Hello. I was wondering if anyone had suggestions in terms of what exploratory analysis to carry out for my dissertation with the following data.
I measured N=26 participants pre and post an activity, thus I have 3 continuous variables of the difference between scores. The data was non-normally distributed with a couple of outliers in each of the variables. Transforming the data did not change it much and I decided against removing the outliers. My main analysis was a bootstrapped paired-samples t test.
I also collected demographic data such as household income, age and sex at birth and data related to the activity (i.e. frequency of activity before survey; length of time spent in activity before post-survey completion) - thus I have several categorical variables.
I was thinking to conduct Jonckheere-Terpstra test for the 'length of time spent...' in order to see if there is a significant exponential increase/decrease in the continuous variables related to the time spent in activity.
In terms of co-variate, there are some relations that have been pointed out in literature before, so I could look at the relationship between the dependent variables.
What I am interested in is to explore whether there are any differences between the continuous variables (considering they do not meet normality assumption and they present with outliers, n=26) when grouped with the different categorical data i.e. did participants age 30-49 experience a higher decrease in anxiety levels ?
I am thinking that once I do some type of descriptive exploratory analysis to see if there are differences I could employ a test which will explore the significance for this relationship? Again, I am not sure what would this be with the combination of data that I have.
Mara Nicola , I recommend:
1) For the exploratory analysis: Since your data is not normally distributed, you may consider to use a non-parametric test for the differences of continuous variables across categories of interest. I personally recommend Kruskal-Wallis - such really a cool one.
2) Inferential analysis: A GLM model is what you are looking for. The link function depends on the nature of the stochastic process of the dependent variable of interest, e.g. logistic for a binomial process (a binary dependent variable), poisson for a count outcome or gaussian for a continuous dependent variables, etc.
Thank you Rolando! I was thinking of Kurskal-Wallis but was unsure about whether it meets the design - it makes sense now that I only have to use the differences as independent variables.
Great suggestion about the GLM, we weren't taught it and didn't come across it yet, so it really wasn't in my mind - I will have to look into this, cheers!
Krustal wallis for ANOVA-MANOVA with data that show lack of normality and that allows to evaluate by categories and instead of tests to use U of Mann witnney.
Hello Mara,
The basic approach you took for pre-post comparisons (bootstrapped correlated t-tests) was a reasonable choice, given the information furnished in your query. While I might have suggested manova instead (one test instead of three), manova (whether bootstrapped or not) tends not to be as powerful, though it can be more sensitive because it takes into account more information.
As regards your subsequent comparisons based on categorical demographic features, bootstrapped error estimates are still a better option than many others. However, do note than an N of 26 doesn't offer very much statistical power once you start looking at/for differences among subgroups, no matter what analytic method you select. It might be instructive to look at a priori power estimations (perhaps via G*Power: https://www.psychologie.hhu.de/arbeitsgruppen/allgemeine-psychologie-und-arbeitspsychologie/gpower.html) in order to have a clue as to how much or little risk of Type II error you're likely flirting with by running such analyses. Note that the G*Power estimates are likely to be optimistic as well, since the presumption is that the typical parametric assumptions are satisfied, whereas you're convinced that this is not the case for your data set.
Good luck with your work.
You're welcome Mara Nicola :)
Complementing the answer of David Morse , since your N = 26, you may want to consider using Bayesian methods, too. Bayesian methods are the rock n' roll of statistics and are extremely powerful when properly used.
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