# T-Test Calculator - T-Distribution Critical Values Table

To use the T-Test Calculator, enter two sets of numbers, and click calculate button

Give Us Feedback

## T-Test Calculator

T-Test Calculator is used to evaluate the T-value using the value of two data sets and also provides a Step-by-Step solution to every problem.

## What is meant by T-value?

The t-value is a statistical measure that is used in hypothesis testing to determine the significant difference between the means of two groups of datasets. It represents the difference between the means of two groups and the relative variability or variation of each group.

### Formula:

T-Value = {Mean (x) - Mean (y)} / √(var (x) / n1) + (var (y) / n2)

Where,

• n1 = total number or element of the first data set.
• n2 = total number or element of the second data set.
• var(x) = variance of a 1st dataset.
• var(y) = variance of a 2nd dataset.

## How to find a t-test?

Example 1:

If the two data sets are given as {2, 5, 10, 12} and {1.6, 13, 23, 2.04} then calculate the T-value.

Solution:

Step 1:

Write the data.

T-Value =?, x = {2, 5, 10, 12}, y = {1.6, 13, 23, 2.04}

Step 2:

Write the Formula of the T-value.

T-Value = {Mean (x) - Mean (y)} / √(var (x) / n1) + (var (y) / n2)

Where, n1 = total number or element of the first data set.

n2 = total number or element of the second data set.

var(x) = variance of a 1st dataset.

var(y) = variance of a 2nd  dataset.

Step 3:

Now find the mean and variance of both datasets.

Mean for Dataset x.

x = 2+5+10+124

x = 7.250

Variance for Dataset x.

 xi xi - X (xi - X)2 2 -5.25 27.56 5 -2.25 5.06 10 2.75 7.56 12 4.75 22.56 ∑ xi = 29.00 ∑ (xi - X)2 = 62.74

Variance = s2 = ∑ (xi - X)2/(n-1)

Now put the values in the above formula.

Variance = s2 = 62.744/3

Variance = s2 = 20.91

Variance = s2 = 20.91

Mean for Dataset y.

Y = 1.6+13+23+2.044

Y = 9.910

Variance for Dataset y.

 yi yi - Y (yi - Y)2 1.6 -8.31 69.06 13 3.09 9.55 23 13.09 171.35 2.04 -7.87 61.94 ∑ yi = 39.64 ∑ (yi - Y)2 = 311.90

Variance = s2 = ∑ (yi - Y)2/n-1

Now putting values in the above formula.

Variance = s2 = 311.904 /3

Variance = s2 = 103.97

Variance = s2 = 103.97

Step 4:

Now put all values in the formula of step 2 to evaluate the T-Value.

T-Value = {Mean (x) - Mean (y)} / √(var (x) / n1) + (var (y) / n2)

T-Value = {7.25 – 9.91} / √(20.91)/4) + (103.97) /4)
T-Value = {- 2.66} / √(5.33) + (25.99)

T-Value = - 2.66/5.59

T-Value = - 0.48

T-Value = -0.48