Calculation of Sample Size PPT

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 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.

2. How Does the Calculator Work?

The calculator uses the standard sample size formula for means:

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

Where:

\( n \) — Required sample size (count)
\( Z \) — Z-score corresponding to confidence level (unitless)
\( \sigma \) — Population standard deviation (units)
\( e \) — Margin of error (units)

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

3. Importance of Sample Size Determination

Details: Adequate sample size prevents Type I and Type II errors, ensures statistical power, and provides reliable results that can be generalized to the population.

4. Using the Calculator

Tips: Enter Z-score based on confidence level (1.96 for 95%, 2.58 for 99%), estimated standard deviation from pilot studies or literature, and desired margin of error. All values must be positive.

5. Frequently Asked Questions (FAQ)

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 to estimate variability.

Q3: What is an appropriate margin of error?
A: Typically 5% or less, but depends on research context. Smaller margins require larger samples but provide more precise estimates.

Q4: Does this work for proportions?
A: No, this formula is for means. For proportions, use \( n = \frac{Z^2 \times p(1-p)}{e^2} \) where p is the estimated proportion.

Q5: Should I adjust for expected dropout?
A: Yes, increase your calculated sample size by 10-20% to account for potential participant attrition during the study.