Chi-square formula

About Chi-square formula

The Chi-square test compares two statistical data sets using the Chi-square formula. One of the most useful non-parametric statistics is Chi-Square. To find out, the chi-square test is utilised, whether a distribution of people distributed across categories differs from what would be expected by chance.

A low Chi-Square test score indicates that your observed data closely matches your expected data.

The data does not fit well if the Chi-Square test statistic is very large. The null hypothesis can be rejected if the chi-square value is large.

One technique to show a relationship between two categorical variables is to use Chi-Square. In statistics, there are two sorts of variables: numerical and non-numerical variables. Using the above observed and expected frequencies, the value can be determined.

Chi-Square Calculation Formula

The Chi-Square is denoted by χ2and the formula is: χ2= ∑ (O − E)2/ E

Where,

O = Observed frequency

E = Expected frequency

∑ = Summation

χ2= Chi-Square value

Solved Example of Chi-square formula

Example: For the following data, compute the chi-square value:

  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)

Sol: Calculate Chi Square using the formula below.:

χ2= ∑ (O − E)2/ E

Calculate this formula one by one for each cell. For instance, consider cell #1 (Male/Full Stop):

The observed number is: 6
The expected number is: 6.24

Therefore, (6 – 6.24)2/6.24 = 0.0092

Carry on like this for the remaining cells, then add the final numbers for each cell to get the final Chi-Square number. There are six total cells, so your final Chi-Square number should be the sum of those six integers. To get all the Maths formulas check out the main page. 

Pdf of Chi-square formula

Chi-square formula

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