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IQ Score Interpretations in Atkins Cases




              Kevin S. McGrew, PhD

                        Director
       Institute for Applied Psychometrics (IAP)
Additional info re:
Kevin McGrew and IAP
 can be found at the
MindHub™ web portal

www.themindhub.com
For additional information and to stay current (ICDP blog)




                        www.atkinsmrdeathpenaltly.com
ICDP




            ….




….               ….
ICDP
ICDP
ICDP
IQ Score Interpretations in Atkins Cases




A recently successful Atkins case (state agreed to LWOP a few weeks
  prior to evidentiary hearing) is bases of presentation but will be
           augmented with information from other cases
Case involved the Flynn Effect:
But we will not be covering today

Recommended article (more at ICDP
            blog)




             ICDP
“Outliers” –
    why?


State expert built argument around the
WAIS-R scores being the best estimates of
defendants true intelligence (underlying
“You can’t fake bad” strategy ) and
dismissed other scores as most likely due to
malingering—arguments not based on
sound and reliable methods of science

State expert failed in professional due
diligence to consider scientific based
explanations of the consistencies and
inconsistencies in the complete collection
of scores
Median of all = 68




                                     It is statistically or
                                     mathematically inappropriate
                                     to compute the arithmetic
                                     average (mean) of IQ scores.
                                     The median is
                         Strong      acceptable, under certain
                     convergence     circumstances
                     of indicators
                                     The only way to compute an
                                     average (mean) IQ score is to
                                     use a complex equation that
                                     incorporates the reliabilities
                                     of all scores and the
                                     intercorrelations among all
                                     scores

                                     Median is acceptable metric
Fundamental Issue: Comparability
          (Exchangeability) of IQ Scores




Intellectual Functioning: Conceptual Issues
       Kevin S. McGrew and Keith F. Widaman

   AAIDD Death Penalty Manual Chapter (in preparation)
Fundamental Issue: Comparability of IQ Scores


     “Not all scores obtained on intelligence tests
 given to the same person will be identical”
 (AAIDD, 2010, p. 38)

     The global (full scale) IQ from different tests are
 frequently similar…Other times the IQ scores will
 be markedly different…a finding that often produces
 consternation for examiners and recipients of
 psychological reports
Fundamental Issue: Comparability of IQ Scores




Floyd et al. (2008) used generalizability theory methods to evaluate IQ-
IQ exchangeability across ten different IQ battery global composite g-
score composites (comprised of 6 to 14 individual tests) across
approximately 1,000 subjects
Fundamental Issue: Comparability of IQ Scores




             Average (mdn) r = .76 – lets round to .80

Coefficient of determination r2 x 100 = 64 % shared variance



                    Test A           Shared
  .r = .80                          common
                                     abilities
              Test B
Fundamental Issue: Comparability of IQ Scores


                        Test A      Shared
        .r = .80                   common
                                    abilities
                   Test B




                   “psychologists can anticipate that 1 in 4
             individuals taking an intelligence test battery
             will receive an IQ more than 10 points
             higher or lower when taking another
             battery”



Floyd et al. (2008)
The standard error of the difference (SEdiff)
   must be used to ascertain if the scores in
         question are reliably different
           SEdiff = 15 x SQRT[2 - r11 - r22]



                Test A reliability    = .95
                Test B reliability    = .93

       1 SEdiff (68 % confidence)      = 5.2 points
       2 SEdiff (95 % confidence)      = 10.4 points

Before interpreting the scores from these two IQ tests as
 being significantly difference, an IQ-IQ difference of at
           least 10+ points would be required



 Easier way via use of confidence band rule-of-thumb
e.g., WAIS-R score            The higher
The standard error of                   differences represent
 the difference (SEdiff)                                                   WAIS-R
                                       reliable differences with
confidence band rule-                    all other obtained IQ           scores is a
       of-thumb                                   scores                scientifically
                                                                         based fact
                                                                        in this case.
                                    e.g., Not                            One needs
                                      sign.                               to accept
                                    different                              and to
                                   from each
                                                                        explain why.
                                      other


