# [Rasch] A little puzzle

Stuart Luppescu s-luppescu at uchicago.edu
Fri May 25 07:05:44 EST 2007

```Hello, I have a little puzzle. I'm equating two forms of a test given in
the fall and spring. Each consists of two different tasks. The equating
design is common people: one group of students took the fall and spring
forms at the same time. So, the equating calibration is a simultaneous
calibration of the data from all four tasks.

At a colleague's suggestion, I calibrated each of the four tasks
separately and compared the item difficulties. The item difficulties
from the separate-by-task calibrations correlate with the item
difficulties from simultaneous calibration on the order 0.97 to 0.999.
But the puzzling thing is that the standard deviations of the items in
the simultaneous calibration is consistently lower than in the separate
calibration.

Fall                          Spring
Sep          Simultaneous        Sep          Simultaneous
___________     ____________       __________    _____________
Task A   2.04          1.71               1.67           1.21
Task B   3.12          1.75               2.13           1.85

Can anyone explain to me why this should be?

Thanks.
--
Stuart Luppescu -=-=- slu <AT> ccsr <DOT> uchicago <DOT> edu
CCSR at U of C ,.;-*^*-;.,  ccsr.uchicago.edu
(^_^)/    才文と智奈美の父
Thank God I'm an atheist!
--
Stuart Luppescu -=-=- slu <AT> ccsr <DOT> uchicago <DOT> edu
CCSR at U of C ,.;-*^*-;.,  ccsr.uchicago.edu
(^_^)/    才文と智奈美の父
Thank God I'm an atheist!

```

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