Useful Summary Tables

Response	Explanatory	Numerical_Quantity	Parameter	Statistic	Function
quantitative	-	mean	$μ$	$\bar{x}$	t_test()
categorical	-	proportion	$p$	$\hat{p}$	prop_test()
quantitative	categorical	difference in means	$μ_{1} - μ_{2}$	${\bar{x}}_{1} - {\bar{x}}_{2}$	t_test()
categorical	categorical	difference in proportions	$p_{1} - p_{2}$	${\hat{p}}_{1} - {\hat{p}}_{2}$	prop_test()
quantitative	quantitative	correlation	$ρ$	$r$	cor.test()

Response	Explanatory	Numerical_Quantity	Test_Statistic	Distribution	Assumptions
quantitative	-	mean	$\frac{\bar{x} - μ_{o}}{s / \sqrt{n}}$	$t (d f = n - 1)$	$n \geq 30$ or data are normal
categorical	-	proportion	$\frac{\hat{p} - p_{o}}{\sqrt{\frac{\hat{p} (1 - \hat{p})}{n}}}$	$N (0, 1)$	Ten successes, Ten failures
quantitative	categorical	difference in means	$\frac{{\bar{x}}_{1} - {\bar{x}}_{2} - 0}{\sqrt{\frac{s_{1}^{2}}{n_{1}} + \frac{s_{2}^{2}}{n_{2}}}}$	$t (d f = min (n_{1}, n_{2}) - 1)$	$n_{1}, n_{2} \geq 30$ or data are normal
categorical	categorical	difference in proportions	$\frac{{\hat{p}}_{1} - {\hat{p}}_{2} - 0}{\sqrt{\frac{\hat{p} (1 - \hat{p})}{n_{1}} + \frac{\hat{p} (1 - \hat{p})}{n_{2}}}}$	$N (0, 1)$	Ten successes, Ten failures in each category
quantitative	quantitative	correlation	$\frac{r - 0}{\sqrt{\frac{1 - r^{2}}{n - 2}}}$	$t (d f = n - 2)$	$n \geq 30$

Response	Explanatory	Numerical_Quantity	Confidence_Interval	Distribution	Assumptions
quantitative	-	mean	$\bar{x} \pm t^{*} s / \sqrt{n}$	$t (d f = n - 1)$	$n \geq 30$ or data are normal
categorical	-	proportion	$\hat{p} \pm z^{*} \sqrt{\frac{\hat{p} (1 - \hat{p})}{n}}$	$N (0, 1)$	Ten successes, Ten failures
quantitative	categorical	difference in means	${\bar{x}}_{1} - {\bar{x}}_{2} \pm t^{*} \sqrt{\frac{s_{1}^{2}}{n_{1}} + \frac{s_{2}^{2}}{n_{2}}}$	$t (d f = min (n_{1}, n_{2}) - 1)$	$n_{1}, n_{2} \geq 30$ or data are normal
categorical	categorical	difference in proportions	${\hat{p}}_{1} - {\hat{p}}_{2} \pm z^{*} \sqrt{\frac{{\hat{p}}_{1} (1 - {\hat{p}}_{1})}{n_{1}} + \frac{{\hat{p}}_{2} (1 - {\hat{p}}_{2})}{n_{2}}}$	$N (0, 1)$	Ten successes, Ten failures in each category
quantitative	quantitative	correlation	$r \pm t^{*} \sqrt{\frac{1 - r^{2}}{n - 2}}$	$t (d f = n - 2)$	$n \geq 30$