                            e.g., None of          If 95 % SEM confidence bands
                            these 6 tests          for compared scores do not
                              are sign.            touch, the difference is likely a
                           different from          reliable difference and
                            one another            hypotheses about the difference
                                                   should be enteratined

                                                   If 95 % SEM confidence bands
                                                   for compared scores
                                                   overlap, then the difference is
                                                   likely not a reliable difference
                                                   and should not generate
                                                   significant hypotheses about
                                                   score differences.
IQ-IQ score differences: Scientific
            hypotheses that warrant exploration




• Test administration or scoring errors
• Practice effects
• Malingering / effort
• Norm obsolescence (Flynn effect)
                                                Today will focus only
• Content differences between different tests     on select topics –
  or different revisions of the same test        only those relevant
• Little known psychometric problems with       to this example case
                                                  and some of the
  some of the “gold standards”                   more unknown or
• Individual/situational factors for person        misunderstood
                                                        issues
  or specific test session
Unscientific IQ-IQ score difference
                    hypthoses I have seen or read




                                   Will focus only on
                                  select topics – esp.
                                 those relevant to the
Voodoo psychometrics               example case and
                                   some of the more
                                      unknown or
                                 misunderstood issues
Outliers – why?

Most likely scientific explanations in this case

 Ability content differences between different
tests or different revisions of the same test

     •“Drilling down” further – changes in g-
     loadings/saturation of subtests included
     on WAIS-R and WAIS-III/IV
High g
IQ test battery subtest
                                T1      Intelligence test battery
g-loadings or saturation                Individual test g (general
                                T2
                                        Intelligence) loadings
                                T3
  General intelligence (g)              Derived from factor analysis
                                T4
                                        Think of a general
                                        intelligence pole that is
                                T5      saturated with more g-ness
                                        (like magnetism) at the top
                                T6      and less g-ness at the
                                        bottom.
                                T7
                                        Factor analysis orders the
                                T8      tests on the pole based on
                                        their saturation of g-ness
                                T9

                                T10

                             Low g


                             Subtests
WISC/WISC-R/WAIS/WAIS-R MR/ID subtest g-loading pattern research

              Also astounding is the study-by-study consistency in the subtests that emerge as
              “easy” (Picture Completion, Object Assembly, Block Design) or “hard”
              (Arithmetic, Vocabulary, Information) for diverse samples of retarded populations




(Kaufman, 1979, p.203)




                                                                               (28 studies)
Plot of ________ 1988 and 1993 WAIS-R Subtest Scaled Scores by g (general intelligence) loadings


                                             16
                                             15                                                                    1988 WAIS-R
                                                                                                                   1993 WAIS-R
     ________ WAIS-R subtest scaled scores




                                             14
                                                                                                                                            High subtest
                                             13                                                                                             scaled score
                                                                 PicA
                                             12
                                             11           Dig
                                                          Spn                PicC
                                             10                                     BlkD
                                                    Dig
                                              9     Sym                                    Arith
                                              8
                                                                                                   Cmp
                                              7                 Ob                                   Sim           Voc
                                                                Asm
                                              6                                                            Info

                                              5
                                              4                                                                                             Low subtest
                                             0.55                     0.65                 0.75                   0.85             0.95     scaled score

                                                                WAIS-R Subtest g (general intelligence loadings
                                                                          (Kaufman, 1990, p. 253)
                                                                                                                           High g: More
Low g: less cognitively
                                                                                                                            cognitively
  abstract/complex
                                                      (Fair or moderate g)          (Good or high g)                     abstract/complex
Plot of _________WAIS-R Subtest Scaled Scores by g (general intelligence) loadings

