Table 33.1, 33.2 Differential group functioning DGF pairwise 
This Table identifies Differential Group Functioning DGF interactions between classificationgroups of persons (identified by DIF=, referencing the person labels) and classificationgroups of items (identified by DPF=, referencing the item labels) using the column selection rules. Differential average classificationgroup performance (DGF) is powerful when looking for latent classes among the persons. Differential bundle functioning (DBF) is powerful when looking for local dependence among the items. For more details, see Table 30 (DIF) and Table 31 (DPF). A graphing technique can be used to display DIF item characteristic curves for nonuniform DIF.
Table
33.1 DGF report (paired person classes on each item class)
33.2 DGF report (paired item classes on each person class)
33.3 DGF report (list of person classes within item class)
33.4 DPF report (list of item classes within person class)
We put a code in the person label of every person indicating whether the person belongs to the Control Group, "C", or the Treatment Group, "T". The column for this code is the Differential Item Functioning DIF= column. Then, if we want a report for every item, it is a DIF analysis, Winsteps Table 30.
If we want to group items, then we put a code in the item label of every item which indicates the item group to which the item belongs. The column for this code is the Differential Person Functioning, DPF= column. Then, if we want a report for every person, it is a DPF analysis, Winsteps Table 31.
If we want to do "person group" with "item group" . Then this is DGF (Differential Group Functioning). Person DIF= column and Item DPF= column, Winsteps Table 33.
DGF analysis: the logodds model for an individual person in the group and item in the group is:
log(Pni1/Pni0) = Bgn  Dhi  Mgh
where
Bgn is the overall estimate from the main analysis of the ability of person n (who is in group DIF g)
Dhi is the overall estimate from the main analysis of the difficulty of item i (which is in DPF group h)
Mgh is the interaction (bias, DGF) for person group g on item group h. This is estimated from all persons in group g combined with all items in group h.
The DGF dialog displays when Table 33 is called from the Output Tables or Plots menus.
Table 33.1
DGF CLASSLEVEL BIAS/INTERACTIONS FOR DIF=@GENDER AND DPF=$S1W1

 PERSON DGF DGF DGF PERSON DGF DGF DGF DGF JOINT RaschWelch ITEM 
 CLASS SCORE SIZE S.E. CLASS SCORE SIZE S.E. CONTRAST S.E. t d.f. Prob. CLASS 

 F .00 .06 .28 M .01 .16 .27 .22 .39 .57 452 .5708 1 
 F .01 .18 .50 M .00 .00 .61 .18 .79 .23 101 .8208 2 
 F .04 .50 .83 M .04 .76 1.04 1.26 1.33 .95 32 .3484 3 
 F .01 .00< 3.00 M .01 .00< 2.40 .00 3.84 .00 32 1.0000 4 
 M .01 .16 .27 F .00 .06 .28 .22 .39 .57 452 .5708 1 
 M .00 .00 .61 F .01 .18 .50 .18 .79 .23 101 .8208 2 
 M .04 .76 1.04 F .04 .50 .83 1.26 1.33 .95 32 .3484 3 
 M .01 .00< 2.40 F .01 .00< 3.00 .00 3.84 .00 32 1.0000 4 

The most important numbers in Table 33.1: The DGF CONTRAST is the difference in difficulty of the item between the two groups. This should be at least 0.5 logits for DGF to be noticeable. "Prob." shows the probability of observing this amount of contrast by chance, when there is no systematic item bias effect. For statistically significance DGF on an item, Prob. ≤ .05.
Table 33.2
DGF CLASSLEVEL BIAS/INTERACTIONS FOR DIF=@GENDER AND DPF=$S1W1

 ITEM DGF DGF DGF ITEM DGF DGF DGF DGF JOINT RaschWelch PERSON 
 CLASS SCORE SIZE S.E. CLASS SCORE SIZE S.E. CONTRAST S.E. t d.f. Prob. CLASS 

 1 .00 .06 .28 2 .01 .18 .50 .24 .57 .42 119 .6774 F 
 1 .00 .06 .28 3 .04 .50 .83 .56 .87 .64 30 .5261 F 
 1 .01 .16 .27 2 .00 .00 .61 .16 .67 .24 100 .8097 M 
 1 .01 .16 .27 3 .04 .76 1.04 .92 1.07 .86 25 .3973 M 
 2 .01 .18 .50 1 .00 .06 .28 .24 .57 .42 119 .6774 F 
 2 .01 .18 .50 3 .04 .50 .83 .32 .97 .33 39 .7420 F 
This Table contrasts, for each item class, the size and significance of the Differential Item Functioning for pairs of person classifications.
DGF class specification defines the columns used to identify DGF classifications, using DIF= and DPF=, see the selection rules.
Reading across the Table 33.1 columns:
PERSON CLASS identifies the CLASS of persons specified with DIF=, e.g., the first here is CLASS is "F".
DGF estimates with the the iterativelogit (RaschWelch) method:
DGF SCORE is the average response scorepoint difference between the observed and the expected scores for this PERSON CLASS on this ITEM CLASS. Higher scores mean locally higher ability or locally lower difficulty.
DGF SIZE is the differential difficulty of this item (scaled by USCALE=) for this class, with all else held constant, e.g., .07 is the relative difficulty for Kid Class F on Item Class1. The more difficult, the higher the DGF measure.
.52> reports that this measure corresponds to an extreme maximum personclass score. EXTRSCORE= controls extreme score estimate.
1.97< reports that this measure corresponds to an extreme minimum personclass score. EXTRSCORE= controls extreme score estimate.
6.91E reports that this measure corresponds to an item with an extreme score, which cannot exhibit DIF
DGF S.E. is the standard error of the DGF SIZE (scaled by USCALE=).
PERSON CLASS identifies the CLASS of persons, e.g., the second CLASS is "M".
DGF SCORE is the average response scorepoint difference between the observed and the expected scores for this PERSON CLASS on this ITEM CLASS.
DGF SIZE is the differential difficulty of this item for this class, with all else held constant, e.g., .15 is the relative difficulty for Kid Class M on Item Class1. The more difficult, the higher the DGF measure.
DGF S.E. is the standard error of the second DGF SIZE.
DGF CONTRAST is the difference between the two DGF SIZE, i.e., size of the DGF across the two classifications of persons, e.g., .07  .15 = .23 (usually in logits). A positive DGF contrast indicates that the item is more difficult for the first, lefthandlisted CLASS. See details in Table 33.3.
JOINT S.E. is the standard error of the DGF CONTRAST = sqrt(first DIF S.E.² + second DIF S.E.²), e.g., .38 = sqrt(.27² + .27²)
t gives the DGF significance as a Student's tstatistic = DGF CONTRAST / JOINT S.E. The ttest is a twosided test for the difference between two means (i.e., the estimates) based on the standard error of the means (i.e., the standard error of the estimates). The null hypothesis is that the two estimates are the same, except for measurement error.
d.f. is the joint degrees of freedom. This is shown as the sum of the sizes of two classifications (see Table 33.3 less 2 for the two measure estimates, but this estimate of d.f. is somewhat high, so interpret the ttest conservatively, e.g., d.f. = (426 A + 1 D  2) = 425. When the d.f. are large, the t statistic can be interpreted as a unitnormal deviate, i.e., zscore.
INF means "the degrees of freedom are so large they can be treated as infinite", i.e., the reported tvalue is a unit normal deviate.
Prob. is the twosided probability of Student's t. See tstatistics.
ITEM CLASS is the item classification specified by DPF=. Here the first ITEM CLASS is "1"
Each line in the Table is repeated with the PERSON CLASSes in reversed order.
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