1. What is a T-Score?

The T-score measures how far a sample mean is from the population mean in standard error units. It's used in hypothesis testing, confidence intervals, and comparing sample means to population means.

2. How Does the Calculator Work?

The calculator uses the T-score formula:

Where:

• \( \bar{X} \) — Sample mean
• \( \mu \) — Population mean
• \( s \) — Sample standard deviation
• \( n \) — Sample size

Explanation: The numerator measures the difference between sample and population means, while the denominator standardizes this difference by the standard error of the mean.

3. Interpretation of T-Score

Details: Higher absolute T-scores indicate greater deviation from the population mean. The significance depends on degrees of freedom (n-1) and chosen significance level.

4. Using the Calculator

Tips: Enter all required values. Sample standard deviation must be ≥0 and sample size must be ≥1. The calculator handles both positive and negative differences.

5. Frequently Asked Questions (FAQ)

Q1: When should I use a T-score instead of a Z-score?
A: Use T-scores when population standard deviation is unknown and sample size is small (typically n < 30). For large samples, Z-scores are appropriate.

Q2: What does a T-score of 0 mean?
A: A T-score of 0 means the sample mean exactly equals the population mean.

Q3: How is this related to p-values?
A: The T-score can be converted to a p-value using the t-distribution with n-1 degrees of freedom.

Q4: What's the difference between one-tailed and two-tailed tests?
A: One-tailed tests look for deviation in one direction only, while two-tailed tests consider both directions. This affects how you interpret the T-score.

Q5: Can I use this for paired samples?
A: For paired samples, you would calculate differences first and use μ=0 (testing if mean difference is zero).