$$n=\frac{Z_{1-\frac{\alpha}{2}}^2\sigma_d^2}{d^2}$$

$$n=\frac{Z_{1-\frac{\alpha}{2}}^2 \left[P_1(1-P_1)+P_2(1-P_2)\right]}{d^2}$$

$$n=\frac{ \left\{ Z_{1-\frac{\alpha}{2}}\sqrt{2\overline{P}(1-\overline{P})}+Z_{1-\beta}\sqrt{P_1(1-P_1)+P_2(1-P_2)}\right\}^2}{(P_1-P_2)^2}$$

$$n=\frac{(Z_{1-\frac{\alpha}{2}}+Z_{1-\beta})^2}{2(\arcsin\sqrt{P_2}-\arcsin\sqrt{P_1})^2}$$

$$n=\left(\frac{Z_{1-\frac{\alpha}{2}}+Z_{1-\beta}}{ES}\right)^2$$

$$ES=\frac{\mu_1-\mu_0}{\sigma}$$

$$n=\frac{\left\{Z_{1-\frac{\alpha}{2}}\sqrt{P_0(1-P_0)} + Z_{1-\beta}\sqrt{P_a(1-P_a)}\right\}^2}{(P_a - P_0)^2}$$

$$n=2\left(\frac{Z_{1-\frac{\alpha}{2}}+Z_{1-\beta}}{ES}\right)^2$$

$$ES=\frac{\mu_1-\mu_2}{\sigma}$$

$$\sigma=\sqrt{\frac{(n_1-1)s^2_1+(n_2-1)s^2_2}{n_1+n_2-2}}$$

$$n=\left(\frac{Z_{1-\frac{\alpha}{2}}+Z_{1-\beta}}{ES}\right)^2$$

$$ES=\frac{\mu_d}{\sigma_d}$$

$$\sigma=\sqrt{\frac{(n_1-1)s^2_1+(n_2-1)s^2_2}{n_1+n_2-2}}$$

$$n=2\left(\frac{Z_{1-\frac{\alpha}{2}}+Z_{1-\beta}}{ES}\right)^2$$

$$ES=\frac{p_1-p_2}{\sqrt{p(1-p)}}$$

$$p=\frac{p_1+p_2}{2}$$

$$n=\frac{\left\{Z_{1-\frac{\alpha}{2}}(OR+1)+Z_{1-\beta}\sqrt{(OR+1)^2-(OR-1)^2PD}\right\}^2}{(OR-1)^2PD}$$

$$OR=\frac{P10}{P01}$$

$$PD=P10+P01$$

$$n=\frac{Z_{1-\frac{\alpha}{2}}^2(2\sigma^2)}{d^2}$$

$$n=\frac{2\sigma^2(Z_{1-\frac{\alpha}{2}}+Z_{1-\beta})^2}{(\mu_1-\mu_2)^2}$$

σ: được tính bằng công thức

$$\sigma=\sqrt{\frac{\sigma_1^2+\sigma_2^2}{2}}$$

$$n=\frac{Z_{1-\frac{\alpha}{2}}^2}{[log_e(1-\varepsilon)]^2} \left[ \frac{1-P_1}{P_1}+\frac{1-P_2}{P_2} \right]$$

$$n=\frac{ \left\{ Z_{1-\frac{\alpha}{2}}\sqrt{2\overline{P}(1-\overline{P})}+Z_{1-\beta}\sqrt{P_1(1-P_1)+P_2(1-P_2)}\right\}^2}{(P_1-P_2)^2}$$

$$n=\frac{Z_{1-\frac{\alpha}{2}}^2}{[log_e(1-\varepsilon)]^2} \left[ \frac{1}{P_1(1-P_1)}+\frac{1}{P_2(1-P_2)} \right]$$

$$n=\frac{ \left\{ Z_{1-\frac{\alpha}{2}}\sqrt{2P_2(1-P_2)}+Z_{1-\beta}\sqrt{P_1(1-P_1)+P_2(1-P_2)}\right\}^2}{(P_1-P_2)^2}$$

$$n=\frac{Z_{1-\frac{\alpha}{2}}^2P(1-P)N}{d^2(N-1)+Z_{1-\frac{\alpha}{2}}^2P(1-P)}$$

Đang cập nhật

$$n=\frac{Z_{1-\frac{\alpha}{2}}^2Sens(1-Sens)}{d^2*P}$$

$$n=\frac{Z_{1-\frac{\alpha}{2}}^2Spec(1-Spec)}{d^2*(1-P)}$$

$$n=\frac{(HR+1)^2(Z_{1-\frac{\alpha}{2}}+Z_{1-\beta})}{(HR-1)^2(2-p_1-p_2)}$$

$$HR=\frac{ln(p_1)}{ln(p_2)}$$

$$n=\frac{2(Z_{1-\frac{\alpha}{2}}+Z_{1-\beta})}{H^2}$$

$$H=\frac{|\mu_1-\mu_2|-d}{\sigma}$$

$$n=\frac{2(Z_{1-\frac{\alpha}{2}}+Z_{1-\beta})}{H^2}$$

$$H=\frac{|p_1-p_2|-d}{\sqrt{p_1(1-p_1)+p_2(1-p_2)}}$$

$$n=\frac{2(Z_{1-\alpha}+Z_{1-\beta})}{H^2}$$

$$H=\frac{|\mu_1-\mu_2|-d}{\sigma}$$

Công thức giống với công thức tính cỡ mẫu của nghiên cứu tương đương, ngoại trừ việc dùng Z_1-α=1.645 (kiểm định một phía) thay cho dùng Z_1-α/2 = 1.96 trong nghiên cứu tương đương

$$n=\frac{2(Z_{1-\alpha}+Z_{1-\beta})}{H^2}$$

$$H=\frac{|p_1-p_2|-d}{\sqrt{p_1(1-p_1)+p_2(1-p_2)}}$$

Công thức giống với công thức tính cỡ mẫu của nghiên cứu tương đương, ngoại trừ việc dùng Z_1-α=1.645 (kiểm định một phía) thay cho dùng Z_1-α/2 = 1.96 trong nghiên cứu tương đương

$$n=\frac{2\sigma^2[Z_{1-\frac{\alpha}{2}}+Z_{1-\beta}]^2VIF}{\gamma\delta^2}$$

$$VIF=1+(\gamma-1)ICC$$

$$ICC=\frac{\sigma^2_u}{\sigma^2_u+\sigma^2_e}$$