I can find the reference of Hypothesis Test for Difference Between Proportions (LARGE SAMPLE) in many text books. But the sample I have is quite small. Could anyone please suggest the reference document explaining how to do Hypothesis Test for Difference Between Proportions (SMALL SAMPLE)?Thank you very much for your help.Kind Regards,Becool

In a math statistics course there exist sections related to small sample testing.

You should set up the problem as a 2 x 2 contingency table, and then apply the appropriate procedure for small sample contingency table testing, Fisher's Exact Test. The above link gives a made up example: 3 of 40 women questioned say they have an e-mail address, while 15 of 60 men have an e-mail address. Is there any evidence that these proportions are statistically different? The contingency table would be:..........................female malee-mail address ........3......15no e-mail address..37......45 The two-tailed p-value for this example is 0.033, so the difference is significant at the 5% level.

From contingency table you can build ROC curves ... for small sample size, a colleagueused a Bayesian approach (large sample size correspond to frequentist statistics)Receiver Operating Characteristic Analysis for Intelligent Medical Systems—A New Approach for Finding Confidence Intervals Julian Tilbury, Peter Van-Eetvelt, Jon Garibaldi, John Curnow, and Emmanuel C. IfeachorIEEE Transactions Biomedical Engineering, Vol. 47, No. 7, July 2000, pp. 952-963.Evaluation of Intelligent Medical SystemsJulian Tilbury (PhD Thesis University of Plymouth, 2002)PDFs are available at http://www.tech.plymouth.ac.uk/spmc/sta ... lbury.html

x square and t statistic focus on Small sample test.why not construct one from them?