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

Used with moderate size random samples 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 Job Stress Position on police force Low High Total Sergeant 86 30 116 Patrol Officer 24 60 84 Total 110 90 N= 200 Analyze  Descriptive Statistics  Crosstabs Select “Statistics,” check “Chi-Square”

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, 2 is 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

Chi-Square exercise POSITION  STRESS ASSIGNMENT Position on police force Job Stress Patrol Officer Sergeant Total Low 86 30 116 High 24 60 84 Total 110 90 N= 200 Job Stress Position on police force Low High Sergeant 78% 33% Patrol Officer 22% 67% Total 100% 100% 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

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

HYPOTHESIS: GENDER (M/F)  CYNICISM (measured on a 10-point scale) 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 -x2 t = -------------- 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)

HYPOTHESIS: GENDER  CYNICISM T-test exercise HYPOTHESIS: GENDER  CYNICISM M & F cynicism scores 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 9 M 10 M 6 M 5 M 4 F 5 F 4 F 6 F 3 F 7 F 8 Filename: Gender Cynicism.sav

Ratio

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”

HYPOTHESIS: DISTRICT  SCORES ANOVA exercise HYPOTHESIS: DISTRICT  SCORES State Scores C 8 C 6 C 4 C 2 C 9 C 3 C 1 C 7 C 5 K 8 K 5 K 6 K 3 K 2 K 7 K 4 V 5 V 7 V 9 V 4 V 6 V 3 V 8 V 2 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

More practice with ANOVA Dist Perf CalifLow.sav

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

Correlation and regression All 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

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

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

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