1. What is the T Statistic?

The t-statistic is a ratio of the departure of an estimated parameter from its hypothesized value to its standard error. It is used in hypothesis testing via the t-test.

2. How Does the Calculator Work?

The calculator uses the t-statistic formula:

Where:

• \( x \) — Sample mean
• \( \mu \) — Population mean
• \( s \) — Sample standard deviation
• \( n \) — Sample size

Explanation: The numerator measures how far the sample mean deviates from the population mean, while the denominator scales this difference by the standard error of the mean.

3. Importance of T Statistic

Details: The t-statistic is fundamental in determining whether to reject the null hypothesis in a t-test. It helps assess if observed differences between groups are statistically significant.

4. Using the Calculator

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

5. Frequently Asked Questions (FAQ)

Q1: When should I use a t-statistic?
A: Use it when comparing sample means, especially with small sample sizes (typically n < 30) or when population standard deviation is unknown.

Q2: What's the difference between t-statistic and z-score?
A: Both measure how many standard deviations away a point is, but t-statistic is used when sample sizes are small or population variance is unknown.

Q3: How do I interpret the t-statistic value?
A: Higher absolute values indicate greater deviation from the null hypothesis. Compare it to critical values from the t-distribution.

Q4: What assumptions does the t-test make?
A: Assumes data are approximately normally distributed, especially important with small sample sizes.

Q5: Can I use this for paired samples?
A: For paired samples, you would calculate differences first and then use a single-sample t-test on those differences.