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I have questionnaire data from subjects divided into 3 groups, G1, G2 and G3. Subjects had to answer a question, and they had the options A1, A2 or A3 to choose from. The correct answer depended on the group a subject was in: for G1 and G2 the correct answer was A1, and for G3 it was A2. A3 was never the correct answer.

I would like to compute a statistic that would tell me whether this sample, as a whole, were giving correct answers or not.

Had this been a 2x2 contingency table instead of a 3x3, I know that a chi-squared test would have given me the answer. For instance, a non-significant Yates-corrected χ2 would have suggested that subjects are answering by chance. I'm not sure, however, what test I need to use for this 3x3 contingency table. Someone suggested to me that a log-linear analysis or a correspondence analysis might be appropriate, however none of these are included in my stats package (Statistica, by StatSoft/Dell).

Thanks for any help.

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    $\begingroup$ "a non-significant Yates-corrected χ2 would have suggested that subjects are answering by chance" -- well, not quite. Failure to reject doesn't imply the null is actually true. Failing to reject is consistent with the subjects answering at random, but it's also consistent with subjects answering differently than at random, but at a smaller effect size than you were able to detect at your sample size. $\endgroup$ – Glen_b Sep 27 '14 at 15:25
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If all you want to know is whether the group as a whole is giving right answers, then create a new variable "Answer right" that is 1 if G = 1 or 2 and A = 1 or if G = 3 and A = 2. (And deal with missing data appropriately).

Then get the proportion of 1's to that variable.

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  • $\begingroup$ Thanks. Given the nature of the particular questions/answers, this would not really be a good idea to do. Is there any statistic I could apply to the 3x3 contingency table as it is, without re-arranging the data into a smaller-order (2x2) table? $\endgroup$ – z8080 Sep 27 '14 at 14:46
  • $\begingroup$ I think the question to ask of the stats is, actually, best phrased as "Does this sample, on average, have a disproportionate bias towards any one of the three answers?". This would assume the answers are equally likely apriori, which in this would be appropriate. How would that question be tested? $\endgroup$ – z8080 Sep 27 '14 at 14:54
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    $\begingroup$ If you want to answer your question, then what I said does it. You don't need a 2x2 table either, as you are not asking anything about the groups you are asking about the sample as a whole. You could test whether the proportion in my solution is 0.5 using a one way chisquare on the 2x1 table. $\endgroup$ – Peter Flom Sep 27 '14 at 16:45
  • $\begingroup$ In that case, it works out that 1/3 of the sample can tell the correct answer while 2/3 of it can't. Statistica only seems to be able to do chi-square tests for 2x2 tables, not 2x1. Could you point me to any online calculators for 1-sample chi-square tests? What I found required data input as an NxN matrix... $\endgroup$ – z8080 Sep 27 '14 at 18:01
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    $\begingroup$ I don't know of any. You can do it in SAS or R, which is what I use. $\endgroup$ – Peter Flom Sep 28 '14 at 11:18

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