1. What is a T Score?

The T Score (or t-statistic) measures how far the sample mean deviates from the population mean in terms of standard error units. It's used in t-tests to determine if there's a significant difference between sample and 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 (standard error) scales this difference by the sample variability and size.

3. Importance of T Score

Details: T scores are fundamental in hypothesis testing, particularly in Student's t-tests. They help determine whether observed differences are statistically significant or likely due to random chance.

4. Using the Calculator

Tips: Enter all required values (sample mean, population mean, standard deviation, and sample size). Standard deviation must be ≥0 and sample size must be ≥1.

5. Frequently Asked Questions (FAQ)

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

Q2: What does a high t-score indicate?
A: A higher absolute t-score indicates a greater difference between sample and population means relative to the variability in the data.

Q3: How is the t-score related to p-value?
A: The t-score is converted to a p-value using the t-distribution, which indicates the probability of observing such a result if the null hypothesis were true.

Q4: Can t-scores be negative?
A: Yes, t-scores can be negative when the sample mean is less than the population mean.

Q5: What's the difference between one-tailed and two-tailed t-tests?
A: One-tailed tests check for an effect in one direction only, while two-tailed tests check in both directions (more conservative).