BIOM301 Chapter 11 Applications of Chi Square 2 O E 2 E Chi Square Statistic Qualitative Data smoke Three Types of Chi Square Tests o Goodness of Fit Test o Test of Independence o Test of Homogeneity All test use the same equation o Have Observed numbers Counts o Ex The number of men vs women that smoke or don t o TABLE 8 o O Observed Number o E Expected Number o 1 tailed tests interest is the right tail big 2 values small 2 values Can t reject Null Chi Square Tests Goodness of Fit Tests multinomial experiments 1 variable Tests of Independence 2 variables Tests of Homogeneity treatment effects 2 variables Hypothesis Testing 1 State your question ID Population 2 State your Ho and Ha define symbols 3 Test your hypothesis statistically a Remember to Check assumption that all EXPECTED values are at least 5 4 State the decision about Ho give evidence Goodness of Fit Test GOF Does the data fir a binomial distribution Key Points o You have a single list of observed numbers in categories o Question drives hypotheses Ho Data follow expected distribution Ha Data don t follow expected distribution o Hypotheses often verbal statements df for GOF test categories 1 o all GOF tests are 1 tailed only care if Obs Exp is a big value Inferences concerning Contingency Tables 2 Qualitative Variables Two Types o Test of Homogeneity Experimental Treatment differences o Test of Independence Association Both generate expected numbers and df the same way o Difference Type of question being asked Degrees of Freedom for Contingency Tables o df rows 1 columns 1 Test of Independence Association Asking if 1 factor is INDEPENDENT of another factor So hypotheses stated as State using YOUR variables in hypothesis o Ho Factor A is independent of Factor B in this population o Ha Factor A is NOT independent of Factor B in this population Independence vs Association o These are opposite terms If 2 variables ARE independent they are NOT associated If 2 variables are NOT independent they ARE associated o Ho No difference or no effect statement so should be that the 2 variables ARE independent or ARE NOT associated o Calculating Sample Statistics Need to calculate expected values Short cut is expected value row total column total grand total Assumption all expected values are 5 is met 1 tail test only care if differences are large between observed and expected values Tests of Homogeneity Treatment Effects 2 variables in a contingency table o This time one of the variable either the row or the column is controlled by the experimenter Used to analyze experimental results o Ho usually stated in terms of population proportions You set up a study to test whether a Drug is better than a Placebo at treating chest pain randomly assign people to a treatment o Ho pDrug pPlacebo o Ha pDrug pPlacebo o Where p population proportion free of chest pain Assume data sampled randomly and 0 05 We are asking if different populations 1 population is patients getting drug other is patients getting placebo have the same proportion of patients pain free at end of study o When testing your hypothesis statistically remember to Check assumption that all EXPECTED values are at least 5 o Look at the observed vs expected numbers KEY NOTES Chi Square tests work best if there are not a lot of categories Tests of Homogeneity are comparing 2 populations so it will always be a 2 x something If assumption of all expected values 5 not met can use Chi Square Exact Test Things to Know for Exam Need to be able to identify which type of chi square test would be used Also need to know how to calculate expected df Ho and Ha how to do 4 steps of statistical testing Assumptions of Chi Square Test
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