ARMS general part

ARMS Lectures & Seminars
Inhoudsopgave
Lecture 1. Mutiple lineair regression.............................................................................................................. 2

Lecture 2. Moderation & mediation............................................................................................................... 9

Lecture 3. ANOVA & ANCOVA...................................................................................................................... 15

Lecture 4. Factorial ANOVA & MANOVA....................................................................................................... 22

Lecture 5. Repeated measures analysis and mixed designs...........................................................................29

Seminar 1. Bootstrapping............................................................................................................................. 35

Seminar 2. Open science.............................................................................................................................. 48

Overview of techniques............................................................................................................................... 50

,Lecture 1. Mutiple lineair regression
The birth order effect
Scientific research has demonstrated that firstborns have a higher IQ than laterborns. Do
you believe this to be true?

Galton (1874) noticed that the number of firstborns among eminent scientists was
remarkably large.
- Researchers started to study birth order with IQ and observed a significant positive
relation.

Does this imply a real effect of birth order on IQ?
- Critically review the way the studies were performed
o Representative sample?
o Reliable measurs of variables?
o Correct analyses and correct interpretation of results?
- Critically consider alternative explanations for the statistical association
o Association ≠ causation
o Does effect remain when additional variables are included?

Adding variables
Simple linear regression: involves 1 outcome (Y) and 1 predictor (X).
- Outcome = DV = dependent variable = e.g. IQ
- Predictor = IV = independent variable = e.g. birth order




 Observed y-score of person I is partly predicted by the model but the
prediction will not be perfect; error in prediction ei (residual).


Multiple linear regression: involves 1 outcome and multiple predictors.

,The relevance of a predictor
1. The amount of variance explained (R2). i.e. the seizes of the residuals




2. The slope of the regression line (B1)




Multiple linear regression (MLR)
MLR examines a model where multiple predictors are included to check their unique linear
effect on Y.

Things you need to know about MLR:
a. The model
b. Types of variables in MLR
c. MLR and Hierarchical MLR
o Hypotheses
o Output
o Model fit: R2, and R2-change
o Regresseion coeffeicients: B and Beta (= standardized B)
d. Exploratory MLR (sptewise) versus confirmatory MLR (forced entry)
e. Model assumptions important to MLR

, A. The model




B. Types of variables
Formal distinction in 4 measurement levels: nominal, ordinal, interval, and ratio.

For choice of analysis, we usually distinguish:
- “Nominal + Ordinal” a.k.a. categorical or qualitative
- “Interval + Ratio” a.k.a. continuous or quantitative or numerical

MLR requires continuous outcome and continuous predictors. But categorical predictors can
be included as dummy variables.

 Dummy coding in MLR models
Is gender a predictor or grade?
- Grade on scale 0 – 10 where numbers have numerical meaning. OK.
- Gender coded as 1 = male; 2 = female. This categorical and not numerical. Not OK.
- Dummy variable has only values 0 and 1 (e.g. 1 = male; 0 = female).