The row and column totals of the observed frequencies are
2.0-2.5 | 2.5-3.0 | 3.0-3.5 | 3.5-4.0 | Total | |
No 2nd Year | 38 | ||||
No 3rd Year | 31 | ||||
Return for 3rd Year | 120 | ||||
Total | 80 | 17 | 36 | 56 | 189 |
The numbers in the right margin are called the row totals while the numbers in the bottom margin are called the column totals . Now, calculate the relative frequency distribution of row totals. This is called the marginal distribution for the rows, or the marginal attrition distribution in this case.
2.0-2.5 | 2.5-3.0 | 3.0-3.5 | 3.5-4.0 | Total | |
No 2nd Year | 38 (20.1%) | ||||
No 3rd Year | 31 (16.4%) | ||||
Return for 3rd Year | 120 (63.5%) | ||||
Total | 80 | 17 | 36 | 56 | 189 (100%) |
If the two variables are independent, then we expect the attrition
distribution for each column to be the same.
Extrapolating the marginal attrition distribution to each column,
we get the following expected frequencies