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
