# [Rasch] Invariance

Trevor Bond trevor.bond at jcu.edu.au
Thu Jan 5 23:41:50 EST 2006

```Dear Rama

your simple question has many components, but for a simple answer to this:
Question 1: What is the test of invariance for the item measures?
Have they really remained invariant within the allowable range of
error?
A simple spreadsheet as shown at the end of Chapter 5 of Bond and Fox
(2001) provides the steps for doing the calculations and plotting the
results.

best wishes
Trevor
At 5:50 PM +0530 5/1/06, Rama Guinda wrote:
>Dear All,
>I have a question. Thanks for any reaction to my problem.
>I Rasch analysed 4 polytomous items with the Winsteps. The items
>where 4 texts each with 20 gaps to be filled by the test-takers. In
>order to avoid the problem of local dependence I considered each
>text a super item. I had 160 cases.
>The item measures are .74, .06, -.29 and -.50.
>Then I divided the group into two (a high ability and a low ability
>group) on the basis of a  reading test which contains 14
>dichotomously scored items. Students with scores from 0 to 7 went
>into the low ability group and the ones with scores from 8 to 14
>went into the high ability group. The reading test has a significant
>but low correlation with the gap fill task (.53).
>I had 98 cases in the low ability group and 62 cases in the high
>ability group. To study the item invariance I separately analysed
>the data for each group.
>The item measures for the low ability group are: .62, .10, -.25, -.47.
>The item measures for the high ability group are: .94, .02, -.38, -.58.
>The order of the difficulty of the items remains the same in all three groups.
>Question 1: What is the test of invariance for the item measures?
>Have they really remained invariant within the allowable range of
>error?
>
>Best
>Rama
>
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--
Trevor G BOND Ph D
Educational Psychology, Counselling & Learning Needs
D2-2F-01A EPCL Dept.
Hong Kong Institute of Education
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