Chi Square Formula
Chi Square is one of the most useful non-parametric statistics. Chi Square 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 reject the null hypothesis.
A 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. The Chi Square is denoted by X^{2} and the formula is:
\[\LARGE X^{2}=\sum \frac{(O-E)^{2}}{E}\]
O = Observed frequency
E = Expected frequency
$\sum$ = Summation
$X^{2}$ = Chi Square value
Solved Examples
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:
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, $\frac{(6-6.24)^{2}}{6.24} = 0.0092$
Continue doing this for the rest of the cells, and add the final numbers for each cell together for the final Chi Square number. There are 6 total cells, so at the end you should be adding six numbers together for you final Chi Square number.