Re: Within-subjects proportional data

Ely wrote:
> I may be missing something very obvious, but I am stuck on the following
> problem and hope someone can advise:
>
> I want to do a psychology experiment where participants will be tested on
> their ability to detect targets under two conditions. One each trial they
> see one target paired with one distractor. They can either pick the target
> (correct), pick the distractor (false alarm) or pick nothing (miss).
>
> I am predicting that one condition will produce more correct hits, but am
> also interested in whether condition affects the proportion of each type of
> error (false alarm or miss). There are 12 trails per participant. I can't
> use signal detection because there are 3 choices on each trail, and I can't
> use chi-square because there are multiple trails per participant.
>
> Testing the number of correct hits in each condition is easy enough by
> calculating number of correct identifications out of 12 for each
> participant. I could also separately compare the number of false alarms and
> the number of misses between conditions. But obviously these measures are
> not independent, and apart from the problem of multiple testing, what I
> really want to know is whether the proportion of each type of error differs
> between conditions.
>
> I could take the errors for each participant and calculate the proportion of
> false hits to misses in each condition and use these proportions for
> analysis. However, the overall number of errors will be different for each
> participant, and may be very small, meaning that proportions will tend to
> take extreme values and the range of variation in proportions is restricted.
> Also one condition is predicted to produce a smaller number of errors than
> the other, meaning it will have more extreme proportions. I presume I should
> do an arcsin transformation on the proportions, but I am concerned that the
> test would still be unsound.
>
> Does this sound like a serious violation of t-test assumptions, and should I
> abandon this design and go back to the drawing board? Or is there some other
> way of treating the data that I have missed? I would rather make sure that
> the data will be analysable before collecting it.
>
> Any thoughts appreciated...
>
> Janet

See J.P.Shaffer, The analysis of variance mixed model with allocated
observations: Application to repeated measurement designs, Journal
of the American Statistical Association, 76 (1981), 607-611.

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