Biostatistics with R/Some Important Sampling Distributions

Summary of Formulars with R

Formular Number	Name	Formular	Formular with R
5.3.1	z-transformation for sample mean	$Z={\frac {{\bar {X}}-\mu _{x}}{\sigma /{\sqrt {n}}}}$	Example
5.4.1	z-transformation for difference between two means	$Z={\frac {({\bar {X}}_{1}-{\bar {X}}_{2})-(\mu _{1}-\mu _{2})}{\sqrt {{\frac {\sigma _{1}^{2}}{n_{1}}}+{\frac {\sigma _{2}^{2}}{n_{2}}}}}}$	Example
5.5.1	z-transformation for sample proportion	$Z={\frac {{\bar {p}}-p}{\sqrt {\frac {p(1-p)}{n}}}}$	Example
5.5.2	Continuity correction when x < np	$Z_{c}={\frac {{\frac {x+.5}{n}}-p}{\sqrt {pq/n}}}$	Example
5.5.3	Continuity correction when x > np	$Z_{c}={\frac {{\frac {X+.5}{n}}-p}{\sqrt {pq/n}}}$	Example
5.6.1	z-transformation for difference between two proportions	${\displaystyle }$	Example
Symbol Key