance level - increase effect size - increase sample size Chapter 21: Notes From Pass and Textbook - Strong link between confidence interval and hypothesis testing; Same set of assumptions and conditions  independence  randomization  Success/failure >10  Less than 10% condition - we can reject or accept null hypothesis; if our confidence interval does not show our null; reject - to arrive at same conclusion (accept our reject both methods need to have same condition)  each value in CI is a plausible value for unknown population parameter. Values located outside are considered implausible.  Confidence interval: two sides; correspond to two sided tests Error Decision Matrix: 1) H0 True -> Reject (Type I error) - reject null when you should not - the lower the alpha; the lower this type of Error can occur alpha of 0.01 includes bigger range than alpha of 0.1 there we increase significance level, 90 % vs. 99% - widen the net; better able to catch - chance of this error, 1%, 5%, 10% : it’s the Alpha Ho True: Accept - correct decision - the chances of this happening are 99%, 95% 0r 90% Ho is False - if we reject the ho; this is correct; rejecting null when you should Power; the ability to correctly reject the null when the time’s right
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