The researchers of this study investigated the impact of various counselling therapies on participants' wellbeing. It was hypothesised that: (1) participants undertaking CBT would report increase wellbeing scores compared to participants undertaking 'psychoanalysis' therapy, and (2) participants undertaking psychoanalysis therapy would report more wellbeing compared to participants exposed to behavioural therapy. If I was to use a 1 way ANOVA for this Analysis what analysis would I use for the following question? -

After examining their results (from Part A) the researchers were interested in including an additional variable into their model: mental health diagnosis (there are two categories of mental health diagnosis accordingly if the participant has a diagnosed mental health disorder or not 0=no; 1= yes). This new study consists of the following hypotheses: (1) participants undertaking CBT would report increase wellbeing scores compared to participants undertaking 'psychoanalysis' therapy, AND behavioural therapy and (2) this difference in wellbeing would differ for participants who have a mental health diagnosis compared to those who do not have a mental health diagnosis.

Would this be a 2 way ANOVA?