In my thesis I was solving sample size estimations problems in different statistical analysis with different conditions, witch had to be fulfilled. I demonstrated how to dissolve equation for sample size from confidence interval or significance level alpha, from power of test, when to use approximation and iteration, how to estimate sample size from generated table and with root finding. I will show derived formulas from asymptotic normal distribution, exact normal distribution, skewed distribution and $\chi^2$-distribution for sample proportion, sample average, Pearson correlation coefficient, odds ration and sample variance. I've discovered that for normal distributed test statistics sample size formula is dissolved directly from confidence interval and power of test, while for non-normal distributed test statistics we use approximations and iteration or we determined sample size based on generated table and with root finding.
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