I have two learning curves that need to be compared to establish which learning method is better. Each learning curve is estimated with 11 samples for each of 5 repetitions (total 55 samples per learning curve). Is there a better method than comparing 11 samples on learning curve A with 11 samples on learning curve B at each repetition (five comparisons) with ANOVA?
Thanks in advance for your answers or comments, I will recommend everyone who answers something useful.
Prof. Antonio Maffei your expertise on the matter would be appreciated.
Hello Andrea,
If the five observations per sample represent some measure of success/performance or some measure of errors committed at that point in time (and the 5 observation periods were the same for all cases), then you could evaluate whether the two batches had equal or unequal learning curves by:
1. Repeated measures anova (assuming the measure you're recording at each observation was continuous and metric);
2. Growth curve model
3. Testing for equality of polynomial estimates of fitted curves (though, with sample sizes of 11 for each batch, this won't be a tremendously sensitive test).
4. Probably, a host of other options as well.
Good luck with your work.
Thank you David Morse!
If there is no general answer, here are the details in my case: I am measuring the ability of 11 people to execute an assembly task better and better with repetitions (5 repetitions per person) when aided and when not aided with a video tutorial before the task. The learning curve I refer to is the mean of these 11 curves, which looks like an exponential decay (assembly time per repetitions). On average, the 5 observations (assembly time) show a progressive improvement (less time needed to assemble at every repetition). However, without averaging, the curve slightly varies from person to person.
In the experiment, a control group (11 people) receives no aid and a test group (11 people) receives a video aid before the task. I need to compare the performances of control and test groups, (11x5)x2 samples. The intuitive thing is to plot the two average learning curves on top of each other and see the difference. Though, I'd like to use proper statistical methods to make an analysis.
Given your graphs if you have sufficient data I would recommend a growth curve model comparison. These were developed by C R Rao principally and follow-ups by many others. Google search can help you find a reasonable growth curve model. If insufficient data is a available I would tend to try a repeated measures model. A good reference is the notes by Prof Davidian. Google Davidian NCSU statistics dept course notes on longitudinal statistical models. These are excellent. Best wishes, David Booth
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