Study Sample Size Calculator

Sample Size Formula for Means:

\[ n = \frac{Z^2 \times \sigma^2}{e^2} \]

Required Sample Size (n):

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1. What is Sample Size Calculation?

Sample size calculation determines the number of participants needed in a study to detect a statistically significant effect. For means with known population standard deviation, we use the formula: \( n = \frac{Z^2 \times \sigma^2}{e^2} \).

2. How Does the Calculator Work?

The calculator uses the sample size formula for means:

\[ n = \frac{Z^2 \times \sigma^2}{e^2} \]

Where:

\( n \) — Required sample size
\( Z \) — Z-score corresponding to confidence level (1.96 for 95% confidence)
\( \sigma \) — Population standard deviation
\( e \) — Margin of error

Explanation: This formula calculates the minimum number of participants needed to estimate a population mean with specified precision and confidence level when the population standard deviation is known.

3. Importance of Sample Size Determination

Details: Proper sample size calculation ensures studies have adequate power to detect meaningful effects, prevents wasting resources on underpowered studies, and provides valid statistical conclusions.

4. Using the Calculator

Tips: Enter Z-score (typically 1.96 for 95% confidence), population standard deviation, and desired margin of error. All values must be positive numbers.

5. Frequently Asked Questions (FAQ)

Q1: What is a Z-score and how do I choose it?
A: Z-score represents the number of standard deviations from the mean. Common values: 1.645 (90% confidence), 1.96 (95% confidence), 2.576 (99% confidence).

Q2: What if I don't know the population standard deviation?
A: Use a t-distribution based sample size calculation instead, which uses sample standard deviation and accounts for additional uncertainty.

Q3: How do I determine the margin of error?
A: Margin of error represents the maximum expected difference between sample mean and population mean. It depends on your study's precision requirements.

Q4: What are common sample size considerations?
A: Consider expected effect size, statistical power (typically 80%), confidence level, and practical constraints like budget and participant availability.

Q5: Should I adjust for expected dropout rates?
A: Yes, multiply calculated sample size by 1/(1-dropout rate) to account for anticipated participant attrition during the study.