My apologies for this question. I am new to this type of analysis.
I am studying four students. Examining changes in mathematical cognition over time and fact retrieval following an authentic time lapse in instruction. The students will be tested at four times over the course of the year. The data sources are at home videos created by the students as they think aloud while working on mathematics.
I would like to use latent growth curve analysis as the statistical tool for analysis. I am not clear on whether this small sample size would make this inappropriate or whether there is a better choice.
I would like to examine changes over time in these students' mathematical thinking.
This is a very small sample. It might be better to look at these four students qualitatively.
Anna Wolf posted on Tuesday, December 02, 2014 - 5:03 pm
I conducted two separate generalized growth mixture models for two different outcome measures. In each model, the slope of the class trajectories was regressed on intervention status (i.e. using a dummy code: intervention vs control group).
My results showed a three class model was best fit for both models. Intervention effects were significant for one of the trajectories (in both models). However, the size of the classes (and the groups within each class) is very small. In one analysis the intervention group had n = 21 participants and the control n = 2; whilst another had n = 12 experimental and n = 2 in the control.
Are these models still valid given the small n?
P.S. I'd also like to say how useful I find your discussion board and advice - thank you!
I would worry about replicability of your results with such small sample sizes unless you have many time points. Having only n=2 in a class gives a very fragile solution that is not trustworthy.
Anna Wolf posted on Tuesday, December 02, 2014 - 7:18 pm
Thanks so much for your prompt response.
Apologies for not making myself clear in my previous post. I actually have a total of n = 23 and n = 14 in the classes showing treatment effects across the two models.
That is, the numbers I was referring to in my last post was the n of the experimental and control participants in each class. I was advised to determine the separate n for each group (after conducting the generalized growth mixture model) to provide clearer idea of the experimental vs control comparison in each class..
So, does having n = 23 and n = 14 in each class still create a fragile solution that isn't trustworthy? From my understanding from a paper by Jung & Wickrama (2008), given that these classes had more than 1% of total count they were acceptable. Is this correct?
If you do think that the solution is still fragile, do you recommend I select another model?
When it comes to sample size in each class you should relate that to how many class-specific class parameters you have.
With small sample sizes you may want to do a Monte Carlo study in Mplus. You can use the SVALUES option to take your parameter estimates as data-generating parameters. This study tells you if your parameter estimates are well recovered, if the SEs are well estimated, and the power to reject for each parameter. See UG chapter 12.