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

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