Cochran's sample size formula

cochran.md

Steps for sample size (Cochran's formulas):

I. Cochran's sample size formula for categorical data for an alpha level a priori at .05 (error of 5%) = n0=(t)2*(p)(q)/(d)2=384

Where: n0 is the sample size, t is the value for the selected alpha level, e.g. 1.96 for (0.25 in each tail) a 95 percent confidence level. p is the estimated proportion of an attribute that is present in the population. q is 1-p. (p)(q) are the estimate of variance. d is the acceptable margin of error for proportion being estimated, so the confidence interval, in decimals.

II. Cochran’s correction formula, when pop. <50.000 is: n1 = 384/(1+384/528)= 222

Where: population size =528 Where n0 = required return sample size according to Cochran’s formula= 384 Where n1 = required return sample size because sample > 5% of population

Reference: Cochran, W. G. (1977). Sampling techniques (3rd ed.). New York: John Wiley & Sons.

How do you calculate a sample size using Cochran's formula, where the larger beneficiary population is 180,000 people? Kindly take me step by step, including:

1. identifying the symbols in the formula with actual figures
2. Work out the finer details of how the sample size is arrived at.
3. No assumptions should be made about my knowledge of statistical methods.

Thank you

I would like to learn sample size calculation for complex baseline study and evaluation
Thanks
Yeshewamebrat

how can I find d