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T Value Formula:
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The t-value is a statistic that measures the difference between the sample mean and the hypothesized population mean in terms of the standard error. It's used in t-tests to determine if there is a significant difference between groups.
The calculator uses the t-value formula:
Where:
Explanation: The t-value represents how many standard errors the sample mean is from the hypothesized mean. A larger absolute t-value indicates a greater difference from the null hypothesis.
Details: The t-value is crucial for hypothesis testing in statistics. It helps determine whether to reject the null hypothesis and is used to calculate p-values in t-tests.
Tips: Enter the sample mean, hypothesized mean, standard deviation, and sample size. All values must be valid (n > 0, std ≥ 0).
Q1: What's the difference between t-value and z-score?
A: T-values are used when population standard deviation is unknown (using sample std) and sample sizes are small, while z-scores are used when population parameters are known.
Q2: What is a good t-value?
A: The significance depends on degrees of freedom and desired confidence level. Typically, absolute t-values greater than 2 are considered statistically significant for moderate sample sizes.
Q3: How does sample size affect the t-value?
A: Larger sample sizes generally produce more reliable t-values. As sample size increases, the t-distribution approaches the normal distribution.
Q4: Can t-value be negative?
A: Yes, a negative t-value indicates the sample mean is less than the hypothesized mean, while positive indicates it's greater.
Q5: What's the relationship between t-value and p-value?
A: The t-value is used to calculate the p-value, which determines statistical significance. Larger absolute t-values correspond to smaller p-values.