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Lecture 7: Hypothesis Testing and ANOVA

Lecture 7: HypothesisTesting and ANOVAG oals Introduction to ANOVA Review of common one and two sample tests Overview of key elements of Hypothesis testingHypothesis Testing The intent of Hypothesis Testing is formally examine twoopposing conjectures (hypotheses), H0 and HA These two hypotheses are mutually exclusive andexhaustive so that one is true to the exclusion of theother We accumulate evidence - collect and analyze sampleinformation - for the purpose of determining which ofthe two hypotheses is true and which of the twohypotheses is falseThe Null and Alternative Hypothesis States the assumption (numerical) to be tested Begin with the assumption that the null Hypothesis is TRUE Always contains the = signThe null Hypothesis , H0:The alternative Hypothesis , Ha: Is the opposite of the null Hypothesis Challenges the status quo Never contains just the = sign Is generally the Hypothesis that is believed to be true bythe researcherOne and Two Sided tests Hypothesis tests can be one or two sided (tailed) One tailed tests are directional:H0: 1 - 2 0HA: 1 - 2 > 0 Two tailed tests are not directional:H0: 1 - 2 = 0HA: 1 - 2 0P-values After calculating a test statistic we convert this to a P-value by comparing its value to distribution of teststatistic s under the null Hypothesis Measure of how likely

Fisher’s Exact Test Wilcoxon-Mann-Whitney Test Two sample t-test Compare two unpaired groups Paired t-test Wilcoxon Test McNemar’s Test Compare two paired groups Wilcoxon Test Binomial Test One sample t-test Compare one group to a hypothetical value. General Form of a t-test! T= x "µ ...

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