T Value (Critical Value) Calculator

T critical value calculator is used to calculate the critical value of t using a degree of freedom and significance level alpha.

What is the t distribution table?

The 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 t distribution".

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.

How to find the critical value of t?

Example :Find critical value

Let’s calculate the value of t without using the t & z value calculator.

Solution

Follow these steps to calculate the t value using the 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

Verify the values using our critical value of the t calculator.

T Distribution Table

A T distribution differs from the normal distribution by its degrees of freedom. A distribution is 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. 

Use the following t critical value table (t score table) for calculating the t value using t table.