Table S.1
Methods to Compute Some Confidence Intervals


Parameter of Interest

Conditions

95% CI

Page Number

Proportion (π)

Large n, 0 <p< 1

Equation 12.11

264

Small n, any p

Figure 12.5

272

Any n, p
= 0 or 1 (confidence bound)

Table 12.4

273

Mean (μ)

Large n, σ
known, almost any underlying distribution

Equation 12.14

266

Small n, σ
known, underlying Gaussian

Equation 12.14

266

Small n, σ
known or unknown, underlying nonGaussian

Table 12.5 (CI for median)

275

Any n, σ
unknown, underlying Gaussian

Equation 12.15

266

Large n, σ
unknown, underlying nonGaussian

Equation 12.15

266

Median

Gaussian distribution

Equation 12.18b

268

NonGaussian conditions

Table 12.5

275

Difference in proportions (π1
– π2)

Large n1,
n2 – Independent
samples

Equation 12.20

269

Large n1,
n2 – Paired samples

Equation 12.23

271

Difference in means (μ1 – μ2) (σ unknown)

Independent samples



Large n1, n2 – Almost any underlying distribution

Equation 12.21

269

Small n1, n2 – Underlying Gaussian

Equation 12.21

269

Paired samples

Same as for one sample after taking the difference


Relative risk

Large n1,
n2 – Independent
samples

Equation 14.4

351

Large n1,
n2 – Paired samples

Same as for OR when prevalence is small (Equation 14.21)

351

Attributable risk

Large n1,
n2 – Independent
samples

Same as for (π1 – π2)


Large n1,
n2 – Paired samples

Equation 14.12

355

Number needed to treat

Large n1,
n2 – Independent
samples

Section 14.1.3.3

355

Odds ratio

Large n1,
n2 – Independent
samples

Equation 14.18

360

Large n1,
n2 – Paired samples

Equation 14.21

362

Regression coefficient and intercept (simple linear)

Large n (Gaussian residuals)

Use Equation 16.7

435

Regression line (confidence band)

Large n (Gaussian residuals)

Section 16.2.1.5

437

Logistic coefficient

Large n

Section 17.2.2

480

Median effective dose

Upanddown trial

Section 15.1.4

386
