Question:

A psychologist compared the effectiveness of Cognitive Behavioural Therapy (CBT) and eye movement desensitisation and reprocessing (EMDR) for the treatment of post-traumatic stress disorder (PTSD).

Clients with PTSD were recruited and randomised into either the CBT or EMDR group. A group of 5 psychologists were trained in both treatment methods. Individual clients were treated by the same psychologist across the study. The Clinician-Administered PTSD Scale (CAPS) was used to assess severity of PTSD symptoms before and after the course of therapy.

They then analysed the difference in CAP Scale. The predictor variables were psycholo- gist, and treatment method.

(a) Write the statistical model for this as an equation.

The statistical model is:

ijk = ij +ijk

=+i +j+ij+ijk

th age group.

• &’ is the mean of the population of responses corresponding to the th level of factor A (age group) and the th level of factor B (learning group). Thus it is the population mean corresponding to each treatment. This can be broken down into components using &’=+&+’+&’, where

• is the overall population mean of the response. Thus it is the average number of words remembered across all age groups and learning conditions.

• & is the fixed effect of the th level of factor A (age group) on the response (number of words remembered).

• ’ is the fixed effect of the th level of factor B (learning group) on the response (number of words remember

red).

• &’ is the interaction effect of the th level of factor A (age group) and th level of factor B (learning group) on the response (number of words remembered).

• &’ is the error term of the observation, &’, assumed to be distributed normally with a mean of zero and variance of 5. It is the remaining unexplained variation after the effects of factor A (age group) and factor B (learning group) and any interaction effect have been accounted for.