My study is on the effectiveness of a mindfulness-based intervention on reducing stress and anxiety among students.
The experimental group was provided with the intervention, while the control group was not, as you would expect.
I have used Wilcoxon's signed-rank test to analyse the scores of stress and anxiety within the control group, and within the experimental group, separately.
However, I cannot seem to understand what test I should use the compare the post-intervention scores between the control group and the experimental group.
If your n is less than 30 nonparametric tests are preferred. How big groups do you have?
One persistent misconception is that you cannot use the t-test on small samples (when pressed, people mutter something about “less than 30” but aren’t sure). Actually, you can. And the t-test performs well in samples as small as N=2! ( de Winter, 2013). Indeed, with very small samples indeed, the Wilcoxon-Mann Whitney test is unable to detect a significant difference, while the t-test is (Altman & Bland, 2009).
It’s also worth pointing out that the idea that the data should be normally distributed before using a t-test, or linear regression, is a myth. It is the measurement errors that need to be normally distributed. But even more important, studies with non-normal data have shown that the t-test is extremely robust to departures from normality (Fagerland, 2012; Fagerland, Sandvik, & Mowinckel, 2011; Rasch & Teuscher, 2007).
References
- Altman, D. G., & Bland, J. M. (2009). Parametric v non-parametric methods for data analysis. Bmj, 338(apr02 1), a3167–a3167. http://doi.org/10.1136/bmj.a3167
- de Winter, J. (2013). Using the Student’s t-test with extremely small sample sizes. Practical Assessment, Research & Evaluation, 18(10), 1–12.
- Fagerland, M. W. (2012). t-tests, non-parametric tests, and large studies--a paradox of statistical practice? BMC Medical Research Methodology, 12, 78. http://doi.org/10.1186/1471-2288-12-78
- Fagerland, M. W., Sandvik, L., & Mowinckel, P. (2011). Parametric methods outperformed non-parametric methods in comparisons of discrete numerical variables. BMC Medical Research Methodology, 11(1), 44. http://doi.org/10.1186/1471-2288-11-44
- Rasch, D., & Teuscher, F. (2007). How robust are tests for two independent samples? Journal of Statistical Planning and Inference, 137(8), 2706–2720.
Use Wilcoxon signed rank test for paired comparision (e.g. before and after), while mann whitney for independent 2 groups.
Please check the attached file for your understandings
You can consider the Friedman test, which is a non-parametric alternative to the one-factor ANOVA test for repeated measures. You have repeated measures, before and after, you should account for this. Another alternative would be ANCOVA.
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