I intend to compare the effect of some operational practices on performance between two countries using the same questionnaire. What is the appropriate statistical test if the objective is to determine whether there are significant differences between the two countries concerning the effect of those practices on performance? Would a sample of 70 respondents from each country be sufficient?
It would primarily depend on how you measure performance (as in would the response variable be dichotomous or ordinal or continuous).
If you are going to compare a dichotomous output between the two countries, then a quick way you can compare the two proportions (proportion of respondents in country x with the outcome compared to the proportion in y) is using a two proportion z-test. You can choose between the two-sided test or the one-sided, depending on how you formulate your hypothesis. However, you will have to make sure the certain conditions are met. http://stattrek.com/hypothesis-test/difference-in-proportions.aspx?Tutorial=AP
If performance is a continuous variable then you can quickly compare the means of the sample across the two countries (mean value of the response in country x with the mean value in country y). Again, you will have to make sure certain conditions are met. http://stattrek.com/hypothesis-test/difference-in-means.aspx?Tutorial=AP
You are not limited to these two tests. It will depend not just on the response variable, but your sample size and other parameters too.
The link below will give you a quick idea of what tests you could possibly use. There are different versions of each test and the appropriate one will depend on if your data meets the test requirements.
http://www.ats.ucla.edu/stat/stata/whatstat/whatstat.htm
Your sample size will depend on your data type, the variability in the population and the difference you expect to see between the two countries. You might also have to trade-off statistical reliability with real-world resource availability when choosing sample size.
The you very much Lijoy Varghese for the valuable information
Various statistical tests, see attached link to 100 Statistical Test book by Kanji Gopal.
SAMPLE SIZE: n1 = 70 and n2 = 7=. Total n = n1 + n2 = 140. Is this enough? It should be. Minimum sample size to verify data distribution and get fair representation of the population generally is n = 30. See attached.
It has been suggested that for multiple regression there should be at least ten sample counts per indicator variable. (Nunnally, (1967, 355). According to Nunnally, in single regression, minimum sample size may be as little as ten counts. Nunally's suggestion is consistent with the Anderson-Darling test for data distribution where the minimum sample size is or at least 6 counts for data distribution test in non-parametric case. (Anderson and Darling, 1954, 765-769). Other writers proposed 30 counts in order for the study to avail itself to the full benefits of the Central Limit Theorem (CLT). (Agresti and Min, 2012).
REFERENCES:
[1] Westland, J. Christopher (2010). "Lower bounds on sample size in structural equation modeling". Electron. Comm. Res. Appl. 9 (6): 476–487.
[2] Nunnally, J. C. (1967). "Psychometric Theory". McGraw-Hill, New York: 355.
[3] Yamane, Taro. 1967. Statistics: An Introductory Analysis, 2nd Ed., New York: Harper and Row.
[4] Stephens, M. A. (1974). "EDF Statistics for Goodness of Fit and Some Comparisons". Journal of the American Statistical Association 69: 730–737.
[5] Anderson, T.W. and Darling, D.A. (1954). "A Test of Goodness-of-Fit". Journal of the American Statistical Association 49: 765–769.
http://fcc-statistics.wikispaces.com/file/view/100+Statistical+Tests.pdf
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