# Biostatistics with R/Hypothesis Testing

## Summary of Formulars with R

Formular Number Name Formular Formular with R
7.1.1, 7.1.2, 7.2.1 z-transformation (using either ${\displaystyle \mu }$  or ${\displaystyle \mu _{0}}$  ) ${\displaystyle z={\frac {{\bar {x}}-\mu }{\sigma /{\sqrt {n}}}}}$  Example
7.2.2 t-transformation ${\displaystyle t={\frac {{\bar {x}}-\mu _{0}}{s/{\sqrt {n}}}}}$  Example
7.2.3 Test statistic when sampling from a population that is not normally distributed ${\displaystyle z={\frac {{\bar {x}}-\mu _{0}}{s/{\sqrt {n}}}}}$  Example
7.3.1 Test statistic when sampling from normally distributed populations:population variances known ${\displaystyle z={\frac {({\bar {x}}_{1}-{\bar {x}}_{2})-(\mu _{1}-\mu _{2})_{0}}{\sqrt {{\frac {\sigma _{1}^{2}}{n_{1}}}+{\frac {\sigma _{2}^{2}}{n_{2}}}}}}}$  Example
7.3.2 Test statistic when sampling from normally distributed populations:population variances unknown and equal Example Example
7.3.3, 7.3.4 Test statistic when sampling from normally distributed populations: population variances unknown and unequal Example Example
7.3.5 Sampling from populations that are not normally distributed Example Example
7.4.1 Test statistic for paired differences when the population variance is unknown Example Example
7.4.2 Test statistic for paired differences when the population variance is known Example Example
7.5.1 Test statistic for a single population proportion Example Example
7.6.1, 7.6.2 Test statistic for the difference between two population proportions Example Example
7.7.1 Test statistic for a single population variance Example Example
7.8.1 Variance ratio Example Example
7.9.1, 7.9.2 Upper and lower critical values for � x Example Example
7.10.1, 7.10.2 Critical value for determining sample size to control type II errors Example Example
7.10.3 Sample size to control type II errors Example Example
5.5.3 Continuity correction when x > np Example Example
5.6.1 z-transformation for difference between two proportions Example Example
Symbol Key