### Author Topic: Item Separation Index in ConQuest?  (Read 991 times)

#### ug

• Newbie
• Posts: 1
##### Item Separation Index in ConQuest?
« on: February 20, 2019, 10:24:54 AM »
Dear ConQuest community,
In order to estimate the number of item strata (H) of a scale with dichotomously coded items according to Wright & Masters (1982, p. 92) I would like to calculate the item separation index (G). In ConQuest's documentation (manual, command reference, tutorials) I can't find any information about this index or its parts (adjusted item standard deviation and root mean square calibration error). Does anyone know a way to have ConQuest provide these measures? Is it possible to derive them from the item separation reliability?
Many thanks in advance!
Best regards,
Urs

#### dan_c

• Administrator
• Jr. Member
• Posts: 76
##### Re: Item Separation Index in ConQuest?
« Reply #1 on: February 21, 2019, 03:58:39 AM »
...
I would like to calculate the item separation index (G). ...
Is it possible to derive them from the item separation reliability?

Hi Urs,

ACER ConQuest doesn't produce an item separation index, but it is related to the item separation reliability.

Check out this link: https://www.rasch.org/rmt/rmt63i.htm

You can see here that the relationship between the separation reliability and index is given by:

Separation Ratio = G = (True SD)/(RMSE)

Separation Reliability = R = (True SD)^2/(Observed SD)^2

where (True SD)^2 = (Observed SD)^2 - (RMSE)^2

and therefore:

R = G^2/(1+G^2)

and with a bit of algebra, you can approximate G = sqrt(R/(1-R))

And if you compare with the reported values in the table in the link above, you can see it's pretty close:

 R G G = sqrt(R/(1-R)) 0 0 0.00 0.5 1 1.00 0.7 1.5 1.53 0.8 2 2.00 0.9 3 3.00 0.94 4 3.96