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Table 3 Estimates of proportion observed, proportion expected and agreement measures, by scenarios

From: Observer agreement paradoxes in 2x2 tables: comparison of agreement measures

Scenario

Type of table

Po

Pe

k ^

B ^

PABAK

AC 1 ^

α ^

Δ ^

Δ ^ a + 1

Paradox 1:

         

1

Symmetrical balance

.85

.50

.70

.72

.70

.70

.70

.68

.68

2

Symmetrical imbalance

.85

.78

.32

.82

.70

.81

.55

.69

.68

3

Perfect symmetrical imbalance

.90

.905

-.05

.895

.80

.89

-

.78

.77

Paradox 2:

P O set at 0.60

         

4

Symmetrical imbalance

.60

.54

.13

.41

.20

.27

.15

.21

.20

5

Asymmetrical imbalance

.60

.46

.26

.4

.20

.21

.33

.32

.31

6

Perfect symmetrical imbalance

.60

.52

.17

.38

.20

.23

.18

.19

.19

7

Asymmetrical imbalance

.60

.475

.24

.42

.20

.23

.32

.32

.31

8

Asymmetrical imbalance

.60

.48

.23

.38

.20

.20

.25

.24

.24

 

P O set at 0.90

         

9

Perfect symmetrical imbalance

.90

.82

.44

.88

.80

.88

.68

.78

.77

10

Symmetrical imbalance

.90

.62

.74

.85

.80

.84

-

.83

.82

 

P O low (≤50%)

         

11

Perfect symmetrical balance

.50

.50

0

.25

0

0

0

0

0

12

Asymmetrical imbalance

.50

.50

0

.26

0

-.11

0

.01

.01

13

Perfect symmetrical balance

.40

.50

-.20

.16

-.20

-.20

-

-.19

-.19

14

Perfect symmetrical balance

.10

.50

-.80

.01

-.80

-.80

-.18

-.77

-.77