Аналитика

$\hat{p}=\frac{X}{n}$

$\text{uplift}_{\%}=\frac{\hat p_B-\hat p_A}{\hat p_A}\cdot 100\%$

$\Delta = \hat p_B-\hat p_A$

$SE(\hat p)=\sqrt{\frac{\hat p(1-\hat p)}{n}}$

$z = \frac{\hat p_B-\hat p_A}{SE_{\Delta}}$

$p \approx 2\,(1-\Phi(|z|)),\; \text{а без калькулятора: }|z|\approx1{,}64\Rightarrow p\approx0{,}10,\;1{,}96\Rightarrow0{,}05,\;2{,}58\Rightarrow0{,}01$

$(\hat p_B-\hat p_A)\pm z_{1-\alpha/2}\cdot SE_{\Delta}$

$n \approx \frac{(z_{1-\alpha/2}+z_{1-\beta})^2\left[p_A(1-p_A)+p_B(1-p_B)\right]}{MDE^2},\; n_A=n_B=n$

$MDE = (z_{1-\alpha/2}+z_{1-\beta})\sqrt{\frac{\hat p_A(1-\hat p_A)}{n_A}+\frac{\hat p_B(1-\hat p_B)}{n_B}}$

$\text{Power} \approx 1-\Phi\left(z_{1-\alpha/2}-\frac{|\Delta|}{SE_{\Delta}}\right),\;\beta\approx\Phi\left(z_{1-\alpha/2}-\frac{|\Delta|}{SE_{\Delta}}\right)$

$\bar{x}=\frac{x_1+x_2+\dots+x_n}{n}$

$Me=x_{(\frac{n+1}{2})}\quad\text{для нечетного }n$

$Mo=\text{значение с максимальной частотой}$

$R=x_{max}-x_{min}$

$s^2=\frac{\sum_{i=1}^{n}(x_i-\bar{x})^2}{n-1}$

$s=\sqrt{\frac{\sum_{i=1}^{n}(x_i-\bar{x})^2}{n-1}}$

$IQR=Q_3-Q_1$

$x<Q_1-1.5\cdot IQR\quad\text{или}\quad x>Q_3+1.5\cdot IQR$

$CV=\frac{s}{\bar{x}}\cdot100\%$

$z=\frac{x-\bar{x}}{s}$

$\text{DAU/MAU} = \frac{\text{DAU}}{\text{MAU}}\cdot 100\%$

$\text{Retention} = \frac{N_{\text{active at end}}}{N_{\text{cohort start}}}\cdot 100\%$

$\text{Churn} = \frac{N_{\text{churned}}}{N_{\text{period start}}}\cdot 100\%$

$\text{ARPU} = \frac{R}{\text{MAU}}$

$\text{ARPPU} = \frac{R}{N_{\text{paying}}}$

$\text{LTV} \approx \text{ARPU} \cdot \text{Gross Margin} \cdot L$

$\text{CAC} = \frac{C_{\text{marketing}} + C_{\text{sales}}}{N_{\text{new customers}}}$

$\text{CR}_{i\to i+1}=\frac{U_{i+1}}{U_i}\cdot100\%$

$\text{Activation Rate} = \frac{N_{\text{activated}}}{N_{\text{registered}}}\cdot100\%$