Rank-order correlation of ___ 1993 WAIS-R                                                                Rank-order correlation of ___ 1988 WAIS-R
  subtest scores test g-loadings is -.71.                                                                  subtest scores test g-loadings is -.68.
                                                 16
                                                 15                                                                    1988 WAIS-R
      ___________ WAIS-R subtest scaled scores


                                                                                                                       1993 WAIS-R
                                                 14
                                                                                                                                                High subtest
                                                 13                                                                                             scaled score
                                                                     PicA
                                                 12
                                                              Dig
                                                                                                       This is a form of internal
                                                 11                              PicC
                                                              Spn                                  convergence validity evidence for
                                                 10
                                                        Dig
                                                                                        BlkD                   MR/ID Dx
                                                  9     Sym                                    Arith
                                                  8
                                                                                                       Cmp
                                                  7                 Ob                                   Sim           Voc
                                                                    Asm
                                                  6                                                            Info

                                                  5
                                                  4                                                                                             Low subtest
                                                 0.55                     0.65                 0.75                   0.85             0.95     scaled score

                                                                    WAIS-R Subtest g (general intelligence loadings
                                                                              (Kaufman, 1990, p. 253)
                                                                                                                               High g: More
 Low g: less cognitively
                                                                                                                                cognitively
   abstract/complex
                                                          (Fair or moderate g)          (Good or high g)                     abstract/complex
Plot of _________WAIS-R Subtest Scaled Scores by g (general intelligence) loadings

Dropped from battery in WAIS-IV revision                                                    Eliminated from FS IQ in WAIS-IV revision (supplemental subtest)

                                                   16
                                                   15                                                                    1988 WAIS-R
         __________ WAIS-R subtest scaled scores


                                                                                                                         1993 WAIS-R
                                                   14
                                                                                                                                                  High subtest
                                                   13                                                                                             scaled score
                                                                       PicA
                                                   12
                                                   11           Dig
                                                                Spn                PicC
                                                   10                                     BlkD
                                                          Dig
                                                    9     Sym                                    Arith
                                                    8
                                                                                                         Cmp
                                                    7                 Ob                                   Sim           Voc
                                                                      Asm
                                                    6                                                            Info

                                                    5
                                                    4                                                                                             Low subtest
                                                   0.55                     0.65                 0.75                   0.85             0.95     scaled score

                                                                      WAIS-R Subtest g (general intelligence loadings
                                                                                (Kaufman, 1990, p. 253)
                                                                                                                                 High g: More
    Low g: less cognitively
                                                                                                                                  cognitively
      abstract/complex
                                                            (Fair or moderate g)          (Good or high g)                     abstract/complex



Eliminated from FS IQ in WAIS-III revision (supplemental subtest) & dropped from battery in WAIS-IV revision
The WAIS-III/IV batteries include more complex tests (than the WAIS-R) and are
                   better indicators of general intelligence




               The state expert would not recognize (continued to ignore)
               this scientific fact and held on to the WAIS-R scores as the
               most accurate – the rest of lower scores due to malingering
Outliers – why?



 Most likely scientific explanations in
                this case

• Ability content differences
  between different tests or
  different revisions of the same test

• Little known psychometric
  problems with some of the “gold
  standards”
CHC IQ Test Batteries DNA Fingerprints
The publisher, in both the WAIS-III/WAIS-IV manuals, describes changes in abilities
  measured to improve the battery to be consistent with contemporary research




                        The state expert would not recognize (continued to ignore)
                        this scientific fact and held on to the WAIS-R scores as the
                        most accurate – the rest of lower scores due to malingering
Recommended article re: CHC theory of intelligence

               (Many more at ICDP blog)
Continuum of Progress: Intelligence Theories and the Evolution of the Wechsler Adult IQ Battery

