Sample Size and Power Calculators

Sample size to estimate mean Use this calculator to find the minimum sample size required to estimate population mean $\mu$. Sample Size to estimate mean Confidence Level ($1-\alpha$) Select 90% 95% 98% 99% Standard Deviation ($\sigma$) Margin of Error ($E$) Calculate Results Z value: Required Sample Size : ($n$) Sample size required to estimate mean The minimum sample size required to estimate the population mean $\mu$ is $$ \begin{aligned} n &= \bigg(\frac{z*\sigma}{E}\bigg)^2 \end{aligned} $$

Sample size required to estimate means Sample Size to estimate means Confidence Level ($1-\alpha$) Select 90% 95% 98% 99% Standard Deviation ($\sigma$) Margin of Error ($E$) Calculate Results Z value: Required Sample Size : ($n$) Sample size required to estimate difference between means of independent samples The formula to estimate the sample size required to estimate the mean of two independent samples is $$ n_i =2\bigg(\frac{z\sigma}{E}\bigg)^2; i=1,2 $$ where $n_i$ is the sample size for $i^{th}$ group, $z$ is the $Z_{\alpha/2}$, $\sigma$ is the population standard deviation and $E$ is the margin of error.

Sample size required to estimate means dependent samples Sample Size to estimate means(paired) Confidence Level ($1-\alpha$) Select 90% 95% 98% 99% Standard Deviation ($\sigma_d$) Margin of Error ($E$) Calculate Results Z value: Required Sample Size : ($n$) Sample size required to estimate difference between means of dependent samples The formula to estimate the sample size required to estimate the mean of two dependent samples is $$ n =\bigg(\frac{z\sigma_d}{E}\bigg)^2 $$ where

Sample size to estimate proportion Use this calculator to find the minimum sample size required to estimate proportion $p$. Sample size to estimate proportion Confidence Level ($1-\alpha$) Select 90% 95% 98% 99% Proportion of success ($p$) Margin of Error ($E$) Calculate Results Z value: Required Sample Size : ($n$) Sample size required to estimate proportion The minimum sample size required to estimate the proportion is $$ \begin{aligned} n &= p(1-p)\bigg(\frac{z}{E}\bigg)^2 \end{aligned} $$

Sample size to estimate proportions Use this calculator to find the minimum sample size required to estimate proportions $p_1-p_2$. Sample size to estimate proportions Confidence Level ($1-\alpha$) Select 90% 95% 98% 99% Proportion of success ($p_1$) Proportion of success ($p_2$) Margin of Error ($E$) Calculate Results Z value: Required Sample Size : ($n$) Sample size required to estimate proportions The minimum sample size required to estimate the proportions $p_1-p_2$ is

Sample size to test mean Use this calculator to find the minimum sample size required to test mean $\mu$. Sample Size to test mean Confidence Level ($1-\alpha$) Select 90% 95% 98% 99% Power ($1-\beta$) Select 80% 85% 90% 95% 98% 99% Mean under H0 : ($\mu_0$) Mean under H1 : ($\mu_1$) Standard Deviation ($\sigma$) Calculate Results Effect Size ($ES$) Z value: $Z_{1-\alpha/2}$ Z value: $Z_{1-\beta}$ Required Sample Size : ($n$) Sample size to test mean The $ES$ is defined as $$ ES=\frac{|\mu_1-\mu_0|}{\sigma} $$

Sample size to test means $\mu_1-\mu_2$ Use this calculator to find the minimum sample size required to test mean $\mu_1-\mu_2$. Sample Size to test means Confidence Level ($1-\alpha$) Select 90% 95% 98% 99% Power ($1-\beta$) Select 80% 85% 90% 95% 98% 99% First group mean : ($\mu_1$) Second group mean : ($\mu_2$) Standard Deviation : ($\sigma$) Calculate Results Effect Size ($ES$) Z value: $Z_{1-\alpha/2}$ Z value: $Z_{1-\beta}$ Required Sample Size : ($n$) Sample size to test means $\mu_1-\mu_2$ The $ES$ is defined as $$ ES=\frac{|\mu_1-\mu_2|}{\sigma} $$ where

Sample size to test mean difference $\mu_d$ in dependent samples Use this calculator to find the minimum sample size required to test mean difference $\mu_d$. Sample Size to test means (paired) Confidence Level ($1-\alpha$) Select 90% 95% 98% 99% Power ($1-\beta$) Select 80% 85% 90% 95% 98% 99% Mean of difference: ($\mu_d$) Standard Deviation : ($\sigma_d$) Calculate Results Effect Size ($ES$) Z value: $Z_{1-\alpha/2}$ Z value: $Z_{1-\beta}$ Required Sample Size : ($n$) Sample size to test means of dependent samples The $ES$ is defined as $$ ES=\frac{|\mu_d|}{\sigma_d} $$ where

Sample size required to test proportion Use this calculator to find the minimum sample size required to estimate proportion $p$. Sample Size to test proportion Confidence Level ($1-\alpha$) Select 90% 95% 98% 99% Power ($1-\beta$) Select 80% 85% 90% 95% 98% 99% Proportion under H0 : ($p_0$) Proportion under H1 : ($p_1$) Calculate Results Effect Size ($ES$) Z value: $Z_{1-\alpha/2}$ Z value: $Z_{1-\beta}$ Required Sample Size : ($n$) Sample size required to estimate proportion The minimum sample size required to estimate the proportion is $$ \begin{aligned} n &\approx \bigg(\frac{Z_{1-\alpha/2}+Z_{1-\beta}}{ES}\bigg)^2 \end{aligned} $$

Sample size to test proportions Use this calculator to find the minimum sample size required to test the proportions $p_1-p_2$. Sample Size to test proportion Confidence Level ($1-\alpha$) Select 90% 95% 98% 99% Power ($1-\beta$) Select 80% 85% 90% 95% 98% 99% First group proportion: ($p_1$) Second group proportion: ($p_2$) Calculate Results Effect Size ($ES$) Z value: $Z_{1-\alpha/2}$ Z value: $Z_{1-\beta}$ Required Sample Size : ($n$) Sample size to test proportions The formula for determining the sample size required in each group t ensure that the test has a specified power is