## Sampsize

Sample size for:

 Sample size for a study comparing percentages

 Proportion 1 % Proportion 2 % Power % (default 90%) Ratio n2/n1 (default 1) Alpha risk % (default 5%) One-sided test One-sample test Cluster sampling design: Intraclass correlation Number of clusters or, (not both) Number of observations

 Example 1: Someone claims that US females are more likely than US males to study French. Our null hypothesis is that the proportion of female French students is 0.5. We wish to compute the sample size that will give us a 80% power to reject the null hypothesis if the true proportion of female French students is 75%. The values 50 and 75 should be entered in the fields "Proportion 1" and "Proportion 2", respectively, 80 in the field "Power", the ratio and alpha risk may be left to their default values. The check box "One-sided test" should be left unchecked, but the check box "One-sample test" should be checked because the null hypothesis is that the percentage of females is 50% in the population. Sampsize returns a sample size of n = 29.  Cluster sampling: The sampled population will be drawn from 8 universities. We know that students within a given university are more alike than students from different universities. We suspect that the intraclass correlation is fairly high (0.1), and wish to correct the above sample size to take into account the sampling design. We check the "Cluster sampling design" check box, enter 0.1 in the "intraclass correlation" field and 8 in the "number of clusters" field. Sampsize returns a corrected sample size of n = 96, with an average of 24 students sampled in each university.   Example 2: We want to conduct a survey on people's opinions of the President's performance. Specifically, we want to determine whether members of the President's party have a different opinion from people with another party affiliation. We estimate that only 25% of members of the President's party will say that the President is doing a poor job, whereas 40% of other parties will rate the President's performance as poor. We compute the sample size for alpha = 5% (two-sided) and power = 90% by entering the values 25 and 40 as "Proportion 1" and "Proportion 2", respectively, 90 for "Power", "Ratio" and "Alpha" risk are left at their default values (1 and 5). We leave both check boxes unchecked. Sampsize returns an estimated sample size of 216 for each groups.

 Power determination: percentages

 Proportion 1 % Proportion 2 % sample size n1 Ratio n2/n1 (default 1) Alpha risk % (default 5%) One-sided test One-sample test

 Example: Following the calculation for the survey on the President's performance, we realize that we can sample only n1 = 300 members of the President's party and a sample of n2 = 150 members of other parties, due to time constraints. We wish to compute the power of our survey, and type 25 in the "Proportion 1" field, 40 in the "Proportion 2" field, 300 in the "Sample size n1" field, 0.5 in the "Ratio n2/n1" field and leave the other fields with their default values. Sampsize returns an estimated power of 87.9%.

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