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Comparing the means of the two groups Research Questions: • Is group A’s mean different from group B’s mean? (2 tailed) • Is group A’s mean greater than group B’s mean? (1 tailed) Example: Are people willing to pay more for GREEBN vs. YELLOW chocolate? Group A Group B GREEN chocolate YELLOW chocolate Willing to pay $3.2 Willing to pay $2.9
T test is an inferential statistic We will discuss two more: chi square and regression What are inferential statistics?
Research Question Inferential StatisticsCompare means of 2 numeric variables T testRelate 2 numeric variables Pearson Correlation rRelate 2 categorical variables Pearson Chi SquareUse 1+ IVs to explain 1 numeric DV Regression
Understand Pearson Chi Square • Definition/Purpose • Mathematical concepts • Assumptions • Reporting chi square results Understand regression • Definition/Purpose • Mathematical concepts • Assumptions • Assessing model fit • Reading SPSS outputs • Reporting regression results
Purpose – See if there’s a relationship between 2 categorical variables Example of categorical variables: Giant Eagle store – Market District? (yes/no) Has child play area (yes/no) Gender (male/female) Commit fraud (yes/no) Example Research Questions: • Are Giant Eagle’s Market District stores more likely than other GE stores to have a child play area? • Are men more likely than women to commit fraud?
EXPECTED VALUES FOR DATA YOU HAVENULL HYPOTHESIS: NO COLLECTEDDIFFERENCE BETWEENMEN/WOMEN Fraud No Fraud Fraud No FraudMen (20) 2 (20%) 10 Men 19 (95%) 1Women (30) 3 (20%) 15 Women 9 (30%) 21Question: Do your data differ significantly from what’sexpected for “no difference between men/women?”
Count is the actual data/observations Expected Count is the theoretical expected values (table on left on last slide)20.576 is the chi 1 is the degree of The test is significant square value freedom (p < .001)
There was a significant association betweengender and fraud commitment X2(1,N=50)=20.576, p <.001. Based on the contingencytable, men appear to have a greater likelihood ofcommitting fraud than women.
Independence – Each case contributes to only one of the cells in the contingency table Each cell should be expected to have a value of at least 5 Each variable is normally distributed
What’s the purpose of Chi Square? What kind of research question is it designed to answer?