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Conditions of application

Assumption checking. Conditions of application. Assumptions for mixed models and RM ANOVA. Linearity The outcome has a linear relationship with all of the predictors Homoscedasticity The residuals are equally variable at any level of the predictors Normality of the residuals.

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Conditions of application

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  1. Assumption checking Conditions of application

  2. Assumptions for mixed models and RM ANOVA • Linearity • The outcome has a linear relationship with all of the predictors • Homoscedasticity • The residuals are equally variable at any level of the predictors • Normality of the residuals

  3. Fitting the model • Fit the same model from last week: • SIGNAL = (b0 + u0) + b1ACCELERATION + b2COIL + b3COILxACCELERATION + ε • Be sure to use the long dataset, and ALL values of RESOLUTION • ACCELERATION is a covariate, not a factor • SAVE the residuals and the predicted values

  4. Residual plots • Create a histogram of the residuals (Analyze → Descriptive Statistics → Frequencies → Chart), and a scatterplot of the residuals v.s. the predicted values (Graphs → Chart builder). • What are we testing for? • Linearity (no pattern) • Homoscedasticity (constant variance) • Normality of residuals (bell-shaped histogram)

  5. Analyze the residual plots • Do our plots look okay? • Scatterplot • Looks decent • Histogram • Looks plausibly normal, given the sample size • Weird bi-modality

  6. Normality tests • Go to Analyze → Descriptive Statistics → Explore

  7. Tests of normality • Check the Shapiro-Wilk and the Kolmogorov-Smirnov • Neither value is statistically significant • What does that mean? • We have no evidence of non-normality • We pass! • Be careful, though: these tests are poor at finding bimodality

  8. Analyze the Q-Q plot • What are we testing? • Normality of the residuals • How does it look? • Decent, except for the extreme tails • Probably okay

  9. RM ANOVA • Back to the wide file! • Fit an RM ANOVA. Ignore RESOLUTION • SAVE Cook's Distance

  10. Checking Cook's D • Transform the dataset to long form • Only keep ID and the Cook's D variables • Plot Cook's D v.s. ID

  11. How does it look? • Not too bad • None of the points are wildly farther than the others • It looks none of the points were wildly influential • Subject 23 had a big impact, though

  12. Now... • Check the conditions of application for the same models, only now only for subjects with RESOLUTION = 2

  13. Tests of normality • Uh-oh • We fail our tests! • And they don't have a lot of power with small samples, so this might be really bad

  14. Q-Q plots • Not looking good. There's something bad happening in the tails

  15. Residual histogram • That spike in the middle is problematic

  16. Residuals v.s. predicted • At least this looks okay

  17. Residuals v.s. acceleration • This explains it: it's the weird interaction between acceleration and coil that we noticed before

  18. Questions? • About the homework?

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