# Effect Size Calculator

Effect size is a concept that evaluates the strength on a numerical scale between two variables. Effect size helps us in determining whether the difference is real or due to a change in factors.

## What is an Effect Size Calculator?

An 'Effect Size Calculator' is a free online tool that calculates the effect size between two data sets. In this calculator, you can enter the data sets and the effect size along with mean and standard deviation will be calculated within a few seconds.

## How to Use Effect Size Calculator?

Follow the steps given below to use the calculator:

**Step 1:**Enter the data sets (separated by comma) in the input box.**Step 2:**Click on**"Calculate"**to find the effect size.**Step 3:**Click on**"Reset"**to clear the field and enter new values.

## How to Find an Effect Size?

To calculate the effect size, we will be using Cohen's d effect size, also known as the difference between the means of two datasets and divided by the standard deviation from the data. The formula is shown below

**d = (x̅ _{1} - x̅_{2}) / s_{pooled}**

**and s _{pooled} = √ [ {s_{1}^{2} + s_{2}^{2}} / 2 ]**

**Therefore, d =** {**(x̅ _{1} - x̅_{2}) ×**

**√2} / √ {s**

_{1}^{2}+ s_{2}^{2}}**and r (effect size) = d / √(d ^{2} + 4)**

Here, d = Cohen's d effect size.

x̅_{1 }and x̅_{2} are the means of two data sets.

r is the effect size of the two data sets.

s_{1 }and s_{2} are the standard deviations of two data sets.

**Solved Example:**

What will be the effect size of the given two datasets (2, 4, 5, 8) and (4, 5, 8, 10)

**Solution:**

Mean of first dataset = 4.75

Mean of second dataset = 6.75

The standard deviation of the first dataset = 2.165

The standard deviation of the second dataset = 2.385

Now, Cohen's d effect size = {(x̅_{1} - x̅_{2}) × √2} / √ {s_{1}^{2} + s_{2}^{2}}

d = {(4.75 - 6.75) × √2} / √ {(2.165)^{2} + (2.385)^{2}}

d = (-2 × 1.414) / √10.37545

d = -2.828 / 3.221

d = - 0.878

and r = d / √(d^{2} + 4)

r = - 0.402

Thus, the effect size of the given data set is - 0.402

Similarly, you can use the calculator for the following:

What will be the effect size of the given two datasets (23, 46, 58, 80) and (42, 54, 87, 30)

What will be the effect size of the given two datasets (1, 7, 9, 10) and (3, 5, 6, 10)

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