I am running an exercise study in which people have to undergo three different experimental conditions each (repeated measures design). Each trial ends with a cycling time trial. Some participants are unable to finish the time trial in one condition as it is too difficult. Can I still perform normal repeated measures ANOVA and assign this not completed trials time of the worst subject?
Tim Podlogar,
From your description, it seems like your experiment was a cross-over design. There are a few details that I might be over thinking; can you clear these up?
- "Each trial ends with a cycling time trial." — Are you considering this the 'washout' periods?
- "Some participants are unable to finish the time trial in one condition as it is too difficult." — Does this mean that missing data is for only one of the experimental conditions?
- "...assign this not completed trials time of the worst subject?" — This isn't clear to me (perhaps only me), can you elaborate?
- How is your data missing (e.g., completely at random, some missingness in all exp. cond. [see above])? What percentage of your data is missing?
Cross-over designs can get complex (at least for my little brain) quickly as more exp. cond./observations are added through time. And, if the sequence isn't randomized for different participants, it can become difficult to tease out the effects of each exp. cond. from the exp. cond. plus what preceded it.
At any rate, my initial thoughts turn to mixed-effects models. They can handle missingness and repeated measures (the correlation thereof). Like cross-over designs they can be a conceptual and practical task. If you use R you might look into the nlme and lme4 packages. You might also have a look one of the versions (differ depending on statistical software used) of Andy Field's "Discovering Statistics Using ___." There are a number of other stats books that have good info on mixed-effects models too.
Being "unable to finish the time trial in one condition as it is too difficult" is a possibly valuable information, and this should not just be replaced by a "missing value" (the "missingness" would not be "at random" -> MNAR, what would indroduce bias). The best approach, to my opinion, is to label these values as (right-)censored, and the censoring value could be the time of the worst subject (or the time that was reserved for the trial to be finished [one could investigate what the effect of that choice would be]).
Thanks for both replies. Let me explain into a bit more details... Study involves some steady state cycling at a predetermined power output that that is of moderate intensity with a fixed time that is followed by a time trial. During the first part, we do some metabolic measurements. Proceeding both exercise bouts there is some dietary intervention. And it looks as one intervention makes it very difficult for some subjects to finish a time trial.
Let me explain how the time trial looks like. They have to complete certain amount of mechanical work and this would equate to cover certain distance on a bicycle. Subjects that could not finish it, were so tired that it would took them a very very long time to complete the time trial, as the intensity at which they would be able to ride at, would be very low. Imagine walking a 42km marathon. Basically they finish because they do not feel they would be able to finish in a reasonable time. If that makes sense. E.g. one subject was clearly hypoglycaemic. Hope this makes some more sense.
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