      General           Dichotomous              Multiple                        Multiple                        Multiple
      Ability (g)         Abilities          Cognitive Abilities             Cognitive Abilities             Cognitive Abilities
                                           (Incomplete; not implicitly       (Incomplete; implicitly          (“Complete”; implicitly
                                           or explicitly CHC-organized     or explicitly CHC-organized          or explicitly CHC-
                                                                                                                    organized


       g

Broad Abilities



      Spearman           Original Gf-Gc     Thurstone PMAs                                                Cattell-Horn-Carroll (CHC)
                                                                                                         Theory of Cognitive Abilities



                                                                                                             CHC is now considered
                                                                                                              to be the consensus
                    W-B (1939; 1946)                                                                         model of the structure
                     WAIS-R (1981)        WAIS-III (1997)          WAIS-IV (2008)                                of intelligence




  The WAIS-III and WAIS-IV revisions made the battery more consistent with contemporary neurocognitive and
  intelligence research. They are more valid indicators of general intelligence (supported by WAIS-III/IV tech
  manuals and independent reviews) than the older WAIS-R.

  The changes in abilities measured from the WAIS-R to the WAIS-III/IV help explain the WAIS-R “outlier” scores

  The WAIS-IV should not be considered “the gold standard” as per the consensus CHC model of intelligence.
Continuum of Progress: Intelligence Theories and the Wechsler Adult IQ Battery
      General           Dichotomous              Multiple                        Multiple                        Multiple
      Ability (g)         Abilities          Cognitive Abilities             Cognitive Abilities             Cognitive Abilities
                                           (Incomplete; not implicitly       (Incomplete; implicitly          (“Complete”; implicitly
                                           or explicitly CHC-organized     or explicitly CHC-organized          or explicitly CHC-
                                                                                                                    organized


       g

Broad Abilities



    Spearman             Original Gf-Gc     Thurstone PMAs                                                Cattell-Horn-Carroll (CHC)
                                                                                                         Theory of Cognitive Abilities



                                                                                                       The revisions made to
                    W-B (1939; 1946)
                     WAIS-R (1981)        WAIS-III (1997)         WAIS-IV (2008)                      other IQ batteries (with
                                                                                                      adult norms SB and WJ)
                                                                                                           also changed the
                                                                                                        composition of their
                                                                                                     composite IQ scores and is
      Stanford-
      Binet LM                              SB-IV (1986)                        SB-V(2003)             a likely source of score
     (1937; 1960;                                                                                     differences that must be
        1972)
                                                                                                              considered


                                             WJ (1977)                                                               WJ III (2001)
                                                                                               WJ-R (1989)            WJ III NU (2005)
Continuum of Progress: Intelligence Theories and the Wechsler Adult IQ Battery
      General           Dichotomous              Multiple                        Multiple                        Multiple
      Ability (g)         Abilities          Cognitive Abilities             Cognitive Abilities             Cognitive Abilities
                                           (Incomplete; not implicitly       (Incomplete; implicitly          (“Complete”; implicitly
                                           or explicitly CHC-organized     or explicitly CHC-organized          or explicitly CHC-
                                                                                                                    organized


       g

Broad Abilities



    Spearman             Original Gf-Gc     Thurstone PMAs                                                Cattell-Horn-Carroll (CHC)
                                                                                                         Theory of Cognitive Abilities




                    W-B (1939; 1946)                                                                     Knowing the ability
                                          WAIS-III (1997)         WAIS-IV (2008)
                     WAIS-R (1981)                                                                    coverage similarities and
                                                                                                      differences is important
                                                                                                        when comparing and
                                                                                                     understanding possible IQ-
      Stanford-                                                                                      IQ differences between the
      Binet LM                              SB-IV (1986)                        SB-V(2003)             latest versions of these
     (1937; 1960;
        1972)                                                                                                  batteries


