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Inferential Statistics

Inferential Statistics. Video ProjectsResearch MethodsANOVA short.wmv ...Chi-square short.wmv ...T-test short.wmv ...Correlation short.wmv ...Correlation partial short.wmv Regression short.wmv.

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Inferential Statistics

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  1. Inferential Statistics \Video Projects\Research Methods\ANOVA short.wmv ...Chi-square short.wmv...T-test short.wmv...Correlation short.wmv...Correlation partial short.wmvRegression short.wmv

  2. Position on police force Job Stress Patrol Officer Sergeant Total Low 116 86 30 High 84 24 60 N= 200 Total 110 90 Test of significance: Chi-Square (X2)(all variables are categorical-nominal) • Used with moderate size random samples • Tests for relationship between two categorical variables • Cells contain the frequency (number) of cases that share corresponding values of the independent and dependent variables • Analyze  Descriptive Statistics  Crosstabs • Select “Statistics,” check “Chi-Square”

  3. Chi-Square evaluates difference between Observed and Expected cell frequencies: • “Observed” are the frequencies based on data collection – our actual measurement of the independent and dependent variables, case by case • “Expected” means the frequencies we would “expect” if there was no relationship • If there is no relationship, 2is zero • The greater the difference, the larger the value of 2 • Ratio of systematic variation to chance variation O= observed frequency E= expected frequency (O - E)22 =  ---------- E • Chi-square is not the best test of significance • Requires moderate-size samples (e.g., 100-300 cases), while other tests of significance can be done with as few as 30 cases • Results it produces are closely tied to sample size • Over-estimate significance with large samples • Under-estimate significance with small samples

  4. Position on police force Job Stress Patrol Officer Sergeant Low 78% 33% High 22% 67% Total 100% 100% Chi-Square exercise POSITION  STRESS Position on police force Job Stress Patrol Officer Sergeant Total Low 116 86 30 High 84 24 60 Total 110 90 N= 200 1. Obtain the Chi-Square (X2) 2. What is the level of significance? 3. Is there a significant relationship between variables? Can we reject the null hypothesis? (use the maximum level set for social science research) ASSIGNMENT Filename: Position stress gender.sav

  5. Based on the obtained Chi-Square, there is less than 1 chance in 1,000 that the relationship between variables is due to chance alone

  6. T-test Independent variable: categorical /// Dependent variable: continuous • HYPOTHESIS: GENDER (M/F)  CYNICISM (measured on a 10-point scale) • Is the difference between the means of each group (M/F) so large that we can reject the null hypothesis – that the difference is a matter of chance? • 1. NUMERATOR: Actual (“observed”) difference between means • 2. DENOMINATOR: Computer estimate of the difference that would be expected by chance alone • x1 -x2t = --------------x1 -x2 • The “t” can be looked up on a table to see whether it is sufficiently large to overcome the null hypothesis, at whatever level of significance one may choose (e.g., .05) • Analyze  Compare Means  Independent Samples T-Test • Be sure to define the groups (categories) of the “Grouping Variable” (the independent variable)

  7. T-test exercise HYPOTHESIS: GENDER  CYNICISM M & F cynicismscores • What are the levels of measurement for each variable? • If gender is the independent variable, and height and weight are dependent variables, what are two possible hypotheses? • What is the appropriate statistic to determine if there is a statistically significant relationship between variables? • Obtain the t-statistic • What is the level of significance? • Is there a significant relationship between variables? Can we reject the null hypothesis? (use the maximum level set for social science research) ASSIGNMENT M 8 M 7 M 7 M 9 M 7 M 10 M 9 M 7 M 7 M 7 M 8 M 6 M 6 M 9 M 7 M 8 M 8 M 7 M 8 M 6 M 5 M 9 M 9 M 10 M 6 M 7 M 8 M 4 M 9 M 9 F 5 F 5 F 4 F 6 F 5 F 3 F 6 F 6 F 7 F 5 F 4 F 5 F 7 F 4 F 4 F 5 F 7 F 4 F 6 F 8 F 8 F 3 F 5 F 6 F 7 F 4 F 4 F 5 F 6 F 3 Filename: Gender Cynicism.sav

  8. Ratio

  9. Analysis of Variance (F) –an extension of the t-test HYPOTHESIS: STATE  SCHOOL PERFORMANCE State 1 mean State 2 mean State 3 mean Between group variance (real, “systematic” relationship between variables) F = Within group variance (estimated relationship due to chance) • A large “F” can overcome the null hypothesis that the differences between means are due to chance • Analyze  General Linear Model  Univariate • Independent variable goes into “Fixed Factor” • In “Options” check Descriptive Statistics • In “Post Hoc” move the IV to the right and check “Tukey”

  10. ANOVA exercise HYPOTHESIS: DISTRICT  SCORES • State Scores • C 8 • C 6 • C 4 • C 2 • C 9 • C 3 • C 1 • C 7 • C 4 • C 5 • K 8 • K 5 • K 6 • K 3 • K 2 • K 6 • K 7 • K 7 • K 8 • K 4 • V 5 • V 7 • V 9 • V 4 • V 6 • V 3 • V 8 • V 8 • V 2 • V 5 Independent Variable: School district Sampled 10 districts in each of three States: (C)alifornia (K)entucky (V)irginia ASSIGNMENT • What are the levels of measurement for each variable? • Obtain the F-statistic • What is the level of significance? • Is there a significant relationship between variables? Can we reject the null hypothesis? (use the maximum level set for social science research) • What proportion of the change in the dependent variable is accounted for by the change in the independent variable? Dependent variable: School score, scale 1-10 points Filename: Distr Perf.sav

  11. More practice with ANOVA Dist Perf CalifLow.sav

  12. Two-Way Analysis of Variance • Group independent variable (e.g. by type of school district) State 1 State 2 State 3 Public  x x x Private  x x x

  13. Correlation and regressionAll variables are continuous • When calculating r and r2, computers will automatically flag significant relationships (* p = .05 ** p = .01 *** p = .001) • Unless random samples were taken from a population, these flags are meaningless • Correlate  Bivariate (two variables only) • Correlate  Partial (bring in a third, “control” variable) • When Partial, move the third variable into the “Controlling for” area

  14. Correlation exercise HYPOTHESIS: HEIGHT  WEIGHT, CONTROLLING FOR AGE R2 = .651 Filename: Height weight age.sav, .xls

  15. Stepwise Multiple Regression (using a dummy variable) • How much more do we learn about changes in weight by bringing in gender? • Nominal independent variables can be “transformed” or “recoded” into “dummy” continuous variables, with a range of 0 to 1. (This is not always a good idea, but it is widely done.) • R2 increases from .59 to .69 • When we “regress” a dependent variable against multiple independent variables, Beta is the best indicator of the strength of the relationship between the variables (scale 0 to 1). Check out the Betas for height and gender. Are both statistically significant? • Analyze  Regression  Linear • In the scrollbox for “Method” specify Stepwise Height weight male.sav

  16. Stepwise Mult. Regression exercise HYPOTHESIS:HEIGHT, MALE, CALORIES  WEIGHT Height weight male calories.sav

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