In Table 30.1 - the hypothesis is "this item has the same difficulty for two groups"
In Table 30.2, 30.3 - the hypothesis is "this item has the same difficulty as its average difficulty for all groups"

In Table 30.4 - the hypothesis is "this item has no overall DIF across all groups"

 

Table 30.4 summarizes the CLASS Differential Item Functioning statistics for each item shown in Table 30.2. Table 30.2 shows a t-statistic for each CLASS. These are summarized as chi-square statistics for each item, indicating whether the observed DIF within each item is due to chance alone. The null hypothesis is that the DIF is statistically zero across the classes.

 

DIF class specification is: DIF=@GENDER

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| KID        SUMMARY DIF               BETWEEN-CLASS       TAP                   |

| CLASSES    CHI-SQUARE   D.F.  PROB.  MEAN-SQUARE t=ZSTD  Number Name           |

|--------------------------------------------------------------------------------|

|       2         .8772      1  .3490       .4398  -.0367       6 3-4-1          |

|       2        2.2427      1  .1342      1.1995   .6040       7 1-4-3-2        |

|       2        1.9207      1  .1658       .9794   .4567      13 1-4-3-2-4      |

|       0         .0000      0 1.0000       .0000   .0000      18 4-1-3-4-2-1-4  |

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KID CLASSES is the count of person CLASSES with estimable DIF for the item.

SUMMARY DIF CHI-SQUARE is the sum of the squared normalized t-statistic values from Table 30.2.

Example: In Table 30.2, the t-statistics for item 13 are -1.07 and 0.94. Then chi-square = 1.07² + 0.94² = 2.03 ≈ 1.9207 with 2 CLASSES, i.e., 1 d.f.

D.F. is the degrees of freedom, the count of CLASSES contributing to the chi-square less 1.

PROB. is the probability of the chi-square. Values less than .05 indicate statistical significance.

 

BETWEEN-CLASS are the Between-Group Fit Statistics (Smith & Plackner, 2009) is testing the hypothesis: "The dispersion of the group measures accords with Rasch model expectations."

MEAN-SQUARE is chi-square divided by its degrees of freedom. It is the size of the misfit (expectation = 1.0, overfit <1.0, underfit >1.0).

t=ZSTD is the significance of the MEAN-SQUARE standardardized as a unit-normal deviate (t-statistic with infinite degrees of freedom).

 

TAP is the item. Number is the item entry number. Name is the item label.

 

Item-Trait Chi-Square

The values in Table 30.4 are equivalent to the item-trait chi-square statistics reported by RUMM with DIF=MA3 (or however many strata are chosen in RUMM). In RUMM, the trait CLASSes are obtained by ordering the persons by measure, omitting extreme scores, and dividing the ordered list as equally as possible into equal size classes, including all persons with the same measure in the same class.