The above sample size calculator provides you with the recommended number of samples required to detect a difference between two proportions. Sample Size Calculation for Comparing Proportions. Note: A reference to this formula can be found in the following paper (pages 3-4 section 3.1 Test for Equality). for a power of 80%, β is 0.2 and the critical value is 0.84) and p 1 and p 2 are the expected sample proportions of the two groups. for a confidence level of 95%, α is 0.05 and the critical value is 1.96), Z β is the critical value of the Normal distribution at β (e.g. Where Z α/2 is the critical value of the Normal distribution at α/2 (e.g. This calculator uses the following formula for the sample size n: In this case you would need to compare 248 customers who have received the promotional material and 248 who have not to detect a difference of this size (given a 95% confidence level and 80% power). Currently 15% of customers buy this product and you would like to see uptake increase to 25% in order for the promotion to be cost effective. The study of the power of these statistical tests is accomplished by means of Monte Carlo method.Before implementing a new marketing promotion for a product stocked in a supermarket, you would like to ensure that the promotion results in a significant increase in the number of customers who buy the product. We have also studied two-sample Wilcoxon test, the criterion of van der Waerden, Smirnov two-sample two-sided test, sign test, runs test (Wolfowitz) and calculated the real significance levels of the criteria for nominal significance level of 0.05. In the article, we have discussed the difference between nominal and real significance levels on the example of nonparametric tests for the homogeneity of two independent samples. Under the real significance level we refer to the highest possible significance level of discrete statistics, not exceeding a given nominal significance level (ie, the transition to the next highest possible value corresponding discrete statistical significance level is greater than a predetermined nominal). However, for the statistics with discrete distribution functions, which, in particular, include all nonparametric statistical tests, the real significance levels may be different from the nominal, differ at times. As such, typically researcher uses the values of three numbers 0.01, 0.05, 0.1, to which may be added a few levels: 0.001, 0.005, 0.02, and others. In the statistical hypothesis testing, critical values often point to a priori fixed (nominal) significance levels. The main conclusion: the use of nominal significance levels instead of real significance levels for discrete statistics is inadmissible for small sample sizes The study of the power of these statistical tests is accomplished by means of Monte Carlo method.
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