1. It's a goodness of fit. You compare a table
| i | ... | ... | l |
j | nij | | | Lj |
... | | | | |
... | | | | |
c | Ci | | | n |
To a table with eij being each cell's Lj×Ci÷n
Then
\(\chi^2=\sum_i^l\sum_j^c{(n_{ij}-e_{ij})^2\over e_{ij}}\)
OR if there is a eij <=5
\(\chi^2=\sum_i^l\sum_j^c{(|n_{ij}-e_{ij}|-.5)^2\over e_{ij}}\)
ie using the Yates correction
A right tail area < alpha rejects H0 , left tail < alpha means the fit is TOO GOOD.
Cheating in results?