ARMS Grasple aantekeningen 2025/2026
Inhoud
ARMS Grasple aantekeningen 2025/2026..............................................................1
Refresh lessons – Part 1.......................................................................................... 3
Introduction......................................................................................................... 3
About correlation................................................................................................. 3
More on correlation and causality.......................................................................3
The linear regression model................................................................................ 3
Estimating the regression line............................................................................. 4
R-squared............................................................................................................ 4
Refresh lessons – part 2.......................................................................................... 5
[WG] Validiteit..................................................................................................... 5
Jasp: intro............................................................................................................ 6
Bayesian hypothesis testing & the Bayes factor.................................................6
Refresh lessons – Part 3.......................................................................................... 7
Introduction ANOVA............................................................................................. 7
More on variances and the F-statistic..................................................................8
Week 1: Bayes and MLR......................................................................................... 9
The Bayesian approach....................................................................................... 9
Assumptions I...................................................................................................... 9
Assumptions II................................................................................................... 10
JASP: Assumptions in MLR................................................................................. 11
Multiple linear regression, including hierarchical MLR.......................................12
JASP: MLR, including hierarchical.......................................................................13
Creating dummy variables................................................................................ 16
JASP: MLR with dummy variables......................................................................17
Multiple regression with dummy variables (interpretation)...............................17
[WG] Article Hadlington et al. (2020)................................................................18
Week 2: Factorial ANOVA...................................................................................... 20
Factorial ANOVA: visually assessing main and interaction effects.....................20
JASP: ANOVA assumptions................................................................................. 21
JASP: factorial ANOVA........................................................................................ 22
Factorial ANOVA................................................................................................. 23
[WG] About multiple testing and error rates.....................................................23
[WG] Follow-up testing and planned contrasts (frequentist only)......................23
, JASP: Follow-up testing and planned contrasts (frequentist only)......................26
Informative hypotheses (Bayes only)................................................................28
JASP: Informative hypotheses (Bayes only).......................................................29
[WG] Article Everett et al. (2019)......................................................................30
Week 3: ANCOVA.................................................................................................. 31
Averages and corrected averages.....................................................................31
JASP: ANCOVA (Frequentist)............................................................................... 33
ANCOVA (Frequentist)........................................................................................ 34
[WG] The FAIR principles................................................................................... 35
ANCOVA as regression....................................................................................... 36
JASP: ANCOVA (Bayesian).................................................................................. 36
ANCOVA (Bayesian)........................................................................................... 37
Supporting the null hypothesis..........................................................................38
[WG] FAIR data Everett et al. (2019).................................................................40
Week 4: Repeated-measures ANOVA....................................................................41
[WG] Within factors and between factors..........................................................41
The sphericity assumption................................................................................ 41
JASP: Repeated measures ANOVA with one factor.............................................43
Repeated measures ANOVA with one factor......................................................44
JASP: Two within factors..................................................................................... 44
Two within factors: interpretation......................................................................45
JASP: Mixed design RM ANOVA..........................................................................45
Mixed design RMA (repeated measures ANOVA)...............................................46
[WG] Article Firk et al. (2018)............................................................................ 47
Week 5: Mediation analysis.................................................................................. 48
[WG] Moderation vs. mediation.........................................................................48
[WG] Bootstrapping........................................................................................... 49
JASP: Mediation (frequentist only).....................................................................51
Mediation analysis............................................................................................. 52
[WG] Mediation analyses Firk et al. (2018)........................................................53
,Refresh lessons – Part 1
Introduction
Simple linear regression there is only one independent variable in the model
About correlation
Correlation coefficient (Pearson) gestandardiseerd nummer om de sterkte van
een lineaire relatie vast te stellen, hoe verder weg van de 0, hoe sterker
Een relatie kan ook non-lineair zijn. Pearson’s r is dan niet de goede maat om dit
te meten.
More on correlation and causality
Just because two variables are correlated, does not mean that one causes the
other. To check whether a variable causes another variable (causation) you would
need to set up an experiment. It’s required to establish that other options can be
ruled out.
