General Linear Model and Anova (wk 6)

Question 1

What is the GLM?

Answer 1

-General linear model -> Modern statistics began with correlation (~1886). Then the t-test was developed (1908). Then regression was developed. All these methods are then part of the General Linear Model.
-GLM -> Works because it assumes that the ‘residuals’ will be normally distributed and that different statistical tests combine linearly (meaning they add together).

Question 2

What is the purpose of GLM statistical tests?

Answer 2

-Assess the strengths and directions of relationships and differences. Strengths of interventions and manipulations. e.g. does an intervention make people more or less fit?
-When you do a regression, you get an ANOVA value

Question 3

What is ANOVA?

Answer 3

-ANOVA -> Analysis of Variance -> All GLM tests analyse variance, but anovas are for categorical differences between:
1. Different conditions on a study (intervention 1 vs intervention 2; drug vs placebo)
2. Different groups in a study (intervention vs control; old vs young; patients vs healthy)
+ Anovas and t-tests are special kinds of linear regression.
+ One categorical predictor (group=independent variable) and One continuous outcome (measure=dependent variable)
-Cannot do an ANOVA on 3 different types of groups

Question 4

What is a one-way ANOVA and factorial (or multi-way) anova?

Answer 4

1. One-way ANOVA -> Three or more groups; one outcome variable
2. Factorial (or multi way) ANOVA -> Two or more groups’ two or more categorical predictor values; one outcome variable.

Question 5

What is a repeated measures (or within-subjects) ANOVA or mixed ANOVA?

Answer 5

3. Repeated measures (or within-subjects) ANOVA -> One group; two or more categorical predictor values; one outcome variable
4. Mixed ANOVA -> Two or more groups; one or more categorical predictor values; one outcome variable

Question 6

Draw the table for the GLM repeated measures designs (one group and one continuous outcome)

Question 7

Draw the table for between and within-participants (two+ groups and one continuous outcome)

Question 8

GLM with:
1. Multiple outcome variables
2. Continuous predictor variable
3. Discrete outcome variable
4. Multiple predictor and outcome variables

Answer 8

• Multiple outcome variables e.g. height/ weight -> MANOVA
• Continuous predictor variable e.g. cholesterol -> ANCOVA
• Discrete outcome variable e.g. diabetes/not -> Logistic regression
• Multiple predictor and outcome variables e.g. cholesterol, height; diabetes/not, weight -> Multivariate regression

Question 9

What is a one-way ANOVA Post-hoc test?

Answer 9

-After finding a significant difference among three or more groups or conditions, you can run some ‘post-hoc’ tests to see which groups were significantly different from each other.

Question 10

Describe interactions in anova results:

Answer 10

-An interaction between two variables is when differences in one variable are affected by differences in another variable
-Statistically, interactions are just the same as main effects
-Whether interactions are special or not depends only on theory and how you entered your date into the anova

Question 11

What are the 3 assumptions in anova?

Answer 11

-Observations are independent i.e. from different people; different times
-Variance of different groups or conditions should be ~equal
-Residuals (‘unexplained variance’ or ‘error’ will be ~normally-distributed

Question 12

Assumptions in RM-ANOVA:

Answer 12

-The differences between levels of a variance should have ~equal variance (if you have 3+ groups or conditions in a variable, check spericity)