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 $\mu$ or $\mu _{0}$ )	$z={\frac {{\bar {x}}-\mu }{\sigma /{\sqrt {n}}}}$	Example
7.2.2	t-transformation	$t={\frac {{\bar {x}}-\mu _{0}}{s/{\sqrt {n}}}}$	Example
7.2.3	Test statistic when sampling from a population that is not normally distributed	$z={\frac {{\bar {x}}-\mu _{0}}{s/{\sqrt {n}}}}$	Example
7.3.1	Test statistic when sampling from normally distributed populations:population variances known	$z={\frac {({\bar {x}}_{1}-{\bar {x}}_{2})-(\mu _{1}-\mu _{2})_{0}}{\sqrt {{\frac {\sigma _{1}^{2}}{n_{1}}}+{\frac {\sigma _{2}^{2}}{n_{2}}}}}}$	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