The linear regression model
The measurement level required for linear regression is interval or ratio. The
regression line is used to predict the value of one variable based on the value of
the other variable. Calculating the predicted value would be easier and quicker.
For that, we need the regression equation.
The first thing you would need to calculate, is the slope of the line (y/x). An
increase in X by one unit results in an increase or decrease in Y of how many
units?
Now that we know the slope, we need to figure out where to place it vertically
on the y-axis. The intercept, the point there the regression line crosses the y-axis.
Often referred to as the “constant” or b0.
Y-value=intercept+slope×X-value
^y =b0 +b1 x
Y dakje is om aan te geven dat het niet de geobserveerde waarde is, maar de
voorspelde waarde.
In many occasions, the intercept by itself can be fairly meaningless and only
serves so support a correct prediction.
, Estimating the regression line
A method statisticians use to draw the most suitable line in a correlation. The
least squares method.
The distance between the true value y and the predicted value ^y is called the
error or the residual. y - ^y.
Positive and negative errors cancel each other. The sum of all errors is zero but
this does not reflect properly how well the line fits the data points. When we
square the errors, they will always be positive and won’t cancel each other. This
way we can look for the line that will result in the smallest possible sum of
squared errors. This method is the least squares method.
The following formula reduces the sum of squared errors to a minimum. It
determines the slope of the line with the smalles sum of squared errors.
You do not need to know this formula
In JASP is bij Coefficients Unstandardized H1 de slope.
Unstandardized H1 (Intercept) = intercept
R-squared
Het is ook belangrijk om de ‘fit’ van het model te weten. Dit meet je met r-
squared, dat is hoe goed de fit van de voorspelling is met een so called
‘goodness of fit’ number. R-squared determines the proportion of the variance of
the response variable that is ‘explained’ by the predictor variable(s). It is a
proportion between 0 and 1.
If R-squared is very small, this does not mean that there is no meaningful
relationship between the two variables. Also, if R-squared is very large, this does
not necessarily mean that the model is useful for predicting new observations.
Inhoud
ARMS Grasple aantekeningen 2025/2026..............................................................1
Refresh lessons – Part 1.......................................................................................... 3
Introduction......................................................................................................... 3
About correlation................................................................................................. 3
More on correlation and causality.......................................................................3
The linear regression model................................................................................ 3
Estimating the regression line............................................................................. 4
R-squared............................................................................................................ 4
Refresh lessons – part 2.......................................................................................... 5
[WG] Validiteit..................................................................................................... 5
Jasp: intro............................................................................................................ 6
Bayesian hypothesis testing & the Bayes factor.................................................6
Refresh lessons – Part 3.......................................................................................... 7
Introduction ANOVA............................................................................................. 7
More on variances and the F-statistic..................................................................8
Week 1: Bayes and MLR......................................................................................... 9
The Bayesian approach....................................................................................... 9
Assumptions I...................................................................................................... 9
Assumptions II................................................................................................... 10
JASP: Assumptions in MLR................................................................................. 11
Multiple linear regression, including hierarchical MLR.......................................12
JASP: MLR, including hierarchical.......................................................................13
Creating dummy variables................................................................................ 16
JASP: MLR with dummy variables......................................................................17
Multiple regression with dummy variables (interpretation)...............................17
[WG] Article Hadlington et al. (2020)................................................................18
Week 2: Factorial ANOVA...................................................................................... 20
Factorial ANOVA: visually assessing main and interaction effects.....................20
JASP: ANOVA assumptions................................................................................. 21
JASP: factorial ANOVA........................................................................................ 22
Factorial ANOVA................................................................................................. 23
[WG] About multiple testing and error rates.....................................................23
[WG] Follow-up testing and planned contrasts (frequentist only)......................23
, JASP: Follow-up testing and planned contrasts (frequentist only)......................26
