1Lecture 8•Logic of Hypothesis Testing•Cross-TabulationDepartment of MarketingDr. Junzhao MaMKF2121Marketing Research Methods1Today’s agenda2•More on hypothesis testing – the intuition behind statistical tests and the concept of a test statistic•Learn about one type of tests of association: cross-tabulation (Chi-square test)Last week we discussed the steps of hypothesis testing1. Problem Definition (RQ)2. Clearly State the Null and Alternative Hypotheses3. Choose the relevant statistical test4. Calculate p-value5. Is p-value<0.05?NoDo not reject nullReject null hypothesisYes3

24Revisit - why do we have to use statistical tests to “answer” RQ?•Sample characteristics ≠population characteristics•Population characteristics is unknown•Think like a detective: what does the evidence (sample characteristics) tell me what really happened (population characteristics)?•Hypothesis testing: the formal process to use the statistical properties of the data to evaluate beliefs about population characteristics (hypothesis)Population?SampleStatistical testing - three levels of understanding•Mechanical – know which button to push in SPSS, what to look for in the output•Mathematical (formula) – nice to have (in the textbook), but not required•Conceptual – the intuition behind the technique used5Example to illustrate the rationale behind the statistical testing (in particular, test statistic)Buyer IDMiles per gallon130.9224.5331.2428.7535.1629728.8823.19311030.21128.41229.31324.214271526.716311723.51829.41926.32027.52128.2•Toyota dealership in the city of New Haven claims that the average miles per gallon (MPG) is 30 for the new Toyota Corolla•A local consumer group collected data from the recent buyers to verify this claim•RQ – Is the new Toyota Corolla’s average MPG equal to 30?

3•Step 2: Hypothesis formulation–H0 (Null): Miles per gallon = 30 milesIn words: the new Toyota Corolla’s average MPG is 30–H1 (Alternative): Miles per gallon ≠30 milesThe new Toyota Corolla’s average MPG is not 307The mechanics: steps needed for hypothesis testing8Step 3 – pick a testHypothesisTestingTest of Association(relational RQ)Test of Differences(comparative RQ)MeansProportions•Different forms of t test•Cross tabulation•Correlation•Multiple regressionStep 4&5 : Execute the test and compare p-value9One-Sample Statistics2528.17203.0339.6068MPGNMeanStd. DeviationStd. ErrorMeanOne-Sample Test-3.01324.006-1.8280-3.0803-.5757MPGtdfSig. (2-tailed)MeanDifferenceLowerUpper95% ConfidenceInterval of theDifferenceTest Value = 30•P-value = 0.006 < 0.05, therefore we reject null hypothesis •Conclusion: Reject the null hypothesis (i.e., the average MPG is not equal to 30)