Effect Size Formula with Problem Solution & Solved Example

The objective of an effect size formula is to compare the two given observations. It is suitable to generate multiple outputs from the comparison of two sets of information.it is also good to forecast or predict many possibilities by a quick comparison. Firstly, you should calculate the mean of observations and subtract the second value from the first.

Also, calculate the standard deviations for both the observations and calculate the square values too. Now plug the values into formula as given below and find the Cohen’s index as needed.

\[\LARGE d \; = \; \frac{M_{1}-M_{2}}{\sqrt{\frac{S_{1}^{2}+S_{2}^{2}}{2}}}\]

From this Cohen’s index, you can calculate the effect-size coefficient by putting the values into formula given below –

\[\LARGE r \; = \; \frac{d}{\sqrt{d^{2}+4}}\]

Where,
d = Cohen’s index
M1 = Mean of first observation.
M2 = Mean of second observation.
S1 = Standard deviation of first observation.
S2 = Standard deviation of second observation.
r = Effect-size coefficient.

Effect size is the statistical approach that is needed to measure the strength or relationship between two variables in a numerical scale. Take an example, if you wanted to calculate the relationship between height of men and height of women then difference between two would the effect size. T

he concept is frequently used for real-life situations by statisticians and denoted by the symbol small r.The value of r generally lies between -1 and +1. The value of effect size can be used to research on population size. There are different methods for finding the effect size and you can use any of them based on the requirements.


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