Sample Size Calculator For Experimental Study

Sample Size Formula:

\[ n = 2 (Z_{1-\alpha/2} + Z_{1-\beta})^2 (\sigma^2 / \delta^2) \]

Z-score for Alpha (Z_{1-α/2}):

unitless

Z-score for Power (Z_{1-β}):

unitless

Standard Deviation (σ):

units

Effect Size (δ):

units

Sample Size Per Group (n):

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1. What is the Sample Size Calculator For Experimental Study?

The Sample Size Calculator for Experimental Study determines the required sample size for two-group experimental designs with specified statistical power. It helps researchers plan studies by estimating the number of participants needed per group to detect a meaningful effect size.

2. How Does the Calculator Work?

The calculator uses the sample size formula:

\[ n = 2 (Z_{1-\alpha/2} + Z_{1-\beta})^2 (\sigma^2 / \delta^2) \]

Where:

\( n \) — Sample size per group (unitless)
\( Z_{1-\alpha/2} \) — Z-score for significance level (e.g., 1.96 for α=0.05)
\( Z_{1-\beta} \) — Z-score for statistical power (e.g., 0.84 for 80% power)
\( \sigma \) — Standard deviation of the outcome measure (units)
\( \delta \) — Effect size to detect (units)

Explanation: This formula calculates the sample size needed per group for a two-arm study to achieve specified statistical power while controlling Type I error rate.

3. Importance of Sample Size Calculation

Details: Proper sample size calculation is crucial for ensuring studies have adequate power to detect meaningful effects, avoiding underpowered studies that may miss true effects, and preventing wasteful oversampling.

4. Using the Calculator

Tips: Enter the Z-scores for your desired significance level and power, the expected standard deviation of your outcome measure, and the minimum effect size you want to detect. All values must be positive numbers.

5. Frequently Asked Questions (FAQ)

Q1: What are typical values for Z_{1-α/2} and Z_{1-β}?
A: Common values are 1.96 for α=0.05 (two-tailed), 0.84 for 80% power, and 1.28 for 90% power.

Q2: How do I estimate standard deviation (σ)?
A: Use pilot data, previous similar studies, or literature reviews. If uncertain, conduct a small pilot study first.

Q3: What is a meaningful effect size (δ)?
A: This depends on your research field and clinical/ practical significance. Consult domain experts and previous literature.

Q4: Does this work for all study designs?
A: This formula is specifically for two-group parallel designs with continuous outcomes. Other designs require different formulas.

Q5: Should I account for dropout or non-compliance?
A: Yes, consider increasing your calculated sample size by 10-20% to account for potential participant dropout or protocol deviations.