What kind of test should I run in SPSS/Jamovi to analyze a Randomized-Controlled trial? I have 3 groups and 2 time points (and small sample sizes)?

Question

I have 3 groups:

Intervention 1 (n=6)

Intervention 2 (n=9)

Treatment as usual (n=12)

And I have 2 time points (pre and post intervention)

What kind of test do you recommend? Thank you!

Answer 1

I recommend an ANCOVA$^{[1]}$. This is multiple regression model of the form:

$$ y_{t_2, i}=\beta_0 + \beta_1\;y_{t_1, i} + \beta_2\;\texttt{group1}_i + \beta_3\;\texttt{group2}_i + \epsilon_i $$

Where $y_{t_1, i}$ and $y_{t_2, i}$ is the outcome at baseline ($t_1$) and follow-up ($t_2$) and $\texttt{group1}$ and $\texttt{group2}$ are indicator variables for the two interventions (so the treatment as usual is the reference group).

In this model, $\beta_2$ and $\beta_3$ are the relevant intervention effects: They denote the average differences of the outcome between the intervention groups and the reference groups after controlling for potential differences at baseline.

This model can be extended in multiple ways. You can add more predictors that help predict the outcome or add interactions between the baseline outcome and the group indicators and so forth. Ideally, you would include the baseline outcome $y_{t_1, i}$ without assuming linearity. A good way of doing this is by including $y_{t_1, i}$ using a restricted cubic spline. Frank Harrell writes about this here.

References

$[1]$ Vickers, A. J., & Altman, D. G. (2001). Analysing controlled trials with baseline and follow up measurements. Bmj, 323(7321), 1123-1124.