Biostatistics with R/Estimation

Summary of Formulars with R

Formular Number	Name	Formular	Formular with R
6.2.1	Expression of an interval estimate	estimator ± (reliability coefficient)× standard error of the estimator	Example
6.2.2	Interval estimate for $\mu$ when $\sigma$ is known	${\bar {X}}\pm z_{(1-\alpha /2)}\sigma _{\bar {x}}$	Example
6.3.1	t-transformation	$t={\frac {{\bar {x}}-\mu }{s/{\sqrt {n}}}}$	Example
6.3.2	Interval estimate for $\mu$ when $\sigma$ is unknown	${\bar {X}}\pm t_{(1-\alpha /2)}{\frac {s}{\sqrt {n}}}$	Example
6.4.1	Interval estimate for the difference between two population means when $\sigma _{1}$ and $\sigma _{2}$ are known	$({\bar {x}}_{1}-{\bar {x}}_{2})\pm z_{(1-\alpha /2)}{\sqrt {{\frac {\sigma _{1}^{2}}{n_{1}}}+{\frac {\sigma _{2}^{2}}{n_{2}}}}}$	Example
6.4.2	Pooled variance estimate	$s_{p}^{2}={\frac {(n_{1}-1)s_{1}^{2}+(n_{2}-1)s_{2}^{2}}{n_{1}+n_{2}-2}}$	Example
6.4.3	Standard error of estimate	$s_{({\bar {X}}_{1}-{\bar {X}}_{2})}={\sqrt {{\frac {s_{p}^{2}}{n_{1}}}+{\frac {s_{p}^{2}}{n_{1}}}}}$	Example
6.4.4	Interval estimate for the difference between two population means when s 1 is unknown	$({\bar {x}}_{1}-{\bar {x}}_{2})\pm t_{(1-\alpha /2)}{\sqrt {{\frac {s_{p}^{2}}{n_{1}}}+{\frac {s_{p}^{2}}{n_{1}}}}}$	Example
6.4.5	Cochran’s correction for reliability coefficient when variances are not equal	$t'_{(1-\alpha /2)}={\frac {w_{1}t_{1}+w_{2}t_{2}}{w_{1}+w_{2}}}$	Example
6.4.6	Interval estimate using Cochran’s correction for t	$({\bar {x}}_{1}-{\bar {x}}_{2})\pm t'_{(1-\alpha /2)}{\sqrt {{\frac {s_{p}^{2}}{n_{1}}}+{\frac {s_{p}^{2}}{n_{1}}}}}$	Example
6.5.1	Interval estimate for a population proportion	${\displaystyle }$	Example
6.6.1	Interval estimate for the difference between two population proportions	${\displaystyle }$	Example
6.7.1–6.7.3	Sample size determination when sampling with replacement	${\displaystyle }$	Example
6.7.4–6.7.5	Sample size determination when sampling without replacement	${\displaystyle }$	Example
6.8.1	Sample size determination for proportions when sampling with replacement	${\displaystyle }$	Example
6.8.2	Sample size determination for proportions when sampling without replacement	${\displaystyle }$	Example
6.9.1	Interval estimate for s 2	${\displaystyle }$	Example
6.9.2	Interval estimate for s	${\displaystyle }$	Example
6.10.1	Interval estimate for the ratio of two variances	${\displaystyle }$	Example
6.10.2	Relationship among F ratios	${\displaystyle }$	Example
Symbol Key