October 2007 Volume 10 Number 4 - Educational Technology ...

2
(7) MNSQ = ∑WniZ ni ∑ Wni = ν i
n n
13
(8) Zstd = ti = ( ν i − 1(3/ ) qi) + ( qi
/3) where = ∑( − ) ∑
q C W ( W )
2 2 2
i ni ni ni
n n
Figure 2. JMLE procedures for estimating both ability and item parameters
Table 1 lists the principles to distinguish examinees and items from unexpected responses, summarized by Bond and
Fox (2001), and Linacre and Wright (1994). The acceptable range for MNSQ is between 0.75 and 1.3, and the Zstd
value should be in the range (-2, +2). Person and item fitness outside the range are considered unexpected responses.
Incorporating the calculation module in the online testing system is helpful for curriculum designers to maintain the
quality of test items by modifying or removing test items with unexpected responses.
Table 1. Fit statistics
MNSQ Zstd Variation Misfit Type
>1.3 >2.0 Too much Underfit