Conditions of application

Assumption checking

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

Fitting the model

Fit the same model from last week:

SIGNAL = (b0 + u

0) + b

1ACCELERATION +

b2COIL + b

3COILxACCELERATION + 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

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)

Analyze the residual plots

Do our plots look okay? Scatterplot

Looks decent

Histogram Looks plausibly normal, given the sample size Weird bi-modality

Normality tests

Go to Analyze → Descriptive Statistics → Explore

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

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

RM ANOVA

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

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

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

Now...

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

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

Q-Q plots

Not looking good. There's something bad happening in the tails

Residual histogram

That spike in the middle is problematic

Residuals v.s. predicted

At least this looks okay

Residuals v.s. acceleration

This explains it: it's the weird interaction between acceleration and coil that we noticed before

Questions?

About the homework?