Re: Comparing percent correct to correct by chance
Donald Burrill [EMAIL PROTECTED] wrote in message [EMAIL PROTECTED]">news:[EMAIL PROTECTED]... 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. I'd kind of expect them to want this one to be one tailed - it would seem strange to be interested in the circumstance where tastebuds do worse than chance (well, it'd be kinky and fun, but would it change your action from no difference? I can conceive of it, but I'd bet not.) Glen = Instructions for joining and leaving this list and remarks about the problem of INAPPROPRIATE MESSAGES are available at http://jse.stat.ncsu.edu/ =
Re: Comparing percent correct to correct by chance
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. Donald F. Burrill [EMAIL PROTECTED] 184 Nashua Road, Bedford, NH 03110 603-471-7128 = Instructions for joining and leaving this list and remarks about the problem of INAPPROPRIATE MESSAGES are available at http://jse.stat.ncsu.edu/ =
Comparing percent correct to correct by chance
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?) Melady - Original Message - From: Donald Burrill [EMAIL PROTECTED] To: Rich Ulrich [EMAIL PROTECTED] Cc: Shizuhiko Nishisato [EMAIL PROTECTED]; [EMAIL PROTECTED] Sent: Wednesday, October 24, 2001 8:20 PM Subject: Re: Graphics CORRESPONDENCE ANALYSIS On Wed, 24 Oct 2001, Rich Ulrich wrote in part: It has been my impression (from google) that CA is more popular in European journals than in the US, so there might be better sites out there in a language I don't read. (CA = correspondence analysis, ou en francais analyse des correspondances) In Canada, and to a lesser extent in the U.S., correspondence analysis is also known under the name dual scaling. For references consult Professor Emeritus Shizuhiko Nishisato of the University of Toronto: Shizuhiko Nishisato [EMAIL PROTECTED]. -- Don. Donald F. Burrill [EMAIL PROTECTED] 184 Nashua Road, Bedford, NH 03110 603-471-7128 = Instructions for joining and leaving this list and remarks about the problem of INAPPROPRIATE MESSAGES are available at http://jse.stat.ncsu.edu/ = = Instructions for joining and leaving this list and remarks about the problem of INAPPROPRIATE MESSAGES are available at http://jse.stat.ncsu.edu/ =
