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Solution to question 10.2

First we need to calculate the expected values:

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:

Formula for kappa

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.

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