T-Value Calculator – Â T Statistic
T-Value Calculator
To calculate T-Value, enter Sample Mean, Population Mean, Sample Standard Deviation, and Sample Size, calculator computes T-Statistic and provides associated P-Value and Degrees of Freedom.
For One-Sample T-Tests, also select the Significance Level (typically 0.05) to determine statistical significance.
How to Find Value of T?
To calculate a T-Value, first determine difference between Sample Mean and Population Mean. Divide this difference by the Standard Error (sample standard deviation divided by square root of sample size).
The resulting value indicates how many standard errors the sample mean is from the population mean, considering sample size and variability.
Formula for T-Value (T Statistic)
Basic T-Value Formula:
t = (x̄ - μ) ÷ (s ÷ √n)
where:
x̄ = Sample mean
μ = Population mean
s = Sample standard deviation
n = Sample size
Standard Error Formula:
SE = s ÷ √n
where:
s = Sample standard deviation
n = Sample size
Degrees of Freedom:
df = n - 1
where:
n = Sample size
Example 1: Basic T-Test
- Sample Mean = 75.5
- Population Mean = 70.0
- Standard Deviation = 8.2
- Sample Size = 30
- T-Value = 3.68
- P-Value = 0.001
Example 2: Small Sample
- Sample Mean = 125.3
- Population Mean = 120.0
- Standard Deviation = 12.5
- Sample Size = 15
- T-Value = 1.64
- P-Value = 0.123
Example 3: Large Sample
- Sample Mean = 45.2
- Population Mean = 42.0
- Standard Deviation = 5.8
- Sample Size = 50
- T-Value = 3.89
- P-Value = 0.0003
Example 4: Precise Measurement
- Sample Mean = 98.6
- Population Mean = 98.2
- Standard Deviation = 0.4
- Sample Size = 25
- T-Value = 5.00
- P-Value = < 0.0001
Example 5: Negative T-Value
- Sample Mean = 82.3
- Population Mean = 85.0
- Standard Deviation = 6.7
- Sample Size = 40
- T-Value = -2.55
- P-Value = 0.015
What is T-Value in Statistics?
A T-Value is a statistical measure that compares a sample mean to a population mean, accounting for sample size and variability. It helps determine if differences between means are statistically significant or due to random chance. The T-Value is crucial in Hypothesis Testing, particularly in situations with small sample sizes or unknown population standard deviation. Larger absolute T-values indicate stronger evidence against the null hypothesis, while the associated P-Value quantifies the probability of observing such results by chance.