Sample Size Calculator

What is Sample Size?

Sample size refers to the number of individuals or observations in a study. It's a crucial aspect of research design that impacts the accuracy and reliability of results. A well-chosen sample size ensures that your study is representative of the population and that your findings are statistically significant.

Formula and Its Components

The formula for calculating sample size depends on whether the population is finite or infinite:

For infinite populations: \[n = \frac{z^2 * p(1-p)}{e^2}\]

For finite populations: \[n = \frac{N * z^2 * p(1-p)}{e^2(N-1) + z^2 * p(1-p)}\]

Where:

• \(n\) = Sample size
• \(z\) = Z-score (based on confidence level)
• \(p\) = Population proportion (0.5 for maximum variability)
• \(e\) = Margin of error (confidence interval)
• \(N\) = Population size (for finite populations)

Calculation Steps

1. Determine the desired confidence level and find the corresponding Z-score.
2. Decide on the margin of error (confidence interval).
3. Estimate the population proportion (use 0.5 if unknown).
4. If applicable, specify the population size.
5. Apply the appropriate formula based on whether the population is finite or infinite.
6. Round up the result to the nearest whole number.

Example Calculation

Let's calculate the sample size for a survey with the following parameters:

• Confidence Level: 95% (Z-score = 1.96)
• Margin of Error: 5%
• Population Size: 10,000

Step 1: Apply the formula for finite population

\[n = \frac{10000 * 1.96^2 * 0.5(1-0.5)}{0.05^2(10000-1) + 1.96^2 * 0.5(1-0.5)}\]

Step 2: Calculate

\[n = \frac{9604}{25.9775} \approx 369.7\]

Step 3: Round up

\[n = 370\]

Therefore, a sample size of 370 is needed for this survey.

Visual Representation

This diagram represents the sample size (370) in relation to the total population (10,000). The blue circle shows the proportion of the population that needs to be sampled to achieve the desired confidence level and margin of error.