Dichotomous mean-square fit statistics

For a general introduction, see Diagnosing Misfit, also Polytomous mean-square fit statistics.

 

Person Responses to Items:

Easy--Items--Hard

Diagnosis of Pattern

Person

OUTFIT MnSq

Person

INFIT MnSq

Point-Measure

Correlation

111¦0110110100¦000

Modeled/Ideal

1.0

1.1

0.62

111¦1111100000¦000

Guttman/Deterministic

0.3

0.5

0.87

000¦0000011111¦111

Miscoded

12.6

4.3

-0.87

011¦1111110000¦000

Carelessness/Sleeping

3.8

1.0

0.65

111¦1111000000¦001

Lucky Guessing

3.8

1.0

0.65

101¦0101010101¦010

Response set/Miskey

4.0

2.3

0.11

111¦1000011110¦000

Special knowledge

0.9

1.3

0.43

111¦1010110010¦000

Imputed outliers *

0.6

1.0

0.62

Right¦Transition¦Wrong

 

 

 

 

 

high - low - high

OUTFIT sensitive to outlying observations

>>1.0 unexpected outliers

>>1.0 disturbed pattern

 

 

low - high - low

INFIT sensitive to pattern of inlying observations

<<1.0 overly predictable outliers

<<1.0 Guttman pattern

 

* as when a tailored test (such as a Binet intelligence test) is scored by imputing all "right" responses to un administered easier items and all "wrong" responses to un administered harder items. The imputed responses are indicated by italics


 

The exact details of these computations have been lost, but the items appear to be uniformly distributed about 0.4 logits apart, extracted from Linacre, Wright (1994) Rasch Measurement Transactions 8:2 p. 360

 

The ZSTD Z-score standardized Student's t-statistic report, as unit normal deviates, how likely it is to observe the reported mean-square values, when the data fit the model. The term Z-score is used of a t-test result when either the t-test value has effectively infinite degrees of freedom (i.e., approximates a unit normal value) or the Student's t-statistic value has been adjusted to a unit normal value.

 

Item Responses by Persons:

High-Person-Ability-Low

Diagnosis of Pattern

Item

OUTFIT MnSq

Item

INFIT MnSq

Point-Measure

Correlation

111¦0110110100¦000

Modeled/Ideal

1.0

1.1

0.62

111¦1111100000¦000

Guttman/Deterministic

0.3

0.5

0.87

000¦0000011111¦111

Miscoded

12.6

4.3

-0.87

011¦1111110000¦000

Carelessness/Sleeping

3.8

1.0

0.65

111¦1111000000¦001

Lucky Guessing

Response set

3.8

1.0

0.65

000¦0010010001¦110

Miskey

4.0

2.3

0.11

111¦1010110010¦000

Imputed outliers *

0.6

1.0

0.62

111¦0101010101¦000

Low discrimination

1.5

1.6

0.46

111¦1110101000¦000

High discrimination

0.5

0.7

0.79

111¦1111010000¦000

Very high discrimination

0.3

0.5

0.84

Right¦Transition¦Wrong

 

 

 

 

 

high - low - high

OUTFIT sensitive to outlying observations

>>1.0 unexpected outliers

>>1.0 disturbed pattern

 

 

low - high - low

INFIT sensitive to pattern of inlying observations

<<1.0 overly predictable outliers

<<1.0 Guttman pattern

 

* as when a tailored test (such as a Binet intelligence test) is scored by imputing all "right" responses to un administered easier items and all "wrong" responses to un administered harder items. The imputed responses are indicated by italics



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