Cheat sheet with formulae

Here’s a link to responses to our example class survey that has formulae for doing all of these things in Sheets. You can simply copy/paste my formulae, making necessary changes as you go.

\[\begin{split} \begin{array}{|c|c|c|} \hline \textbf{purpose} & \textbf{name of statistic} & \textbf{formula} \\ \hline \text{estimate central tendency of quantitative variable} & \text{sample mean, } \bar{y} & \ \frac{1}{n}\sum_{i=1}^n y_i \\ \hline \text{true central tendency of quantitative variable}, y & \text{population mean, } \mu_y & \ \mathbb{E}(Y) \hspace{0.1cm} \text{(don't sweat details)} \\ \hline \text{estimate central tendency of binary variable} & \text{mean of binary variable, } \bar{b} \ & \frac{1}{n}\sum_{i=1}^n b_i \\ \hline \text{estimate spread of quant. var.} & \text{sample variance and sample standard deviation: } \ s^2; s \ & s^2 = \frac{\sum_{i=1}^n (y_i - \bar{y})^2}{n-1}; \ s = \sqrt{\frac{\sum_{i=1}^n (y_i - \bar{y})^2}{n-1}} \\ \hline \text{true spread of quant. var.} & \text{variance and standard deviation: } \sigma^2; \sigma \ & \text{don't sweat details, but } \sigma_Y^2 = \mathbb{E}[(Y-\mu_Y)^2] \\ \hline \text{estimate spread of sampling distribution for sample mean} & \text{standard error, SE} \ & \frac{s}{\sqrt{n}} \\ \hline \text{calculate "how weird" our sample mean is given null, } H_0 & \ \text{step 1: test statistic, } t & t = \frac{\bar{y} - \mu_0}{\frac{s}{\sqrt{n}}} \\ \hline \text{calculate "how weird" our sample mean is given null, } H_0 & \ \text{step 2: probability of a test statistic weirder than ours, } \mathbb{P}(|T| > |t|) \ & \text{software needed, any can do it} \\ \hline \text{calculate plausible band of values for the true mean, } \mu_0 & \ \text{step 1: find number of SEs enclosing } C \text{ AUC} \ & \text{use software. often, } t_{95} \approx +/- 1.96 \\ \hline \text{calculate plausible band of values for the true mean, } \mu_0 & \ \text{step 2: craft confidence interval} & \bar{y} +/- t_{C} {\frac{s}{\sqrt{n}}} \\ \hline \end{array} \end{split}\]