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Sample Size Formula:
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Sample size calculation is a crucial step in research design that determines the number of participants needed to detect a statistically significant effect. Proper sample size ensures study validity and reliability while optimizing resource allocation.
The calculator uses the sample size formula for estimating a population mean:
Where:
Explanation: The formula calculates the minimum number of observations needed to estimate a population mean within a specified margin of error with a given confidence level.
Details: Proper sample size ensures statistical power, prevents Type I and Type II errors, provides reliable results, and optimizes research costs and time. Underpowered studies may fail to detect true effects, while oversized studies waste resources.
Tips: Enter the Z-score based on your desired confidence level (e.g., 1.96 for 95% confidence), estimate the population standard deviation from pilot studies or literature, and specify your acceptable margin of error. All values must be positive numbers.
Q1: What Z-score should I use?
A: Common Z-scores are 1.645 (90% confidence), 1.96 (95% confidence), and 2.576 (99% confidence). Choose based on your required confidence level.
Q2: How do I estimate standard deviation?
A: Use data from pilot studies, previous research, or literature reviews. If unavailable, conduct a small pilot study or use conservative estimates.
Q3: What is an acceptable margin of error?
A: This depends on your research context. Typically 5% or less for social sciences, but may be tighter for medical or engineering applications.
Q4: When is this formula appropriate?
A: For estimating a population mean with continuous data when the population standard deviation is known or estimated.
Q5: What if my population is finite?
A: For finite populations, use the finite population correction: \( n_{adjusted} = \frac{n}{1 + \frac{(n-1)}{N}} \) where N is population size.