1. What is the T Score?

The T Score is a statistical measure used in hypothesis testing that indicates how many standard deviations the sample mean is from the population mean. It's commonly used in t-tests to determine if there is a significant difference between two groups.

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 how much the sample mean differs from the population mean, while the denominator (standard error) accounts for sample size and variability.

3. Importance of T Score Calculation

Details: T Scores are essential for determining statistical significance in experiments and studies, especially when sample sizes are small or population standard deviation is unknown.

4. Using the Calculator

Tips: Enter all required values. Sample size must be at least 1, and standard deviation must be non-negative. The calculator will compute the T Score which can then be compared to critical values from t-distribution tables.

5. Frequently Asked Questions (FAQ)

Q1: When should I use a T Score instead of a Z Score?
A: Use T Score when sample sizes are small (typically <30) or when the population standard deviation is unknown.

Q2: How do I interpret the T Score?
A: Higher absolute T Scores indicate greater difference from the population mean. Compare your T Score to critical values from t-distribution tables based on your degrees of freedom (n-1) and desired significance level.

Q3: What's the relationship between T Score and p-value?
A: The T Score can be converted to a p-value using the t-distribution, which tells you the probability of observing your results if the null hypothesis is true.

Q4: Can T Scores be negative?
A: Yes, negative T Scores indicate the sample mean is below the population mean, while positive scores indicate it's above.

Q5: What are degrees of freedom in t-tests?
A: Degrees of freedom (df) equals n-1. It affects the shape of the t-distribution used to determine statistical significance.