Аналитика

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

$IQR=Q_3-Q_1$

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

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

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

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

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

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

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

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

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

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

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

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

$\mathrm{MAE}=\frac{1}{n}\sum_{i=1}^{n}|y_i-\hat{y}_i|$

$\mathrm{MSE}=\frac{1}{n}\sum_{i=1}^{n}(y_i-\hat{y}_i)^2$

$\mathrm{RMSE}=\sqrt{\frac{1}{n}\sum_{i=1}^{n}(y_i-\hat{y}_i)^2}$

$\mathrm{MAPE}=\frac{100\%}{n}\sum_{i=1}^{n}\left|\frac{y_i-\hat{y}_i}{y_i}\right|$

$\mathrm{WAPE}=\frac{\sum_{i=1}^{n}|y_i-\hat{y}_i|}{\sum_{i=1}^{n}|y_i|}\cdot100\%$

$\mathrm{SMA}_t=\frac{x_{t-k+1}+x_{t-k+2}+\ldots+x_t}{k}$

$\hat{y}_{t+1}=\alpha y_t+(1-\alpha)\hat{y}_t$

$\hat{\beta}_1=\frac{\sum (x_i-\bar{x})(y_i-\bar{y})}{\sum (x_i-\bar{x})^2},\quad \hat{\beta}_0=\bar{y}-\hat{\beta}_1\bar{x}$

$R^2=1-\frac{SS_{res}}{SS_{tot}}$

$s=\sqrt{\frac{SS_{res}}{n-p}}$

$t=\frac{\hat{\beta}_j-\beta_{j,0}}{SE(\hat{\beta}_j)}$

$p=\frac{1}{1+e^{-z}},\quad z=\beta_0+\beta_1x_1+\ldots+\beta_kx_k}$

$\mathrm{Accuracy}=\frac{TP+TN}{TP+TN+FP+FN}$

$\mathrm{Precision}=\frac{TP}{TP+FP}$

$\mathrm{Recall}=\frac{TP}{TP+FN}$

$F_1=\frac{2\cdot Precision\cdot Recall}{Precision+Recall}$

$\mathrm{Specificity}=\frac{TN}{TN+FP}$

$\mathrm{AUC}=\frac{N_{concordant}+0.5N_{tied}}{N_{positive}N_{negative}}$

$\mathrm{Lift}=\frac{\text{response rate in selected group}}{\text{overall response rate}}$

$N=TP+TN+FP+FN$

$n=\frac{z^2p(1-p)}{E^2}$

$n=\frac{2(z_\alpha+z_\beta)^2p(1-p)}{\Delta^2}$

$z=\frac{p_1-p_2}{\sqrt{p(1-p)(1/n_1+1/n_2)}}$

$t=\frac{\bar x_1-\bar x_2}{s_p\sqrt{1/n_1+1/n_2}}$

$t=\frac{\bar x_1-\bar x_2}{\sqrt{s_1^2/n_1+s_2^2/n_2}}$

$\chi^2=\sum\frac{(O-E)^2}{E}$

$\hat p\pm z\sqrt{\frac{\hat p(1-\hat p)}{n}}$

$(p_1-p_2)\pm z\sqrt{\frac{p_1(1-p_1)}{n_1}+\frac{p_2(1-p_2)}{n_2}}$

$d=\frac{\bar x_1-\bar x_2}{s_p}$

$V=\sqrt{\frac{\chi^2}{n(k-1)}}$

$F_1=\frac{2PR}{P+R}$