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T-Statistic Formula:
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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 Student's t-test to determine if there is a significant difference between two sample means.
The calculator uses the t-statistic formula:
Where:
Explanation: The t-statistic measures how many standard errors the difference in means is from zero. A larger absolute t-value indicates a more significant difference.
Details: The t-statistic is fundamental in statistical hypothesis testing, allowing researchers to determine whether observed differences between groups are statistically significant or likely due to chance.
Tips: Enter the difference between the two sample means and the standard error of that difference. The standard error must be a positive non-zero value.
Q1: What's a good t-statistic value?
A: Generally, |t| > 2 indicates statistical significance at the 0.05 level, but the exact threshold depends on degrees of freedom and desired significance level.
Q2: How is this different from z-score?
A: Both measure how many standard deviations an observation is from the mean, but t-statistic is used when sample sizes are small and population variance is unknown.
Q3: What affects the t-statistic?
A: The magnitude of difference between means, sample sizes (through standard error), and variability within each sample.
Q4: When should I use this calculator?
A: When you need to compute the t-statistic for independent two-sample t-tests to compare means between two groups.
Q5: What's the relationship between t-statistic and p-value?
A: The t-statistic is used to calculate the p-value, which indicates the probability of observing such an extreme value if the null hypothesis were true.