Biostatistics 6030Summary for hypothesis testingOne sample problemMean Variance of population known or large n (n>/=200)Z test• 1‐sided• 2‐sidedVariance of population estimated from sample ttest• 1‐sided• 2‐sided2‐sided 1‐sidedCritical value Critical valueP value P valueC. I. One‐Sample Test• In some applications, the variance may be assumed known from prior studies or is very large (200). In this case, we can use One‐Sample Test to replace the test. One‐Sample TestOne‐Sample TestOne‐Sample TestOne‐Sample TestOne‐Sample TestOne‐Sample TestOne‐Sample TestThe Relationship Between Hypothesis Testing and Confidence Intervals• Suppose we are testing 0 0vs. 1 0. 0is rejected with a two‐ sided level test if and only if the two‐ sided for does NOT contain 0. 0is accepted with a two‐ sided level test if and only if the two‐ sided for does contain 0. The Relationship Between Hypothesis Testing and Confidence IntervalsOne sample problemProportion Large sampleZ test• 1‐sided• 2‐sidedSmall sampleExact p value• 1‐sided• 2‐sidedOne sample test for binomial proportionOne sample test for binomial proportionPower for one sample z testPower for one sample z testSample size for testing for the mean of a normal distributionSample size for testing for the mean of a normal distributionPower and sample size for one sample binomial test2 sample problemsMean Longitudinal or matchedPaired t test• 1‐sided• 2‐sided2 independent samplesVariances for 2 populations equal?F testPooled varianceT‐testT test Satterthwaite’s rule for d.f.Y NThe Paired TestThe Paired Testtest for equality of two variancestest for samples of equal variancestest for samples of equal variancestest for samples of unequal variancestest for samples of unequal variancesEstimation of Sample Size for Comparing Two MeansEstimation of Sample Size for Comparing Two MeansEstimation of Power for Comparing Two Means2 sample problemsProportions 2 independent samplesNormal theory methodMatched pair samples20McNemar’s test20Exact testContingency‐table methodTwo sample test for binomial proportionsTwo sample test for binomial proportionsContingency ‐ table methodMcNemar’s TestExact test• This test is valid for any number of discordant pairs but is particularly useful for , when the normal ‐ theor y test cannot
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