Sample Size Calculation For Prospective Study

Sample Size Formula For Comparing Means:

\[ n = \frac{(Z_{\alpha} + Z_{\beta})^2 \times (\sigma_1^2 + \sigma_2^2)}{\delta^2} \]

Z-Score Alpha (Z_α):

(e.g., 1.96 for α=0.05)

Z-Score Beta (Z_β):

(e.g., 0.84 for β=0.20)

Standard Deviation Group 1 (σ₁):

units

Standard Deviation Group 2 (σ₂):

units

Difference (δ):

units

Required Sample Size Per Group (n):

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1. What Is Sample Size Calculation For Prospective Study?

Sample size calculation for prospective studies determines the number of participants needed in each group to detect a statistically significant difference between means with specified power and significance level. This ensures the study has adequate power to answer the research question.

2. How Does The Calculator Work?

The calculator uses the sample size formula for comparing means:

\[ n = \frac{(Z_{\alpha} + Z_{\beta})^2 \times (\sigma_1^2 + \sigma_2^2)}{\delta^2} \]

Where:

\( Z_{\alpha} \) — Z-score for significance level (α)
\( Z_{\beta} \) — Z-score for power (1-β)
\( \sigma_1 \) — Standard deviation of group 1
\( \sigma_2 \) — Standard deviation of group 2
\( \delta \) — Clinically important difference to detect

Explanation: This formula calculates the sample size needed per group to detect a specified difference between group means with desired statistical power and significance level.

3. Importance Of Sample Size Calculation

Details: Proper sample size calculation is essential for study validity. Underpowered studies may fail to detect true effects, while overpowered studies waste resources. This calculation ensures optimal resource allocation and reliable results.

4. Using The Calculator

Tips: Enter appropriate z-scores for your chosen α and β levels, estimated standard deviations for both groups, and the minimum clinically important difference you wish to detect. All values must be positive, with δ > 0.

5. Frequently Asked Questions (FAQ)

Q1: What Are Common Values For Z_α And Z_β?
A: For α=0.05 (two-tailed), Z_α=1.96; for β=0.20 (80% power), Z_β=0.84; for β=0.10 (90% power), Z_β=1.28.

Q2: How Do I Estimate Standard Deviations?
A: Use data from pilot studies, previous research, or literature reviews. If unknown, conservative estimates can be used based on the measurement scale.

Q3: What If Standard Deviations Are Equal?
A: If σ₁ = σ₂ = σ, the formula simplifies to: n = 2 × (Z_α + Z_β)² × σ² / δ².

Q4: Should I Adjust For Multiple Comparisons?
A: Yes, if conducting multiple tests, consider adjusting α level using methods like Bonferroni correction, which would change the Z_α value.

Q5: What About Dropout Rates?
A: Increase the calculated sample size to account for expected dropout rates. For example, if 10% dropout is expected, multiply by 1/(1-0.10) = 1.11.