Effect Size (Definition, Formula)

What is Effect Size?

Effect size is one of the concepts in statistics which calculates the power of a relationship amongst the two variables given on the numeric scale and there are three ways to measure the effect size which are the 1) Odd Ratio, 2) the standardized mean difference and 3) correlation coefficient.

For example suppose in a class of students with boys and girls if the average height of all the boys is greater than the average height of all the girls then with the help of effect size we can make out that whether the difference in the height is moderate, high or not as much. It is also applicable for various statistical applications like correlation.

It is measured in order to find out the strength of the relation of two variables. It is standardized when it is calculated in order to be able to compare the two variables. The effect size is calculated by dividing the difference between the mean of two variables with the standard deviation.

Effect Size Formula

The formula is given below

Effect Size = (µ1-µ2)/α

Examples

Let’s see some simple to advanced examples to understand it better.

Example #1

Let us try to understand the concept with the help of an example. Suppose a class has 12 boys and 12 girls. And the mean height of the boys of the class is 120 cm and the mean height of the girls of that class is 115 cm. Then we can say in a normalized way that the difference is 5 cm. But this does not quantify the effect as this number of 5cm difference is not standardized. Let us say the standard deviation for the two populations in this example is 4 then we can calculate the effect size with the help of the formula.

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Use the following data for the calculation.

Therefore, the calculation will be as follows,

=(120-115)/4

In order to get a sense of the effect of the difference between the two variables we need to divide the difference between the two means of the two sets of the variables with their standard deviation number

From the calculation, we can see that the effect size is 1.3. With the help of this value, we can find out the shape of the distribution and also figure out how much percentage of the population falls under that percentage.

Example #2

Let us try to understand the concept with the help of another example. Suppose a class has 10 boys and 10 girls. And the mean GPA of the boys in the class is 2.64 and the mean GPA of the girls of that class is 3.64. Then we can say in a normalized way that the difference is 1. But this does not quantify the effect as this number of 1 difference is not standardized. Let us say the standard deviation for the two populations in this example is 2 then we can calculate the effect size with the help of the equation.

Use the following data for the calculation of effect size

Therefore, the calculation will be as follows,

=2.64-3.64/2

Example #3

Let us try to understand the concept with the help of another example. Suppose a class has 10 boys and 10 girls. And the mean weight of boys in the class is 60kg and the mean weight of girls in a class is 55 kg. Then we can say in a normalized way that the difference is 5kg. But this does not quantify the effect as this number of 5 kg difference is not standardized. Let us say the standard deviation for the two populations in this example is 3 then we can calculate the effect size with the help of the formula.

Below is given data for calculation of effect size.

Therefore, it can be calculated as follows,

=(60-55)/2

Effect Size Formula Calculator

You can use the following calculator.

μ1
μ2
α
Effect Size Formula

α =

μ1 − μ2
	=
α

0−0
	=	0
0

Relevance and Uses

Effect size is a very important statistical tool. It is a method to measure the relationship between two variables. It is used to find out how much the strength of the relationship between the two variables is. With the help of this value, we can find out the shape of the distribution and also figure out how much percentage of the population falls under that percentage.

You can download this Effect Size Formula Excel Template from here – Effect Size Formula Excel Template

Effect Size