Informative hypotheses (Bayes only)................................................................28
JASP: Informative hypotheses (Bayes only).......................................................29
[WG] Article Everett et al. (2019)......................................................................30
Week 3: ANCOVA.................................................................................................. 31
Averages and corrected averages.....................................................................31
JASP: ANCOVA (Frequentist)............................................................................... 33
ANCOVA (Frequentist)........................................................................................ 34
[WG] The FAIR principles................................................................................... 35
ANCOVA as regression....................................................................................... 36
JASP: ANCOVA (Bayesian).................................................................................. 36
ANCOVA (Bayesian)........................................................................................... 37
Supporting the null hypothesis..........................................................................38
[WG] FAIR data Everett et al. (2019).................................................................40
Week 4: Repeated-measures ANOVA....................................................................41
[WG] Within factors and between factors..........................................................41
The sphericity assumption................................................................................ 41
JASP: Repeated measures ANOVA with one factor.............................................43
Repeated measures ANOVA with one factor......................................................44
JASP: Two within factors..................................................................................... 44
Two within factors: interpretation......................................................................45
JASP: Mixed design RM ANOVA..........................................................................45
Mixed design RMA (repeated measures ANOVA)...............................................46
[WG] Article Firk et al. (2018)............................................................................ 47
Week 5: Mediation analysis.................................................................................. 48
[WG] Moderation vs. mediation.........................................................................48
[WG] Bootstrapping........................................................................................... 49
JASP: Mediation (frequentist only).....................................................................51
Mediation analysis............................................................................................. 52
[WG] Mediation analyses Firk et al. (2018)........................................................53
,Refresh lessons – Part 1
Introduction
Simple linear regression there is only one independent variable in the model
About correlation
Correlation coefficient (Pearson) gestandardiseerd nummer om de sterkte van
een lineaire relatie vast te stellen, hoe verder weg van de 0, hoe sterker
Een relatie kan ook non-lineair zijn. Pearson’s r is dan niet de goede maat om dit
te meten.
More on correlation and causality
Just because two variables are correlated, does not mean that one causes the
other. To check whether a variable causes another variable (causation) you would
need to set up an experiment. It’s required to establish that other options can be
ruled out.
The linear regression model
The measurement level required for linear regression is interval or ratio. The
regression line is used to predict the value of one variable based on the value of
the other variable. Calculating the predicted value would be easier and quicker.
For that, we need the regression equation.
The first thing you would need to calculate, is the slope of the line (y/x). An
increase in X by one unit results in an increase or decrease in Y of how many
units?
Now that we know the slope, we need to figure out where to place it vertically
on the y-axis. The intercept, the point there the regression line crosses the y-axis.
Often referred to as the “constant” or b0.
Y-value=intercept+slope×X-value
^y =b0 +b1 x
Y dakje is om aan te geven dat het niet de geobserveerde waarde is, maar de
voorspelde waarde.
In many occasions, the intercept by itself can be fairly meaningless and only
serves so support a correct prediction.
, Estimating the regression line
A method statisticians use to draw the most suitable line in a correlation. The
least squares method.
The distance between the true value y and the predicted value ^y is called the
error or the residual. y - ^y.
Positive and negative errors cancel each other. The sum of all errors is zero but
this does not reflect properly how well the line fits the data points. When we
square the errors, they will always be positive and won’t cancel each other. This
way we can look for the line that will result in the smallest possible sum of
squared errors. This method is the least squares method.
The following formula reduces the sum of squared errors to a minimum. It
determines the slope of the line with the smalles sum of squared errors.
You do not need to know this formula
In JASP is bij Coefficients Unstandardized H1 de slope.
Unstandardized H1 (Intercept) = intercept
R-squared
Het is ook belangrijk om de ‘fit’ van het model te weten. Dit meet je met r-
squared, dat is hoe goed de fit van de voorspelling is met een so called
‘goodness of fit’ number. R-squared determines the proportion of the variance of
the response variable that is ‘explained’ by the predictor variable(s). It is a
proportion between 0 and 1.
If R-squared is very small, this does not mean that there is no meaningful
relationship between the two variables. Also, if R-squared is very large, this does
not necessarily mean that the model is useful for predicting new observations.
