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Sample Size Formula:
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Sample size calculation for mean estimation determines the number of participants needed in a study to estimate a population mean with a specified level of precision and confidence. This is essential for designing statistically valid research studies.
The calculator uses the sample size formula:
Where:
Explanation: The formula calculates the minimum number of observations needed to estimate the population mean within a specified margin of error with a given confidence level.
Details: Proper sample size calculation ensures that research studies have adequate statistical power, produces reliable results, avoids wasting resources on overly large samples, and prevents inconclusive results from insufficient samples.
Tips: Enter the Z-score based on your desired confidence level (1.96 for 95% confidence), the estimated population standard deviation, and your desired 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).
Q2: How do I estimate the standard deviation?
A: Use data from pilot studies, previous research, or literature in your field. If unknown, conduct a small pilot study first.
Q3: What is a reasonable margin of error?
A: This depends on your research context. Typically, 5% or less is considered acceptable for most social science research.
Q4: Should I round the sample size?
A: Yes, always round up to the nearest whole number since you can't have a fraction of a participant.
Q5: What if my population is finite?
A: For finite populations, use the finite population correction formula: \( n_{adj} = \frac{n}{1 + \frac{n-1}{N}} \) where N is population size.