# Chi Square Formula

The Chi-square formula is used in the Chi-square test to compare two statistical data sets. Chi-Square is one of the most useful non-parametric statistics. The Chi-Square test is used in data consist of people distributed across categories, and to know whether that distribution is different from what would expect by chance.

• A very small Chi-Square test statistic means that your observed data fits your expected data extremely well.
• A very large Chi-Square test statistic means that the data does not fit very well. If the chi-square value is large, you can reject the null hypothesis.

Chi-Square is one way to show a relationship between two categorical variables. There are two types of variables in statistics: numerical variables and non-numerical variables. The value can be calculated by using the given observed frequency and expected frequency.

## Formula for Chi-Square Test

The Chi-Square is denoted by Ï‡2 and the formula is:

 Ï‡2 = âˆ‘ (O âˆ’ E)2 / E

Where,

• O = Observed frequency
• E = Expected frequency
• âˆ‘ = Summation
• Ï‡2 = Chi-Square value

### Solved Example

Question: Calculate the chi-square value for the following data:

 Male Female Full Stop 6(observed) 6.24 (expected) 6 (observed) 5.76 (expected) Rolling Stop 16 (observed) 16.12 (expected) 15 (observed) 14.88 (expected) No Stop 4 (observed) 3.64 (expected) 3 (observed) 3.36 (expected)

Solution:

Now calculate Chi Square using the following formula:

Ï‡2 = âˆ‘ (O âˆ’ E)2 / E

Calculate this formula for each cell, one at a time. For example, cell #1 (Male/Full Stop):

Observed number is: 6
Expected number is: 6.24

Therefore, (6 – 6.24)2 /6.24 = 0.0092

Continue doing this for the rest of the cells, and add the final numbers for each cell together to get the final Chi-Square number. There are 6 total cells, so at the end, you should be adding six numbers together for your final Chi-Square number.