1. What is the T Test Sample Size Calculation?

The sample size calculation for a t-test determines how many participants are needed in each group to detect a specified effect size with adequate statistical power while controlling Type I and Type II error rates.

2. How Does the Calculator Work?

The calculator uses the formula:

Where:

• \( z_{\alpha} \) — Z-score for Type I error (typically 1.96 for α=0.05)
• \( z_{\beta} \) — Z-score for Type II error (typically 0.84 for 80% power)
• \( \sigma \) — Standard deviation of the outcome variable
• \( \delta \) — Effect size (clinically meaningful difference)

Explanation: The formula calculates the sample size needed per group to detect the specified effect size with the given power and significance level.

3. Importance of Sample Size Calculation

Details: Proper sample size calculation ensures studies have adequate power to detect effects while avoiding unnecessary resource expenditure on overly large samples.

4. Using the Calculator

Tips: Enter z-scores for your desired alpha and power levels, the expected standard deviation, and the effect size you want to detect. All values must be positive numbers.

5. Frequently Asked Questions (FAQ)

Q1: What are typical values for z_α and z_β?
A: For α=0.05 (two-tailed), z_α=1.96. For 80% power, z_β=0.84; for 90% power, z_β=1.28.

Q2: How do I estimate standard deviation?
A: Use data from pilot studies, similar published research, or make an educated estimate based on the measurement scale.

Q3: What if I have unequal group sizes?
A: The calculation becomes more complex. You'll need to account for the allocation ratio between groups.

Q4: Does this work for paired t-tests?
A: For paired tests, you would use the standard deviation of the differences rather than the raw values.

Q5: What about non-normal distributions?
A: For severely non-normal data, consider nonparametric alternatives or transformation of data.