# [Rasch] Fwd: Reliability, separation and strata

Fabio La Porta fabiolaporta at mail.com
Wed Mar 1 04:14:15 AEDT 2017

```Hi guys,
I have calibrated a clinical scale using a right skewed calibration sample
(mean person ability: +2.796 logits), which reflects the distribution of
the population to which the scale is administered in real life.

After some post-hoc modifications, the scale has fitted the Rasch model.

The reported reliability coefficient by RUMM (PSI) was 0.867, corresponding
to the following separation statistics:

- G (separation ratio)=2.553
- H (ability strata)=3.738

These values, based on the assumption that the sample follows a normal
distribution, were calculated using the formulas specified in
http://www.rasch.org/rmt/rmt94n.htm

However, in view of the skewed distribution of the sample, I also
calculated the number of statistically distinct levels of performance (G)
using the method suggested in http://www.rasch.org/rmt/rmt144k.htm
in which it is made use of individual estimates and standard errors to
calculate the separation ratio (G) for any given total score value.

Using this method, a completely different picture emerged. Particularly,
the 'new' reliability estimates and coefficients calculated were:

- G (separation ratio)=7
- reliability=0.980
- H (ability strata)=9.667

In other words, unlike to what suggested by the classic method, the scale
seems to have an excellent reliability and separation capability.

So here are my two questions:

1) given the striking difference in values (and clinical meaning) between
the classic method and the second method to what extent can we trust the
first method to calculate G and H? In other words, are there any studies
suggesting when to start using the second method in lieu of the classic
method?

2) So far, I have always reported H, but in practical terms, it is easier
to divide the range of measurement according to the calculated G, as in the
attached table. Thus, I am now a bit confused about the difference between
G and H. Considering that these two statistics give different values, when
is it is useful to trust one rather than the other?

Fabio

TotSc / ExpVal

Location

Std Error

Minimum measure for next level

Separation index (G)

0.143

-6.312

1.41

1

1

-5.157

1.04

-2.814

1

2

-4.335

0.83

-3.039

1

3

-3.751

0.72

-3.146

1

4

-3.294

0.65

-3.208

1

5

-2.913

0.6

-3.246

2

6

-2.581

0.57

-1.259

2

7

-2.282

0.54

-1.294

2

8

-2.007

0.52

-1.319

2

9

-1.748

0.51

-1.338

2

10

-1.501

0.5

-1.350

2

11

-1.261

0.49

-1.359

3

12

-1.027

0.49

0.119

3

13

-0.795

0.48

0.115

3

14

-0.566

0.48

0.111

3

15

-0.339

0.48

0.108

3

16

-0.114

0.48

0.105

3

17

0.109

0.48

0.105

4

18

0.333

0.48

1.454

4

19

0.558

0.48

1.457

4

20

0.787

0.48

1.460

4

21

1.019

0.48

1.464

4

22

1.253

0.49

1.468

4

23

1.489

0.49

1.472

5

24

1.726

0.49

2.879

5

25

1.966

0.5

2.889

5

26

2.215

0.51

2.906

5

27

2.478

0.53

2.933

5

28

2.765

0.56

2.970

5

29

3.088

0.59

3.022

6

30

3.457

0.63

4.817

6

31

3.884

0.69

4.907

6

32

4.399

0.78

5.049

6

33

5.089

0.96

5.345

6

33.809

6.015

1.31

5.969

7
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