Critical value calculator finds the critical values of t distribution according to the probabilities of two alpha values and the degrees of freedom. T-Distribution table refers to a type of probability distribution that is theoretical and resembles a normal distribution. The higher the degrees of freedom, the closer that distribution will resemble a standard normal distribution with a mean of 0, and a standard deviation of 1. It is symmetrical, bell-shaped, and similar to the standard normal curve. The T distribution is also known as the "Student's T Distribution". Use following t critical value table (t score table)
T-Distribution Critical Value Table
Table of Contents:
Critical Value Formula
t = [x – μ] / [s / √ (n)]
In this equation: μ is the population mean, x is the mean of the sample, s is the standard deviation of the sample, and n is the size of the sample.
T critical value calculator is used to calculate the critical value of t using a degree of freedom and significance level alpha. The table given below works as a critical t value calculator. In this post, we will discuss how to calculate t critical value using the below table and the critical value formula as well.
Example: Calculating t value using t table
Follow these steps to calculate t value using t value table:
Step 1: Identify the size of the sample. Assume we have six samples.
n = 6
Step 2: Calculate degrees of freedom. Subtract 1 from the sample size.
df = n – 1 = 6 – 1 = 5
Step 3: Identify the value of the alpha level. Assume this value as 0.05 for now.
α = 0.05
Step 4: In the table given below, search the value of df and its corresponding alpha level value. In this case, we will get:
t = 2.015
Example: Calculate t score using t score formula
Suppose the mean of the sample (x) is 400, population mean (μ) is 270, sample size (n) is 12, and the standard deviation of the sample (s) is 80.
Follow these steps to calculate t critical value using t score formula:
Step 1: Identify all values.
x = 400, μ = 270, s = 80, n = 12
Step 2: Write down the t score formula and substitute the values.
t = [x – μ] / [s / √ (n)]
t = [400 – 270] / [80 / √12]
t = 130 / [80 / 3.46]
t = 5.622
You can use t table calculator to calculate these values conveniently. If you need to perform a T-Test, use our T-Test calculator here.
A T distribution differs from the normal distribution by its degrees of freedom. A distribution used to test a hypothesis about a population mean when the population standard deviation is not known, the sample size is small, and the normal distribution is assumed for the sample mean.