T-Value Calculator
Calculate the T-statistic for a One-Sample T-Test
Calculation Results
T-Value (t): 0
Degrees of Freedom (df): 0
Standard Error (SE): 0
Understanding the T-Value Calculation
The t-value (or t-statistic) is a ratio that quantifies the difference between your sample mean and the hypothesized population mean relative to the variation in your sample data. It is the cornerstone of the t-test, which helps researchers determine if a result is statistically significant.
Variables Explained:
- x̄ (Sample Mean): The average value calculated from your collected data points.
- μ (Population Mean): The theoretical or known average value you are comparing your sample against.
- s (Standard Deviation): A measure of the amount of variation or dispersion in your sample set.
- n (Sample Size): The total number of individual observations or data points in your sample.
How to Interpret the T-Value
A t-value of 0 indicates that the sample results exactly match the null hypothesis. As the t-value increases (either positively or negatively), it suggests a greater difference between the sample and the population mean. To determine if the t-value is "large enough" to be significant, you compare it against a critical value from a t-distribution table using the Degrees of Freedom (n – 1) and your chosen alpha level (usually 0.05).
Practical Example
Imagine a lightbulb manufacturer claims their bulbs last 1,000 hours (μ). You test 25 bulbs (n) and find they last an average of 980 hours (x̄) with a standard deviation of 50 hours (s).
Step 1: Subtract population mean from sample mean: 980 – 1000 = -20.
Step 2: Calculate the square root of the sample size: √25 = 5.
Step 3: Divide standard deviation by the root: 50 / 5 = 10 (Standard Error).
Step 4: Divide the mean difference by the standard error: -20 / 10 = -2.00.
In this case, your t-value is -2.00.