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Effect Size Calculator
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The calculation of effect size of a population is an important one when we compare the two different experimental methods. Since it is an unavoidable measurement effect size calculator is used for the determination of the value. We can calculate the effect size using t-test,mean and standard deviation etc. Here we mentioned about the effect size determination using mean and standard deviation. The equation is given by,

r =
$\frac{d}{\sqrt{d^{2}+4}}$


Where r is the effect size
          d is the cohen's d value. d can be calculated using the given equation

         d=$\frac{m_{1}-m_{2}}{\sqrt{\frac{\sigma_{1}^{2}+\sigma _{2}^{2}}{2}}}$

         m1,m2 are the mean values
         σ1,σ2 are the standard deviations
 

Steps for Effect Size Calculator

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Step 1 :  

Find the value of mean from the given data using the below equation.

m=$\frac{x_{1}+x_{2}+x_{3}+........}{N}$

Where x1,x2,x3..... are the given observations and N is the total number of observations.




Step 2 :  

Calculate standard deviation of the given observations using the given expression.

$\sigma$ =$\sqrt{\frac{1}{N}\sum_{i=1}^{n}(x_{i}-m)^{2}}$




Step 3 :  

Determine the cohen's d value by substituting the values of mean and standard deviation in the given equation.

d=$\frac{m_{1}-m_{2}}{\sqrt{\frac{\sigma_{1}^{2}+\sigma _{2}^{2}}{2}}}$




Step 4 :  

Calculate the effect size by substituting the value of d in the given expression.

r=$\frac{d}{\sqrt{d^{2}+4}}$



Problems on Effect Size Calculator

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  1. The salary of three employees in two different companies are given below. Calculate the effect size?

    Company1: 10000, 12500, 11000

    Company2: 13000, 9000, 14000


    Step 1 :  

    We know the equation for mean value is,


    m=$\frac{x_{1}+x_{2}+x_{3}+........}{N}$


    Mean for first data


    m1=$\frac{33500}{3}$=11166.66


    Mean for second data


    m2=$\frac{36000}{3}$=12000



    Step 2 :  

    The equation for standard deviation is


    $\sigma$ =$\sqrt{\frac{1}{N}\sum_{i=1}^{n}(x_{i}-m)^{2}}$


    For first observation,


    $\sum_{i=1}^{n}(x_{i}-m)^{2}$=1361095.5556+177779.5556+27775.5556=3166666.6668


    $\sigma _{1}$=$\sqrt{\frac{1}{3}\times 3166666.6668}$=1027.4023


    For second observation,


    $\sum_{i=1}^{n}(x_{i}-m)^{2}$=1000000+9000000+4000000=14000000


    $\sigma _{2}$=$\sqrt{\frac{1}{3}\times 14000000}$=2160.2468



    Step 3 :  

    d value can be calculated by using the given equation,


    d=$\frac{m_{1}-m_{2}}{\sqrt{\frac{\sigma_{1}^{2}+\sigma _{2}^{2}}{2}}}$


    d=$\frac{11166.66-12000}{\sqrt{\frac{1027.4023^{2}+2160.2468^{2}}{2}}}$


    d=$\frac{-833.34}{1691.4818}$=-0.4926



    Step 4 :  

    The effect size is given by,


    r=$\frac{d}{\sqrt{d^{2}+4}}$


    r=$\frac{-0.4926}{\sqrt{(-0.4926)^{2}+4}}$


    r=$\frac{-0.4926}{2.0597}$=-0.2391



    Answer  :  

    The effect size of the given data is

     

    r=-0.2391



  2. The rate of four fruits in two different shops are given below. Determine the effect size?

    Shop1: 30, 50, 65, 40

    Shop2: 45, 50, 60, 55


    Step 1 :  

    Mean for first data


    m1=$\frac{185}{4}$=46.25


    Mean for second data


    m2=$\frac{210}{4}$=52.5



    Step 2 :  

    The equation for standard deviation is


    $\sigma$ =$\sqrt{\frac{1}{N}\sum_{i=1}^{n}(x_{i}-m)^{2}}$


    For first observation,


    $\sum_{i=1}^{n}(x_{i}-m)^{2}$=264.0625+14.0625+351.5625+39.0625=668.75


    $\sigma _{1}$=$\sqrt{\frac{1}{4}\times 668.75}$=12.9301


    For second observation,


    $\sum_{i=1}^{n}(x_{i}-m)^{2}$=56.25+6.25+56.25+6.25=125


    $\sigma _{2}$=$\sqrt{\frac{1}{4}\times 125}$=5.5901



    Step 3 :  

    d value can be calculated by using the given equation,


    d=$\frac{m_{1}-m_{2}}{\sqrt{\frac{\sigma_{1}^{2}+\sigma _{2}^{2}}{2}}}$


    d=$\frac{46.25-52.5}{\sqrt{\frac{12.9301^{2}+5.5901^{2}}{2}}}$


    d=$\frac{-6.25}{9.9608}$=-0.6274



    Step 4 :  

    The effect size is given by,


    r=$\frac{d}{\sqrt{d^{2}+4}}$


    r=$\frac{-0.6274}{\sqrt{(-0.6274)^{2}+4}}$


    r=$\frac{-0.6274}{2.0960}$=-0.2993



    Answer  :  

    The effect size of the given data is

     

    r=-0.2993



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