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SPSS Workshop Research Support Center Chongming Yang.

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Presentation on theme: "SPSS Workshop Research Support Center Chongming Yang."— Presentation transcript:

1 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 – 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

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specific group difference – Hypothetical comparisons  Contrast – No Hypothetical comparisons  Post Hoc ANOVA has been replaced by multiple regressions, which can also be replaced by General Linear Modeling (GLM)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

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







22 Model Comparisons Complete Model: Reduced Model: Test F = Ms drop / 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 R = Race(1=white, 2=Black, 3=Hispanic, 4=Others) R d1 d2 d Include all dummy variables in the model, even if not every one is significant.

25 Interaction Create a product term X 2 X 3 Include X 2 and X 3 even effects are not significant Interpret interaction effect: X 2 effect depends on the level of X 3.

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

32 F Test of Effects F = MS between / Ms within (simple repeated) F = Ms treatment / Ms error (with treatment) F = Ms within / Ms interaction (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 epeated_Measures/default.htm epeated_Measures/default.htm Copy data to spss syntax window, select and run Run Repeated measures GLM

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