                                             WJ (1977)                                                               WJ III (2001)
                                                                                               WJ-R (1989)            WJ III NU (2005)
Continuum of Progress: Intelligence Theories and the Wechsler Adult IQ Battery
      General           Dichotomous              Multiple                        Multiple                        Multiple
      Ability (g)         Abilities          Cognitive Abilities             Cognitive Abilities             Cognitive Abilities
                                           (Incomplete; not implicitly       (Incomplete; implicitly          (“Complete”; implicitly
                                           or explicitly CHC-organized     or explicitly CHC-organized          or explicitly CHC-
                                                                                                                    organized


       g

Broad Abilities



    Spearman             Original Gf-Gc     Thurstone PMAs                                                Cattell-Horn-Carroll (CHC)
                                                                                                         Theory of Cognitive Abilities




                    W-B (1939; 1946)                                                                     IQ-IQ score difference
                     WAIS-R (1981)        WAIS-III (1997)         WAIS-IV (2008)                       explanations may require
                                                                                                    knowledge of across and within
                                                                                                         battery revision ability
                                                                                                    coverage understanding. There
                                                                                                      are many possible scenarios
      Stanford-                                                                                       when there is a history of IQ
      Binet LM                              SB-IV (1986)                        SB-V(2003)          testing within the same battery
     (1937; 1960;
        1972)
                                                                                                        system or across battery
                                                                                                                systems


                                             WJ (1977)                                                               WJ III (2001)
                                                                                               WJ-R (1989)            WJ III NU (2005)
Continuum of Progress: Intelligence Theories and Test Batteries

                                                       General              Dichotomous            Multiple                        Multiple                            Multiple
                                                       Ability (g)            Abilities        Cognitive Abilities             Cognitive Abilities                 Cognitive Abilities
                                                                                             (Incomplete; not implicitly       (Incomplete; implicitly             (“Complete”; implicitly
                                                                                             or explicitly CHC-organized     or explicitly CHC-organized         or explicitly CHC-organized



                                                       g

                         Broad Abilities
                          (Neuropsych. Psychometric)
Primary Theories




                                                           Spearman       Original Gf-Gc      Thurstone PMAs                                 Cattell-Horn Carroll (CHC)
                                                                                                                                            Theory of Cognitive Abilities

                                                                          Simultaneous-              PASS
                                                                            Successive        (Planning, Attention,
                                                                                            Simultaneous, Successive)


                                                                                               WJ (1977)                                         WJ-R (1989)             WJ III (2001)
                                                                                                                                                                           WJ III NU (2005)
                                                        Stanford-                               SB-IV (1986)                       SB-V(2003)
  Applied IQ Batteries




                                                        Binet LM
                                                       (1937; 1960;
                                                          1972)       WPPSI-R (1989)       WPPSI-III (2002)                                                  When childhood and adult
                                                                                                                    WISC-IV (2003)
                                                                       WISC-R (1974)        WISC-III 1991)                                                 battery scores are available the
                                                                      W-B (1939; 1946)                              WAIS-IV (2008)
                                                                                           WAIS-III (1997)                                                     interpretation of IQ-IQ
                                                                       WAIS-R (1981)                                                                          differences due to ability
                                                                                                                                                           coverage differences becomes
                                                                                                                                                                 even more complex
                                                                        K-ABC (1983)                                            KABC-II (2004)
                                                                         KAIT (1993)
                                                                                                CAS (1997)
                                                                                                DAS (1990)                      DAS-II (2007)
Knowledge of CHC ability coverage critical       TONI-2/
        when brief special purpose           Ravens/ 100% Gf
 (e.g., nonverbaI) IQ scores are reported
The state expert argued that some of
                        the lower subtest scores (after the
                        WAIS-R’s) was further evidence of
                                   malingering




Voodoo psychometrics
State expert argued
  that variability in
  Wechsler subtest
 scores, esp. lower
 scores post-Atkins
 were obvious sign
   of malingering
  …thus supporting
the conclusion that
 the WAIS-R scores
    were the best
estimate of general
     intelligence

   The implied
 “You can’t fake
smart” strategy or
  interpretation
There is an EXTREME amount of variability in the professional expertise
   in IQ subtest profile interpretation: Scientific/psychometric vs.
                  “clinical” lore-based interpretation




