1. What is the T-Ratio Formula?

The t-ratio (or t-statistic) is used in hypothesis testing to determine if there is a significant difference between the sample mean and the population mean. It's particularly useful when dealing with small sample sizes where the population standard deviation is unknown.

2. How Does the Calculator Work?

The calculator uses the t-ratio formula:

Where:

• \( \text{Sample\_mean} \) — Mean of the sample data
• \( \text{Population\_mean} \) — Hypothesized population mean
• \( \text{Standard\_deviation} \) — Standard deviation of the sample
• \( \text{Sample\_size} \) — Number of observations in the sample

Explanation: The t-ratio measures how many standard errors the sample mean is from the population mean. A larger absolute t-value indicates a greater difference between groups.

3. Importance of T-Ratio Calculation

Details: The t-ratio is fundamental in t-tests, which are used to determine if observed differences between groups are statistically significant or likely due to chance.

4. Using the Calculator

Tips: Enter all values in consistent units. The sample size must be at least 2, and standard deviation must be positive. The result is unitless.

5. Frequently Asked Questions (FAQ)

Q1: When should I use a t-test?
A: Use a t-test when comparing means of small samples (typically n < 30) with unknown population standard deviation.

Q2: What's the difference between t-ratio and z-score?
A: Both measure deviations in standard error units, but t-ratio uses sample standard deviation while z-score uses population standard deviation.

Q3: How does sample size affect the t-ratio?
A: Larger samples generally produce more reliable t-values. The t-distribution approaches the normal distribution as sample size increases.

Q4: What are degrees of freedom in t-tests?
A: Degrees of freedom equal sample size minus 1 (n-1). This affects the shape of the t-distribution used to determine significance.

Q5: How do I interpret the t-ratio value?
A: Compare the absolute value of your t-ratio to critical values from the t-distribution table. Larger values indicate stronger evidence against the null hypothesis.