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T Statistic Formula:
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The t statistic is a measure used in hypothesis testing that follows a t-distribution under the null hypothesis. It quantifies the difference between the sample mean and the population mean in terms of standard error units.
The calculator uses the t statistic formula:
Where:
Explanation: The t statistic measures how many standard errors the sample mean is away from the population mean, helping determine if the observed difference is statistically significant.
Details: The t statistic is crucial for conducting t-tests, which are used to determine if there are significant differences between groups or between a sample and a population. It's widely used in research, quality control, and various scientific fields.
Tips: Enter the mean difference and standard error values. Both values must be valid numbers, and the standard error cannot be zero.
Q1: What is the difference between t statistic and z score?
A: The t statistic is used when population standard deviation is unknown and sample size is small, while z score is used when population standard deviation is known and sample size is large.
Q2: What does a high t value indicate?
A: A high absolute t value (typically > 2) suggests that the observed difference is statistically significant and unlikely to have occurred by chance.
Q3: When should I use a one-tailed vs two-tailed t-test?
A: Use a one-tailed test when you have a specific directional hypothesis, and a two-tailed test when you're testing for any difference without specifying direction.
Q4: What are the assumptions of the t-test?
A: The main assumptions include: normally distributed data, independence of observations, and homogeneity of variances (for independent samples t-test).
Q5: How is the t statistic related to p-value?
A: The t statistic is used to calculate the p-value, which indicates the probability of obtaining results as extreme as the observed results if the null hypothesis is true.