Chi-Square test application 1:
Test Goodness of a fit.
We use the goodness of a fit to test if the observed categorical data follows the hypothesized or expected distribution.
Example 1: P-value Interpretation
Suppose f_exp are the expected number of boys in grade 1 different classes. f_obs are the observed number of boys in grade 1. We want to see if f_obs is the same as the f_exp distribution.
H0(Null Hypotheses): the observation boy students distribution is consistent with the expected distribution.
Boy Students Distribution
| 18 | 10 |
| 15 | 5 |
| 5 | 7 |
| 8 | 18 |
| 4 | 10 |
| 3 | 11 |
We use the following python code to acquire the p-value:
Chisquare(f_obs=[18,15,5,8,4,3], f_exp=[10,5,7,18,10,11])
For this particular example, the p-value=6.02e-08, which is significantly smaller than 0.05. So we reject H0,and conclude the observed boy students distribution is Different from the Expected boy distributions.
Example 2: Data visualization Interpretation
We will graph a Chi-square distribution with degree 5 and size 1000, and use Kernel Density Estimation to fit the graph. We can see this is a pretty good fit.
To be continue…..