It is not permissible to print this equation sheet and use it as your own on an exam where a personal equation sheet is permitted.
Total error $u_{tot}=\sqrt{\Sigma(u_i)^2}$
Systematic error $u_{sys}=\bar{x}-\mu$
Random error $u_{rand}=t_{\alpha,\>n-1}\frac{s}{\sqrt{n}}$
Instrument error $u_{inst}=\frac{1}{2} \cdot r$, where $r$ is the resolution
Propagated Uncertainty $u_w=\sqrt{\Sigma(\frac{\partial f}{\partial x_i}\cdot u_{x_i})^2}$
Significant Figure Rules
$a=\Sigma n_i \Rarr$ The decimal places of $a$ are the fewest of all $n$
$b=\Pi n_i \Rarr$ The significant figures of $b$ are the fewest of all $n$
Confidence Interval
$\bar{x}-t\frac{s}{\sqrt{n}}<\mu<\bar{x}+t\frac{s}{\sqrt{n}}$
$n\ge30 \Rarr \pm z\frac{s}{\sqrt{n}}$
Two sample t-test
$t=(\bar{x}_1-\bar{x}_2)/(\sqrt{\frac{s_1^2}{n_1}-\frac{s_2^2}{n_2}})$
$DF=\lfloor (\frac{s_1^2}{n_1}+\frac{s_2^2}{n_2})^2/(\frac{s_1^4/n_1^2}{n_1-1}+\frac{s_2^4/n_2^2}{n_2-1}) \rfloor$
Chi-Squared Distribution
$\chi^2=\Sigma\frac{(O_i-E_i)^2}{E_i}$
$\chi_{\alpha,\>n-1}^2>\chi^2 \Rarr \mu_o\ne\mu_e$
$S_{xx}=\Sigma x_i^2-\frac{(\Sigma x_i)^2}{n}$
$S_{xy}=\Sigma x_iy_i-\frac{(\Sigma x_i)(\Sigma y_i)}{n}$
$S_{yy}=\Sigma y_i^2-\frac{(\Sigma y_i)^2}{n}$
Total Squared Variance $S_{_T}^2=\Sigma(y_i-\bar{y})^2$
Explained Squared Variance$S_e^2=\Sigma(\hat{y}_i-\bar{y})^2$
Squared Prediction Error $S_r^2=\Sigma(y_i-\hat{y}_i)^2$
$S_{_T}^2=S_e^2+S_r^2$
Regression Model
$\hat{y}=\beta_0+\beta_1x$
$\>\beta_1=\frac{S_{xy}}{S_{xx}}$
$\beta_0=\bar{y}-\beta_1\bar{x}$
Regression Quality
$r^2=\frac{S_e^2}{S_{_T}^2}$
$r'=\sqrt{1-r^2}$
$R^2=1-\frac{S_r^2}{S_{_T}^2}$
Extras
$se=\sqrt{\frac{\Sigma(y_i-\hat{y})^2}{n-2}},\> se_{\beta_0}=se\sqrt{\frac{1}{n}+\frac{\bar{x}^2}{\Sigma(x_i-\bar{x})^2}},\> se_{\beta_1}=\frac{se}{\sqrt{\Sigma(x_i-\bar{x})^2}}$
$\beta_1=r(\frac{s_y}{s_x}),\>\beta_0=\bar{y}-\beta_1\bar{x}$
$a=\frac{n\cdot\Sigma x_iy_i-\Sigma x_i \Sigma y_i}{n\cdot \Sigma x_i^2-(\Sigma x_i)^2},\>\>b=\frac{\Sigma x_i^2\Sigma y_i -\Sigma x_i\Sigma x_iy_i}{n(\Sigma x_i^2)-(\Sigma x_i)^2}$
Transfer Function $f:(I\rarr O)$
Sensitivity $\eta = \Delta y/\Delta x$
Span/Range $[x_{{min}}, x{_{max}}]$
Resolution $r=(V_{{max}}-V{_{min}})/2^n$
Uncertainty/Accuracy $x_i-\mu$