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SPSS Workshop

SPSS Workshop. Research Support Center Chongming Yang. Causal Inference. If A, then B, under condition C If A, 95% Probability B, under condition C. Student T Test (William S. Gossett’s pen name = student). Assumptions Small Sample Normally Distributed

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SPSS Workshop

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  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 • .95 .95 .95 • 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-SnedecorDistribution

  11. F Test • Null hypothesis: • 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specific group difference • Hypothetical comparisons Contrast • No Hypothetical comparisons Post Hoc • ANOVA has been replaced by multiple regressions, which can also be replaced by General Linear Modeling (GLM)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 • Causescab be continuous or categorical • Effect is continuous measure • Mild causal terms  predictors • Objective  identify important

  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 to minimize the sum of square of difference between observed and model estimated/predicted • Through solving many equations

  16. Explained Variance in

  17. Standard Error of

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

  19. Confidence Intervals of

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

  21. Interpretation of • If x increases one unit, y increases 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 http://en.wikipedia.org/wiki/Stepwise_regression • Forward • Backward (preferable)

  24. Dummy-coding of Nominal • R = Race(1=white, 2=Black, 3=Hispanic, 4=Others) R d1 d2 d3 1 1 0 0 1 1 0 0 2 0 1 0 2 0 1 0 3 0 0 1 3 0 0 1 4 0 0 0 4 0 0 0 • 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 http://frank.itlab.us/datamodel/node104.html

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

  28. 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?

  29. 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

  30. Model • = grand mean • = constant of individual i • = constant of jth treatment • = error of i under treatment j • = interaction

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

  32. 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

  33. Exercise • http://www.ats.ucla.edu/stat/spss/seminars/Repeated_Measures/default.htm • Copy data to spss syntax window, select and run • Run Repeated measures GLM

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