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The Formula of Random Sampling (N-n/N-(n-1)). Here P is a probability, n is the sample size, and N represents the population. Now if one cancels 1-(N-n/n), it will provide P = n/N. Moreover, the chance of a sample getting selected more than once is needed: P = 1-(1-(1/N)) n.
The higher the statistical power of a test, the lower the risk of making a Type II error. Power is usually set at 80%. This means that if there are true effects to be found in 100 different studies with 80% power, only 80 out of 100 statistical tests will actually detect them.
The sample size was determined by Fisher's formula of; N = (Z 2 x p(1-p))/d 2 .
If the goal is 80% power to distinguish between hypothesized proportions p1 and p2 with a study of size n, equally divided between the two groups, a conservative sample size is n = [2.8/(p1?p2)]2 or, more precisely, n = 2[p1(1?p1) + p2(1?p2)] · [2.8/(p1?p2)]2.
Cochran's (1977) formula uses two key factors: (1) the risk the researcher is willing to accept in the study, commonly called the margin of error, or the error the researcher is willing to accept, and (2) the alpha level, the level of acceptable risk the researcher is willing to accept that the true margin Page 3 ...