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Lecture 7

lecture 7

7 Pages

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John Kervin

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SOC 222 -- MEASURING the SOCIAL WORLD Session #7 -- TABLES & CHI SQUARE Today’s Objectives: Know… 1. The meaning of “expected frequencies” and their role in chi-square calculations 2. How to run a chi-square test on SPSS 3. How to calculate the degrees of freedom in a crosstab Terms to Know chi square expected frequency observed frequency independence marginals critical value degrees of freedom (df) elaboration STATISTICAL SIGNIFICANCE USING CHI-SQUARE Effect size: percentage difference What is Chi-Square? Called the test 1. Chi-square is a statistic- calculate it from your sample 2. Chi-square is calculated from crosstabs • expected frequency for that cell- as if there were no relationship • observed frequency for that cell 3. From statisticians we know the shape of the sampling distribution for chi-square • A test of independence – looking to see if theres relationship between x and y or not Don’t know whats going on in population How do we estimate probability of making type one error? GETTING a CHI SQUARE VALUE Step 1: Calculating Expected Frequencies 2x2 table, 4 cells • Based solely on the marginals – row and Colum totals in the margins, sums of categories Male Female Not working 161 Working 116 112 165 277 EG: top left: calculate expected number of students in each cell • Variable: working or not- • Category: not working • Overall proportion not working: 161 / 277 • Apply this to the number of males (one gender category): (161 / 277) * 112 = 65.1 **multiply its two margins (112) and (161) and divide by the total (277), the results will be the expected number for the cell, that gives the particular number for that cell • This is the expected number of males not working Male Female 65.1 Not working 161 Working 116 112 165 277 We can do this for each cell. Result: Male Female 65.1 95.9 46.9 69.1 Not working 161 Working 116 112 165 277 Expected frequencies = null hypothesis because they assume nothing has happened Step 2: Compare with Observed Frequencies What is actually found, what sample tells us Male Female 74 87 65.1 95.9 38 78 46.9 69.1 Not working 161 Working 116 112 165 277 Step 3: Calculate Chi-Square Text has: ∑ ( −f )2 ¿ o e fe Should be: (fo−f e2 ¿∑ fe = 4.881 Step 4: Find Critical Value & Significance Level Significance Levels Ns. .10 Weakly, .05 .01- .001- very little chance of making type one error Chi-square table Rows: • Degrees of freedom (df) 2x2 table, one degree of freedom Columns: • Different levels of statistical significance, Cells: • Give the critical value – minimal value chi square must be for that degrees of freedom and significance va
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