# [Rasch] Differential Item Functioning: Help Needed

Mike Linacre rmt at rasch.org
Wed Feb 6 23:49:18 EST 2013

```Svend and folks:

The DIF nomogram is a mathematical abstraction based on cross-plotting a
series of known Reference group sizes and computed Focal group sizes.
Each Focal group size is computed using an inverse Student's t-test with
known significance (.05), known DIF, equal group variances on the item
(based on an item with dichotomous p-value of 80%) and known Reference
group size. See "Unequal sample sizes, equal variance" on
http://en.wikipedia.org/wiki/Student%27s_t-test#Unequal_sample_sizes.2C_equal_variance

Person error and other ambiguities are incorporated into the group
variances. These will be specific to each situation, so the nomogram is
based on (hopefully) reasonably general values of the variances.

According to the nomogram,  0.25 logits DIF between Reference and Focal
groups requires at least 2 times 1500 persons.
0.5 logits DIF between Reference and Focal groups requires at least 2
times 300 persons.

OK?

Mike L.

On 2/6/2013 3:28 AM, Svend Kreiner wrote:
> Hard to say Mike, we need a little more information, e.g.:
>
> What kind of DIF test are you using? Different test may have very different power and may therefore require different sample sizes.
>
> How many items are you using in addition to the DIF item? The number of items has a strong effect on the error of person estimates and therefor also on the power of tests using these estimates (like, for instance, the DIF test in RUMM). Are you assuming that the number of items is infinite so that we have person estimates without error and bias.
>
> What do you mean by "DIF at 80%"?
>
> Best regards
>
> Svend
>
> PS it looks to me as if you need about 2 times 500 persons to disclose DIF equal to 0.25. Is that right? And if that is correct we can say good bye to small samples.

```