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 χ2 and the formula is:
| χ2 = ∑ (O − E)2 / E |
Where,
- O = Observed frequency
- E = Expected frequency
- ∑ = Summation
- χ2 = 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:
χ2 = ∑ (O − 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.
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