I conducted an experiment with 80 subjects, each of them performing 50 trials. I measured the time (in seconds) needed to accomplish each trial.
Trial-after-trial, every subject has the tendency to get faster in accomplishing his task. I can clearly see that there is a kind of "learning effect". By watching at some plots (x=trial_number, y=time), I can see a descending curve that looks like stabilizing towards an asymptotic minimum after the 20th trial.
What kind of numerical analysis can I use to formally report on this effect? How do I "measure" the learning effect? How can I formalize that after the 20th (or so) trial the subject's performance have stabilized?
I do analyses like this all the time. What you need is a multilevel regression using trial as a continuous predictor. Given that you're predicting latency data as a function of trial, I recommend that you consider two variants for the DV - either a general linear model with log-transformed latencies or (if you know how to conduct it), a generalized linear Gamma regression. Both should be multilevel models. Either way, the slope of the time variable assesses the rate of learning. Also, be sure to specify slope and intercept as random effects in your multilevel model to capture the individual differences.
if you have other predictors, they can be considered as moderators of the slope by including an appropriate interaction term.
if you use R, I can send you the syntax - it's very straightforward.
Since this is an experiment, how many conditions were people randomly allocated into? Are you trying to measure where the typical subject in each condition reached near their quickest times?
I have used MANOVA in previous repeated measure design studies, but due to the time interval you may want to consider multiple regression.
I do analyses like this all the time. What you need is a multilevel regression using trial as a continuous predictor. Given that you're predicting latency data as a function of trial, I recommend that you consider two variants for the DV - either a general linear model with log-transformed latencies or (if you know how to conduct it), a generalized linear Gamma regression. Both should be multilevel models. Either way, the slope of the time variable assesses the rate of learning. Also, be sure to specify slope and intercept as random effects in your multilevel model to capture the individual differences.
if you have other predictors, they can be considered as moderators of the slope by including an appropriate interaction term.
if you use R, I can send you the syntax - it's very straightforward.
Daniel Wright: Indeed, I am conducting the study in two conditions. I would like to both find "where the typical subject in each condition reached near their quickest times", as well as compare the two conditions and understand in which the learning effect is "less/more prominent."
Michael E Young: Thanks for the hints. I am new to this kind of analysis and, from the text-only description, it is pretty hard to understand the detailed procedure.
So yes, please, any R code would be helpful :-) I will try later to see if I can adapt it to python/scipy.
Also, any pointer to books/publications/class notes describing the process would be welcome!
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