Statistical test

Proportions

comparisons		Independent samples (Unpaired in case of two)	Dependent samples (Paired in case of two)
Propotions	2	Z test [math]\displaystyle{ \begin{align} z & = \frac{p_1-p_2}{SE_{pooled(p_1-p_2)}} \\ & = \frac{p_1-p_2}{\sqrt{\frac{\bar{p}(1-\bar{p})}{n_1}+\frac{\bar{p}(1-\bar{p})}{n_2}}} \end{align} }[/math]
	3 or more	Enough large sample [math]\displaystyle{ \chi^2 }[/math] test [math]\displaystyle{ \chi^2 = \sum \frac{(O - E)^2}{E} }[/math] [math]\displaystyle{ O }[/math] = observed values [math]\displaystyle{ E }[/math] = expected values	McNemar's [math]\displaystyle{ \chi^2 }[/math] test [math]\displaystyle{ \begin{align} & McNemar's\ \chi^2 \\ & = \frac{(n_1-n_2)^2}{n_1+n_2} \end{align} }[/math] [math]\displaystyle{ n_i }[/math] = number of observations in discordant pair
		Testing linear association [math]\displaystyle{ \chi^2 }[/math] trend test [math]\displaystyle{ \begin{align} & \chi^2 trend \\ & = \frac{(\bar{x_1}-\bar{x_2})^2}{s^2(\frac{1}{n_1}+\frac{1}{n_2})} \\ & s = \sqrt{\sum \frac{(x_i-\bar{x_i})^2}{n-1}} \end{align} }[/math] [math]\displaystyle{ x_i }[/math] = weighted values [math]\displaystyle{ n_i }[/math] = number of observations
		≥1 cell expected value <5 Fisher's exact test very rare in real researches

Means

comparisons		Parametric i.e., normally distributed		Non-parametric i.e., not normally distributed
		Independent samples (Unpaired in case of two)	Dependent samples (Paired in case of two)	Independent samples (Unpaired in case of two)	Dependent samples (Paired in case of two)
Means	2	Enough large sample Z test [math]\displaystyle{ \begin{align} z & = \frac{\bar{x_1}-\bar{x_2}}{SE_{(\bar{x_1}-\bar{x_2})}} \\ & = \frac{\bar{x_1}-\bar{x_2}}{\sqrt{\frac{s_1^2}{n_1}+\frac{s_2^2}{n_2}}} \end{align} }[/math] Small sample size <30 in a group Student's t test [math]\displaystyle{ \begin{align} t & = \frac{\bar{x_1}-\bar{x_2}}{SE_{(\bar{x_1}-\bar{x_2})}} \\ & = \frac{\bar{x_1}-\bar{x_2}}{\sqrt{\frac{(n_1-1)s_1^2+(n_2-1)s_2^2}{(n_1-1)+(n_2-1)}}\sqrt{\frac{1}{n_1}+\frac{1}{n_2}}} \end{align} }[/math] Large discrepancy in SDs between groups Bootstrap Non-parametric Fisher-Behrens Welch	Paired Student's t test [math]\displaystyle{ \begin{align} paired\ t & = \frac{\bar{d}}{SE_d} \\ & = \frac{\bar{d}}{\frac{s}{\sqrt{n}}} \\ \end{align} }[/math] where [math]\displaystyle{ \bar{d} }[/math] is the mean of differences of paired observations	Wilcoxon rank sum test AKA Mann-Whitney test	Wilcoxon signed rank test here 'signed' means 'take into account signs of differences of paired data'
	3 or more	ANOVA	Linear-regression model Repeated measures ANOVA	Kruskall-Wallis test	*needs try to transform data into parametric (e.g., logarithmic), or other considerations