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T-test Formula:
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The t-test for difference in means is a statistical test used to determine if there is a significant difference between the means of two groups. It calculates a t-statistic which can be compared to critical values to assess statistical significance.
The calculator uses the t-test formula:
Where:
Explanation: The t-statistic measures how many standard errors the observed difference is from zero (no difference). Larger absolute t-values indicate stronger evidence against the null hypothesis.
Details: The t-test is fundamental in hypothesis testing, allowing researchers to determine if observed differences between groups are statistically significant or likely due to random chance.
Tips: Enter the mean difference and its standard error. The standard error must be positive. The calculator will compute the t-statistic which can be used for hypothesis testing.
Q1: What does the t-statistic tell us?
A: The t-statistic indicates how far the observed difference is from the null hypothesis value (usually zero) in terms of standard errors.
Q2: How do I interpret the t-value?
A: Compare your t-value to critical values from the t-distribution table. If the absolute value exceeds the critical value, the result is statistically significant.
Q3: What's the difference between one-tailed and two-tailed tests?
A: One-tailed tests check for an effect in one direction, while two-tailed tests check in both directions. Two-tailed is more conservative and commonly used.
Q4: What assumptions does the t-test make?
A: The test assumes normally distributed data, homogeneity of variance (for independent samples), and independent observations.
Q5: When should I use a z-test instead?
A: Use a z-test when population parameters (mean and variance) are known or when sample sizes are very large (>30 is a common rule of thumb).