Sample Size Calculation For Quantitative Study

Sample Size Formula For Means:

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

Required Sample Size (n):

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1. What Is Sample Size Calculation For Quantitative Study?

Sample size calculation for quantitative studies determines the number of participants needed to detect a statistically significant effect. It ensures studies have adequate power while optimizing resources and ethical considerations.

2. How Does The Calculator Work?

The calculator uses the sample size formula for means:

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

Where:

\( n \) — Required sample size (unitless)
\( Z \) — Z-score corresponding to desired confidence level (unitless)
\( \sigma \) — Standard deviation of the population (units)
\( E \) — Margin of error (units)

Explanation: This formula calculates the minimum sample size needed to estimate a population mean with specified precision and confidence level.

3. Importance Of Sample Size Calculation

Details: Proper sample size calculation prevents underpowered studies (Type II errors) and avoids unnecessary resource expenditure on oversized samples. It ensures research validity and reliability.

4. Using The Calculator

Tips: Enter Z-score (common values: 1.96 for 95% CI, 2.58 for 99% CI), 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% CI), 1.96 (95% CI), 2.576 (99% CI).

Q2: How do I estimate standard deviation?
A: Use pilot study data, previous research, or literature values. If unknown, conduct a small pilot study to estimate variability.

Q3: What margin of error should I use?
A: Margin of error depends on research objectives. Smaller margins provide more precision but require larger samples. Typically 5% or less.

Q4: When is this formula appropriate?
A: For estimating population means with continuous data. For proportions, use the proportion sample size formula.

Q5: Should I adjust for expected dropout?
A: Yes, increase calculated sample size by expected dropout rate (e.g., if 10% dropout expected, multiply by 1.1).