Minitab displays two chisquare statistics.
Pearson chisquare statistic:
Likelihoodratio chisquare statistic:
If any cell has an expected frequency less than one, the pvalue for the test is not displayed because the results may not be valid. If some cells have small expected frequencies, consider combining or omitting row and/or column categories.
Yates' correction for 2 x 2 tables is not used.
Term  Description 

O_{ij}  observed frequency in cell (i, j) 
E_{ij}  expected frequency for cell (i, j)

r  number of rows 
c  number of columns 
The expected count is the frequency that would be expected in a cell, on average, if the variables are independent. Minitab calculates the expected counts as the product of the row and column totals, divided by the total number of observations.
Term  Description 

n_{i+}  number of observations in the i^{th} row 
n_{+j}  number of observations in the j^{th} column 
n_{++}  total number of observations 
Raw residual = O_{ij} – E_{ij}
Term  Description 

O_{ij}  observed frequency in cell (i, j) 
E_{ij}  expected frequency for cell (i, j) 
Term  Description 

O_{ij}  observed frequency in cell (i, j) 
E_{ij}  expected frequency for cell (i, j) 
Term  Description 

O_{ij}  observed frequency in cell (i, j) 
E_{ij}  expected frequency for cell (i, j) 
n_{i+}  number of observations in the i^{th} row 
n_{+j}  number of observations in the j^{th} column 
n_{++}  total number of observations 
The contribution to the χ^{2} statistic from each cell is:
Term  Description 

O_{ij}  observed frequency in cell (i, j) 
E_{ij}  expected frequency in cell (i, j) 