On Sun, 28 Oct 2001, Melady Preece wrote:
> Hi. I want to compare the percentage of correct identifications (taste
> test) to the percentage that would be correct by chance 50%? (only two
> items being tasted). Can I use a t-test to compare the percentages?
> What would I use for the s.d. for by chance percentage? (0?)
Standard comparison would be the formal Z-test for a proportion; see
any elementary stats text. If you have a reasonably large sample size,
use the normal approximation to the binomial; if you have a small
sample, it may be necessary to use the binomial distribution itself,
which is considerably more tedious unless you have comprehensive tables.
Sounds as though you'd wish to test H0: P = .50 vs. H1: P <> .50.
For the Z-test, use the S.D. of a proportion associated with the
hypothesized value (.5): SD = SQRT(pq/n) where p = the hyp. value
(.5 in this case), q = 1-p, n = sample size.
You may want to examine the translation of "chance" into a proportion of
.5. I don't think I know what "by chance" means in the context of your
investigation; certainly .5 is a possible interpretation, but I can
imagine situations where it would be incorrect. (For example, if the two
items are always presented in the same order, and there is a predilection
in your population to identify the first correctly more frequently than
the second, just because they're "first" and "second", the "chance"
hypothesis might be more properly represented by a number > .5. This
problem might be countered if the items were presented in counterbalanced
order.)
Also, if the respondents know beforehand what the two items are
(just not which one is which), the situation is different from one in
which the two items might (so far as the respondents know) come from a
long-ish array of items. Thus if the task were to decide between
"chocolate" and "strawberry", the latter might be mis-identified more
often if "raspberry" were [thought to be] a possible alternative.
-- DFB.
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Donald F. Burrill [EMAIL PROTECTED]
184 Nashua Road, Bedford, NH 03110 603-471-7128
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