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Chi Square Calculator
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Chi Square Calculator (or Chi Square Test Calculator or Chi Squared Calculator) is an online tool used to test the cumulative probability on the basis of chi-square statistics, which is used to find out whether the distribution of given category variables are differ from one another or not.
chi-square value can be calculated when observed frequency and expected frequency of a corresponding data is known. Chi square is denoted by $\chi^{2}$ Chi-Square Test Formula
$\chi^{2}$ = $\sum$ $\frac{(O - E)^{2}}{E}$
where,
$\chi^{2}$ = Chi-square value
O = Observed frequency for each category
E = Expected frequency for each category.


 

Step by Step Calculation

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Step 1 :  

Observed the given observed frequency and expected frequency.



Step 2 :  

To find the chi-square value, apply the formula


chi-square value($\chi^{2}$) = $\sum$ $\frac{(O - E)^{2}}{E}$
where,
$\chi^{2}$ = Chi-square value
O = Observed frequency for each category
E = Expected frequency for each category.



Example Problems

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  1. Calculate the chi-square value, if observed frequency is 5 and expected frequency is 10?


    Step 1 :  

    Given observed frequency = 5
    and expected frequency = 10



    Step 2 :  

    chi-square value($\chi^{2}$) = $\frac{(5 - 10)^{2}}{10}$
    $\chi^{2}$ = $\frac{(-5)^{2}}{10}$


    $\chi^{2}$ = $\frac{25}{10}$


    $\chi^{2}$ = 2.5



    Answer  :  

    chi-square value($\chi^{2}$) = 2.5



  2. Calculate the chi-square value for the following data.

             Color Red Green Yellow
    Observed Frequency  15  10  20
    Expected Frequency  20  5  30


    Step 1 :  

    So, for the color red: (Observed frequency - Expected frequency)2 = (15 - 20)2 = 25


    So, for the color green: (Observed frequency - Expected frequency)2 = (10 - 5)2 = 25


    So, for the color yellow: (Observed frequency - Expected frequency)2 = (20 - 30)2 = 100



    Step 2 :  

    Chi-square value for the color red: $\frac{(O - E)^{2}}{E}$


    $\Rightarrow$ $\frac{25}{20}$


    $\Rightarrow$ 1.25


    Chi-square value for the color green: $\frac{(O - E)^{2}}{E}$


    $\Rightarrow$ $\frac{25}{5}$


    $\Rightarrow$ 5


    Chi-square value for the color yellow: $\frac{(O - E)^{2}}{E}$


    $\Rightarrow$ $\frac{100}{30}$


    $\Rightarrow$ 3.333


    So, the chi-square value for the given data is given by = 1.25 + 5 + 3.333



    Answer  :  

    chi-square value($\chi^{2}$) = 9.58300



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