Top

Chi Square Calculator
Top
 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 valueO = Observed frequency for each category E = Expected frequency for each category.

## Step by Step Calculation

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

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

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

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