Sample Size Calculation T Test

Sample Size Formula for T-Test:

\[ n = \frac{t^2 \times s^2}{d^2} \]

Required Sample Size (n):

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1. What is Sample Size Calculation for T-Test?

The sample size calculation for a t-test determines how many participants are needed in each group to detect a specified effect size with a given level of confidence (t-value) and variability (standard deviation). It's essential for designing statistically valid experiments and studies.

2. How Does the Calculator Work?

The calculator uses the sample size formula for t-test:

\[ n = \frac{t^2 \times s^2}{d^2} \]

Where:

\( t \) — T-value (from t-distribution table)
\( s \) — Standard deviation of the outcome variable
\( d \) — Effect size (minimum difference you want to detect)
\( n \) — Required sample size per group

Explanation: The formula accounts for the relationship between statistical power (t-value), variability in data (standard deviation), and the smallest effect size you want to detect.

3. Importance of Sample Size Calculation

Details: Proper sample size calculation ensures your study has adequate power to detect effects while avoiding unnecessary resource expenditure. Underpowered studies may miss important effects, while overpowered studies waste resources.

4. Using the Calculator

Tips: Enter the t-value corresponding to your desired confidence level, the expected standard deviation of your data, and the minimum effect size you want to detect. All values must be positive numbers.

5. Frequently Asked Questions (FAQ)

Q1: How do I determine the appropriate t-value?
A: The t-value depends on your desired confidence level and degrees of freedom. For 95% confidence with large samples, use approximately 1.96.

Q2: What if I don't know the standard deviation?
A: Use estimates from pilot studies or similar research. Sensitivity analysis with different SD values is recommended.

Q3: How does effect size affect sample size?
A: Smaller effect sizes require larger samples to detect. Doubling the effect size reduces required sample size by a factor of four.

Q4: Is this for one-sample or two-sample t-tests?
A: This calculates per-group sample size for two-sample t-tests. For one-sample, divide the result by 2.

Q5: Should I adjust for expected dropout rates?
A: Yes, multiply the calculated sample size by 1/(1 - expected dropout rate) to account for participant attrition.