RM | Unit 250 - Assumptions Part II
Book: Analysing data using linear models
Chapter 7: 7.6, 7.7
Chapter 7.6: General approach to testing assumptions
It is generally advised to always check the residuals. All four assumptions mentioned above can be
checked by looking at the residuals. We advise doing this with three types of plots.
The first is the histogram of the residuals: this shows whether the residuals are more or less
normally distributed. The histogram should show a more or less symmetric distribution. If the plot does
not look asymmetric at all, try to find a transformation of the dependent variable that makes the residuals
more normal. An example of this is to log-transform reaction times.
The second type of plot that you should look at is a plot where the residuals are on the y-axis and
the predicted values for the dependent variable (Yb) is on the x-axis. Such a plot can reveal systematic
deviation from normality, but also non-equal variance.
The third type of plot that you should study is one where the residuals are on the vertical
axis and one of the predictor variables is on the horizontal axis. In this plot, you can spot
violations of the equal variance assumption. You can also use such a plot for candidate predictor
variables that are not in your model yet. If you notice a pattern, this is indicative of dependence,
which means that this variable should probably be included in your model.
Book: Analysing data using linear models
Chapter 7: 7.6, 7.7
Chapter 7.6: General approach to testing assumptions
It is generally advised to always check the residuals. All four assumptions mentioned above can be
checked by looking at the residuals. We advise doing this with three types of plots.
The first is the histogram of the residuals: this shows whether the residuals are more or less
normally distributed. The histogram should show a more or less symmetric distribution. If the plot does
not look asymmetric at all, try to find a transformation of the dependent variable that makes the residuals
more normal. An example of this is to log-transform reaction times.
The second type of plot that you should look at is a plot where the residuals are on the y-axis and
the predicted values for the dependent variable (Yb) is on the x-axis. Such a plot can reveal systematic
deviation from normality, but also non-equal variance.
The third type of plot that you should study is one where the residuals are on the vertical
axis and one of the predictor variables is on the horizontal axis. In this plot, you can spot
violations of the equal variance assumption. You can also use such a plot for candidate predictor
variables that are not in your model yet. If you notice a pattern, this is indicative of dependence,
which means that this variable should probably be included in your model.
