Package 'cochranSize'

Base Sample Size Using Cochran's Formula

Description

Calculates the minimum sample size required for a large (effectively infinite) population using Cochran's formula:

$n_0 = \frac{z^2 \, p (1-p)}{e^2}$

Usage

cochran_n(p = 0.5, e = 0.05, conf.level = 0.95)

Arguments

p	Estimated proportion of the population expected to have the attribute of interest. Defaults to 0.5, the most conservative choice (maximizes required sample size when unknown). Fully adjustable.
e	Desired margin of error (as a decimal, e.g. 0.05 for 5%). Fully adjustable by the user.
conf.level	Confidence level for the estimate. Defaults to 0.95 (95% confidence), but any value strictly between 0 and 1 is accepted (e.g. 0.90, 0.99).

Value

A single numeric value: the unadjusted sample size n0 (not rounded, and without any finite population correction).

Examples

cochran_n()
cochran_n(p = 0.3, e = 0.03, conf.level = 0.99)
cochran_n(e = 0.02, conf.level = 0.90)

---

Finite Population Correction for Cochran's Formula

Description

Adjusts an unadjusted Cochran sample size (n0) for a finite, known population size N, using:

$n = \frac{n_0}{1 + \frac{n_0 - 1}{N}}$

Usage

cochran_n_adj(n0, N)

Arguments

n0	The unadjusted sample size, typically the output of cochran_n.
N	The known size of the population being sampled from.

Value

A single numeric value: the finite-population-corrected sample size (not rounded). A warning is issued if n0 exceeds N, since that indicates the unadjusted sample size already exceeds the entire population.

Examples

n0 <- cochran_n(p = 0.5, e = 0.05, conf.level = 0.95)
cochran_n_adj(n0, N = 1000)

---

Sample Size Calculation Using Cochran's Formula (Convenience Wrapper)

Description

Computes the sample size required for a survey or study using Cochran's formula, optionally applying the finite population correction when a known population size N is supplied. Wraps cochran_n and cochran_n_adj into a single call with readable output.

Usage

cochran_sample_size(N = NULL, p = 0.5, e = 0.05, conf.level = 0.95)

Arguments

N	Optional known population size. If supplied, the finite population correction is applied. If omitted, the population is treated as effectively infinite and only the unadjusted sample size is returned.
p	Estimated proportion of the population expected to have the attribute of interest. Defaults to 0.5 (most conservative). Fully adjustable.
e	Desired margin of error (as a decimal, e.g. 0.05 for 5%). Fully adjustable by the user — not fixed to any convention.
conf.level	Confidence level. Defaults to 0.95 (95%), but any value strictly between 0 and 1 is accepted (e.g. 0.90, 0.99) and is converted internally to the corresponding z-score.

Value

An object of class "cochran_size" (a list) containing:

n0

Unadjusted sample size, rounded up to the nearest integer.

n_adjusted

Finite-population-corrected sample size, rounded up to the nearest integer, or NA if N was not supplied.

p, e, conf.level, N

The input parameters used.

Examples

# Large / unknown population, 95% confidence, 5% margin of error
cochran_sample_size(e = 0.05, conf.level = 0.95)

# Known finite population of 2,000
cochran_sample_size(N = 2000, e = 0.05, conf.level = 0.95)

# Custom expected proportion, 99% confidence, 3% margin of error
cochran_sample_size(N = 500, p = 0.3, e = 0.03, conf.level = 0.99)

---

Print Method for cochran_size Objects

Description

Print Method for cochran_size Objects

Usage

## S3 method for class 'cochran_size'
print(x, ...)

Arguments

x	An object of class "cochran_size".
...	Additional arguments (unused).

Value

Invisibly returns x.

---