Solution to question 10.2
First we need to calculate the expected values:
Radiographer 2 | ||||
Unacceptable | Acceptable | Total | ||
Radiographer 1 | Unacceptable | 185·2 | 57·8 | 243 |
Acceptable | 109·8 | 34·2 | 144 | |
Total | 295 | 92 | 387 |
So the observed proportion of agreement was:
(230 + 79) ÷ 387 = 0·798
And the expected proportion of agreement was:
(185·2 + 34·32) ÷ 387 = 0·567
So, using the formula:
We get:
κ = (0·798 - 0·567) ÷ (1 - 0·567) = 0·53
Note that we round to two decimal places at the end. There is no real point in calculating κ more precisely than this.
Referring to the table in the lecture notes we can see that this value of κ indicates that there is moderate agreement between the two radiographers.