Sample Size Calculation Methods

Sample Size Formulas:

\[ n = \frac{Z^2 p (1-p)}{e^2} \text{ (proportions)} \] \[ n = \frac{Z^2 \sigma^2}{e^2} \text{ (means)} \]

Calculation Type:

Confidence Level:

Expected Proportion (p):

decimal

Standard Deviation (σ):

units

Margin of Error (e):

decimal

Population Size (optional):

count

Required Sample Size (n):

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1. What is Sample Size Calculation?

Sample size calculation is a statistical process used to determine the number of observations or replicates needed in a study to detect an effect of a given size with a specified degree of confidence. Proper sample size ensures study validity and reliability.

2. How Does the Calculator Work?

The calculator uses standard sample size formulas:

\[ n = \frac{Z^2 p (1-p)}{e^2} \text{ (for proportions)} \] \[ n = \frac{Z^2 \sigma^2}{e^2} \text{ (for means)} \]

Where:

\( n \) — Required sample size
\( Z \) — Z-score corresponding to confidence level
\( p \) — Expected proportion (for proportion calculations)
\( \sigma \) — Standard deviation (for mean calculations)
\( e \) — Margin of error

Explanation: The formulas balance precision (margin of error) with confidence level to determine the minimum sample size needed for reliable results.

3. Importance of Sample Size Determination

Details: Proper sample size calculation prevents under-powered studies (missing true effects) and over-powered studies (wasting resources). It ensures statistical validity and generalizability of results.

4. Using the Calculator

Tips: Select calculation type (proportion or mean), choose confidence level, enter expected proportion or standard deviation, specify margin of error. For finite populations, include population size for correction.

5. Frequently Asked Questions (FAQ)

Q1: When to use proportion vs mean calculation?
A: Use proportion for categorical data (percentages, rates) and mean for continuous data (averages, measurements).

Q2: What if I don't know the expected proportion?
A: Use 0.5 (50%) as it provides the most conservative (largest) sample size estimate.

Q3: How to estimate standard deviation?
A: Use pilot study data, previous research, or literature values. If unknown, conduct a small pilot study first.

Q4: What is Cochran's formula used for?
A: Cochran's formula is used when population size is unknown or very large, providing a sample size without finite population correction.

Q5: Can this calculator be used for clinical trials?
A: This provides basic sample size estimates. Clinical trials often require more complex calculations accounting for power, effect size, and drop-out rates.