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	$\overline{X}\pm z_{(1-\alpha /2)}{\sigma }_{\overline{x}}$	Example
6.3.1	t-transformation	$t=\frac{\overline{x}-\mu }{s/\sqrt{n}}$	Example
6.3.2	Interval estimate for $\mu$ when $\sigma$ is unknown	$\overline{X}\pm t_{(1-\alpha /2)}\frac{s}{\sqrt{n}}$	Example
6.4.1	Interval estimate for the difference between two population means when ${\sigma }_1$ and ${\sigma }_2$ are known	$({\overline{x}}_1-{\overline{x}}_2)\pm z_{(1-\alpha /2)}\sqrt{\frac{{\sigma }_1^2}{n_1}+\frac{{\sigma }_2^2}{n_2}}$	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	$s_{({\overline{X}}_1-{\overline{X}}_2)}=\sqrt{\frac{s_p^2}{n_1}+\frac{s_p^2}{n_1}}$	Example
6.4.4	Interval estimate for the difference between two population means when s 1 is unknown	$({\overline{x}}_1-{\overline{x}}_2)\pm t_{(1-\alpha /2)}\sqrt{\frac{s_p^2}{n_1}+\frac{s_p^2}{n_1}}$	Example
6.4.5	Cochran’s correction for reliability coefficient when variances are not equal	$t{\text{'}}_{(1-\alpha /2)}=\frac{w_1{t}_1+w_2{t}_2}{w_1+w_2}$	Example
6.4.6	Interval estimate using Cochran’s correction for t	$({\overline{x}}_1-{\overline{x}}_2)\pm t{\text{'}}_{(1-\alpha /2)}\sqrt{\frac{s_p^2}{n_1}+\frac{s_p^2}{n_1}}$	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