1. What is the T-Ratio?

The t-ratio (or t-statistic) measures how many standard errors the observed value is from the expected value. It's commonly used in hypothesis testing to determine if an observed effect is statistically significant.

2. How Does the Calculator Work?

The calculator uses the t-ratio formula:

Where:

• \( Observed \) — The measured or sample value
• \( Expected \) — The hypothesized or population value
• \( Standard\_error \) — The standard error of the observed value

Explanation: The t-ratio shows how far the observed value deviates from the expected value in units of standard error.

3. Importance of T-Ratio Calculation

Details: The t-ratio is fundamental in statistical hypothesis testing. It helps determine whether to reject the null hypothesis by comparing the calculated t-value to critical values from the t-distribution.

4. Using the Calculator

Tips: Enter the observed value, expected value, and standard error. All values must be valid (standard error must be positive). The result is a unitless t-ratio.

5. Frequently Asked Questions (FAQ)

Q1: What does a high t-ratio mean?
A: A high absolute t-ratio (typically >2) suggests the observed difference is statistically significant, meaning it's unlikely to have occurred by chance.

Q2: How is this different from z-score?
A: Both measure deviations in standard error units, but t-ratio is used when sample sizes are small and population variance is unknown.

Q3: What's the relationship between t-ratio and p-value?
A: The t-ratio can be converted to a p-value using the t-distribution with appropriate degrees of freedom.

Q4: When is t-ratio most useful?
A: In small sample sizes (typically n < 30) or when population standard deviation is unknown.

Q5: Can t-ratio be negative?
A: Yes, a negative t-ratio indicates the observed value is below the expected value.