1. Research Support Center Chongming Yang
SPSS Workshop
Research Support Center
Chongming Yang

2. Causal Inference If A, then B, under condition C
If A, 95% Probability B, under condition C

3. Student T Test (William S. Gossett’s pen name = student)
Assumptions
Small Sample
Normally Distributed
t distributions: t = [ x - μ ] / [ s / sqrt( n ) ]
df = degrees of freedom=number of independent observations

4. Type of T Tests One sample Two independent samples Paired
test against a specific (population) mean
Two independent samples
compare means of two independent samples that represent two populations
Paired
compare means of repeated samples

5. One Sample T Test
Conceputally convert sample mean to t score and examine if t falls within acceptable region of distribution

6. Two Independent Samples

7. Paired Observation Samples
d = difference value between first and second observations

8. Multiple Group Issues Groups A B C comparisons
AB AC BC
Joint Probability that one differs from another
.95*.95*.95 = .91

9. Analysis of Variance (ANOVA)
Completely randomized groups
Compare group variances to infer group mean difference
Sources of Total Variance
Within Groups
Between Groups
F distribution
SSB = between groups sum squares
SSW = within groups sum squares

10. Fisher-Snedecor Distribution

11. F Test Null hypothesis: 𝑥 1 = 𝑥 2 = 𝑥 3 ...= 𝑥 𝑛
Given df1 and df2, and F value,
Determine if corresponding probability is within acceptable distribution region

12. Issues of ANOVA Indicates some group difference
Does not reveal which two groups differ
Needs other tests to identify specific group difference
Hypothetical comparisons Contrast
No Hypothetical comparisons Post Hoc
ANOVA has been replaced by multiple regressions, which can also be replaced by General Linear Modeling (GLM)

13. Multiple Linear Regression
Causes 𝑥 cab be continuous or categorical
Effect 𝑦 is continuous measure
Mild causal terms  predictors
Objective  identify important 𝑥

14. Assumptions of Linear Regression
Y and X have linear relations
Y is continuous or interval & unbounded
expected or mean of  = 0
 = normally distributed
not correlated with predictors
Predictors should not be highly correlated
No measurement error in all variables

15. Least Squares Solution
Choose 𝛽 0 , 𝛽 1 , 𝛽 2 , 𝛽 3 ,... 𝛽 𝑘 to minimize the sum of square of difference between observed 𝑦 𝑖 and model estimated/predicted 𝑦 𝑖
Through solving many equations

16. Explained Variance in 𝑦

17. Standard Error of 𝛽

18. T Test significant of 𝛽 t = 𝛽 / SE𝛽
If t > a critical value & p <.05
Then 𝛽 is significantly different from zero

19. Confidence Intervals of 𝛽

20. Standardized Coefficient (𝛽𝑒𝑡𝑎)
Make 𝛽s comparable among variables on the same scale (standardized scores)

21. Interpretation of 𝛽
If x increases one unit, y increases 𝛽 unit, given other values of X

22. Model Comparisons Complete Model: Reduced Model: Test F = Msdrop / MSE
MS = mean square
MSE = mean square error

23. Variable Selection Select significant from a pool of predictors
Stepwise undesirable, see
Forward
Backward (preferable)

24. Dummy-coding of Nominal 𝑥
R = Race(1=white, 2=Black, 3=Hispanic, 4=Others)
R d1 d2 d3
Include all dummy variables in the model, even if not every one is significant.

25. Interaction Create a product term X2X3
Include X2 and X3 even effects are not significant
Interpret interaction effect: X2 effect depends on the level of X3.

26. Plotting Interaction
Write out model with main and interaction effects,
Use standardized coefficient
Plug in some plausible numbers of interacting variables and calculate y
Use one X for X dimension and Y value for the Y dimension
See examples

28. Diagnostic Linear relation of predicted and observed (plotting
Collinearity
Outliers
Normality of residuals (save residual as new variable)

29. Repeated Measures (MANOVA, GLM)
Measure(s) repeated over time
Change in individual cases (within)?
Group differences (between, categorical x)?
Covariates effects (continuous x)?
Interaction between within and between variables?

30. Assumptions Normality
Sphericity: Variances are equal across groups so that
Total sum of squares can be partitioned more precisely into
Within subjects
Between subjects
Error

31. Model 𝜇 = grand mean 𝜋 𝑖 = constant of individual i
𝜏 𝑗 = constant of jth treatment
𝜀 𝑖𝑗 = error of i under treatment j
𝜋𝜏 = interaction

32. F Test of Effects F = MSbetween / Mswithin (simple repeated)
F = Mstreatment / Mserror (with treatment)
F = Mswithin / Msinteraction (with interaction)

33. Four Types Sum-Squares
Type I  balanced design
Type II  adjusting for other effects
Type III  no empty cell unbalanced design
Type VI  empty cells

34. Exercise
Copy data to spss syntax window, select and run
Run Repeated measures GLM