Response String
Easy............Hard
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INFIT Mean-square
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OUTFIT Mean-square
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Point-measure correlation
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Diagnosis
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I. modeled:
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33333132210000001011
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0.98
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0.99
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0.78
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Stochastically
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31332332321220000000
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0.98
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1.04
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0.81
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monotonic in form
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33333331122300000000
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1.06
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0.97
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0.87
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strictly monotonic
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33333331110010200001
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1.03
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1
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0.81
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in meaning
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II. overfitting (muted):
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33222222221111111100
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0.18
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0.22
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0.92
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Guttman pattern
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33333222221111100000
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0.31
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0.35
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0.97
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high discrimination
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32222222221111111110
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0.21
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0.26
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0.89
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low discrimination
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32323232121212101010
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0.52
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0.54
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0.82
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tight progression
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III. limited categories:
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33333333332222222222
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0.24
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0.24
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0.87
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high (low) categories
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22222222221111111111
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0.24
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0.34
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0.87
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central categories
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33333322222222211111
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0.16
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0.2
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0.93
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only 3 categories
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IV. informative-noisy:
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32222222201111111130
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0.94
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1.22
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0.55
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noisy outliers
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33233332212333000000
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1.25
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1.09
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0.77
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erratic transitions
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33133330232300101000
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1.49
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1.4
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0.72
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noisy progression
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33333333330000000000
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1.37
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1.2
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0.87
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extreme categories
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V. non-informative:
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22222222222222222222
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0.85
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1.21
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0
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one category
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12121212121212121212
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1.5
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1.96
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-0.09
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central flip-flop
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01230123012301230123
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3.62
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4.61
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-0.19
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rotate categories
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03030303030303030303
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5.14
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6.07
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-0.09
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extreme flip-flop
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03202002101113311002
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2.99
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3.59
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-0.01
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random responses
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VI. contradictory:
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11111122233222111111
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1.75
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2.02
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0
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folded pattern *
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11111111112222222222
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2.56
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3.2
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-0.87
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central reversal
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22222222223333333333
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2.11
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4.13
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-0.87
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high reversal
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00111111112222222233
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4
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5.58
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-0.92
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Guttman reversal
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00000000003333333333
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8.3
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9.79
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-0.87
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extreme reversal
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from Smith R.M. (1996) Rasch Measurement Transactions 10:3 p. 516
The z-score standardized statistics 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.
* "folded data" can often be rescued by imposing a theory of "not reached" and "already passed" on to the observations. For instance, in archaeological analysis, the absence of bronze implements can mean a "stone age" or an "iron age" society. A useful recoding would be "1" = "stone age", "2" = "early bronze", "3" = "bronze", "2=>4" = "late bronze", "1=>5" = "iron age". This can be done iteratively to obtain the most self-consistent set of 4's and 5's. (Folding is discussed in Clive Coombes' "A Theory of Data".)
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