# 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 Example
6.6.1 Interval estimate for the difference between two population proportions Example
6.7.1–6.7.3 Sample size determination when sampling with replacement Example
6.7.4–6.7.5 Sample size determination when sampling without replacement Example
6.8.1 Sample size determination for proportions when sampling with replacement Example
6.8.2 Sample size determination for proportions when sampling without replacement Example
6.9.1 Interval estimate for s 2 Example
6.9.2 Interval estimate for s Example
6.10.1 Interval estimate for the ratio of two variances Example
6.10.2 Relationship among F ratios Example
Symbol Key