1. 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

2. 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
N= 200
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, 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 =  E
Chi-square is not the best test of significance
Requires moderate-size samples (e.g., 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. 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
N= 200
Job Stress
Position on police force
Low
High
Sergeant
78%
33%
Patrol Officer
22%
67%
Total % %
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. 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 -x 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)

7. 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 M M M M M M
F 5
F 4
F 6
F 3
F 7
F 8
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. HYPOTHESIS: DISTRICT  SCORES
ANOVA exercise
HYPOTHESIS: DISTRICT  SCORES
State Scores C C C C C C C C C K K K K K K K V V V V V V V V
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

12. More practice with ANOVA
Dist Perf CalifLow.sav

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

14. Correlation and regression All variables are continuous
When calculating r and r2, computers will automatically flag significant relationships (* p = ** p = *** 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

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

16. 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

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