# 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 ${\displaystyle \mu }$  when ${\displaystyle \sigma }$  is known ${\displaystyle {\bar {X}}\pm z_{(1-\alpha /2)}\sigma _{\bar {x}}}$  Example
6.3.1 t-transformation ${\displaystyle t={\frac {{\bar {x}}-\mu }{s/{\sqrt {n}}}}}$  Example
6.3.2 Interval estimate for ${\displaystyle \mu }$  when ${\displaystyle \sigma }$  is unknown ${\displaystyle {\bar {X}}\pm t_{(1-\alpha /2)}{\frac {s}{\sqrt {n}}}}$  Example
6.4.1 Interval estimate for the difference between two population means when ${\displaystyle \sigma _{1}}$  and ${\displaystyle \sigma _{2}}$  are known ${\displaystyle ({\bar {x}}_{1}-{\bar {x}}_{2})\pm z_{(1-\alpha /2)}{\sqrt {{\frac {\sigma _{1}^{2}}{n_{1}}}+{\frac {\sigma _{2}^{2}}{n_{2}}}}}}$  Example
6.4.2 Pooled variance estimate ${\displaystyle s_{p}^{2}={\frac {(n_{1}-1)s_{1}^{2}+(n_{2}-1)s_{2}^{2}}{n_{1}+n_{2}-2}}}$  Example
6.4.3 Standard error of estimate ${\displaystyle s_{({\bar {X}}_{1}-{\bar {X}}_{2})}={\sqrt {{\frac {s_{p}^{2}}{n_{1}}}+{\frac {s_{p}^{2}}{n_{1}}}}}}$  Example
6.4.4 Interval estimate for the difference between two population means when s 1 is unknown ${\displaystyle ({\bar {x}}_{1}-{\bar {x}}_{2})\pm t_{(1-\alpha /2)}{\sqrt {{\frac {s_{p}^{2}}{n_{1}}}+{\frac {s_{p}^{2}}{n_{1}}}}}}$  Example
6.4.5 Cochran’s correction for reliability coefficient when variances are not equal ${\displaystyle t'_{(1-\alpha /2)}={\frac {w_{1}t_{1}+w_{2}t_{2}}{w_{1}+w_{2}}}}$  Example
6.4.6 Interval estimate using Cochran’s correction for t ${\displaystyle ({\bar {x}}_{1}-{\bar {x}}_{2})\pm t'_{(1-\alpha /2)}{\sqrt {{\frac {s_{p}^{2}}{n_{1}}}+{\frac {s_{p}^{2}}{n_{1}}}}}}$  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