Quickly calculate the t-statistic for your data with our user-friendly T-Statistic Calculator. Simply input your sample means, sample sizes, and standard deviations, and get instant results.
T-Statistic Formula
The t-statistic is calculated as follows:
t = (x̄ – μ) / (s / √n)
- t = t-statistic
- x̄ = sample mean
- μ = population mean
- s = sample standard deviation
- n = number of observations in the sample
- √n = square root of n
How to calculate t-statistic?
The t-statistic is calculated by taking the difference between the sample mean (x̄) and the population mean (μ) or hypothesized mean, and then dividing that difference by the standard error of the sample mean.
Here’s a step-by-step calculation of the t-statistic:
- Step 1: Calculate the sample mean (x̄).
- Step 2: Calculate the sample standard deviation (s).
- Step 3: Determine the population mean (μ) or hypothesized mean.
- Step 4: Find the sample size (n).
- Step 5: Put the values into the t-statistic formula and calculate.
T-Statistic Example
Example – We have a sample of 30 students, and we want to test if their average height is significantly different from a hypothesized mean of 170 cm. The sample mean height is 172 cm, and the sample standard deviation is 5 cm.
Solved
Step 1: Sample mean (x̄) = 172 cm
Step 2: Sample standard deviation (s) = 5 cm
Step 3: Population mean (μ) or hypothesized mean = 170 cm
Step 4: Sample size (n) = 30
Step 5: Put the values into the t-statistic formula:
t = (172 – 170) / (5 / √30)
t = 2 / (5 / √30)
t = 2 / (5 / 5.48)
t ≈ 2 / 0.9124
t ≈ 2.19
The t-statistic values is approximately 2.19.