                          VS
Recall the standard error of the difference
  (SEdiff) must be used to ascertain if the
 scores in question are reliably different
Plot of ___________WAIS-R & WAIS-III Similarities scores (+- 95 SEM) - Range of 4

                  20
                  19
                  18
                  17
                  16
                  15
                  14
   Scaled score




                  13
                                                             95% SEM band (median = +- 1.7)
                  12
                  11
                  10
                  9
                  8
                  7
                  6
                                                             Average (median = 5.0)
                  5
                  4
                  3
                  2
                  1
                  0
              6

              8

              0

              2

              4

              6

              8

              0

              2

              4

              6

              8

              0
            98

            98

            99

            99

            99

            99

            99

            00

            00

            00

            00

            00

            01
          1,

          1,

          1,

          1,

          1,

          1,

          1,

          2,

          2,

          2,

          2,

          2,

          2,


                           Date

                                                         No statistically reliable
                                                       difference across all scores
Plot of ______________WAIS-R & WAIS-III Comprehension scores (+- 95 SEM) - Range of 4


                       20
                       19
                       18
                       17
                       16
                       15
                       14
        Scaled score



                       13                                   95% SEM band (median = +- 2.3)
                       12
                       11
                       10
                       9
                       8
                       7
                       6
                                                             Average (median = 5.5)
                       5
                       4
                       3
                       2
                       1
                       0
                   6

                   8

                   0

                   2

                   4

                   6

                   8

                   0

                   2

                   4

                   6

                   8

                   0
                 98

                 98

                 99

                 99

                 99

                 99

                 99

                 00

                 00

                 00

                 00

                 00

                 01
               1,

               1,

               1,

               1,

               1,

               1,

               1,

               2,

               2,

               2,

               2,

               2,

               2,
                              Date


                                                        No statistically reliable
                                                      difference across all scores
Plot of __________ WAIS-R, WAIS-III & WAIS-IV Digit Span scores (+- 95 SEM) – Range of 7

                          20
                          19
                          18         As reported in WAIS-R tech. manual, DS has poor
                          17
                          16
                                     reliability (mdn = .81) – 4th weakest in battery. Thus
                          15         some variability to be expected. And, the WAIS-IV
                          14
                                     DS is a three-component and not two component
           Scaled score



                          13
                          12         test—so they are not measuring the SEM band (median = +- 1.9)
                                                                        95% exact same
                          11
                          10
                                     construct
                          9
                          8
                          7
                          6
                                                                          Average (median = 5.5)
                          5
                          4
                          3
                          2
                          1
                          0
                      6

                      8

                      0

                      2

                      4

                      6

                      8

                      0

                      2

                      4

                      6

                      8

                      0
                    98

                    98

                    99

                    99

                    99

                    99

                    99

                    00

                    00

                    00

                    00

                    00

                    01
                  1,

                  1,

                  1,

                  1,

                  1,

                  1,

                  1,

                  2,

                  2,

                  2,

                  2,

                  2,

                  2,
                                         Date

                               7 point difference                        There is a scientific
                                                                            explanation
Plot of ________WAIS-R, WAIS-III & WAIS-IV Picture Completion scores (+- 95 SEM) - Range of 6


                            On the WAIS-RWAIS-III revision. “Only 50% of the content of Picture
                            Completion and Picture Arrangement was retained from the WAIS-R, and only
                       20
                       19
                            60 % of the Object Assembly items were retained. In addition, the correlations
                       18   between WAIS-R and WAIS-III version of these subtests are relatively low (r’s of
                       17
                            .59 - .63)” ------ 35 – 40 % shared variance
                       16
                       15
                       14
                       13
   (Kaufman &          12                                               95% SEM band (median = +- 2.5 )
Lichtenberger, 20
                PICC




                       11
    02, p. 91)         10
                       9
                       8
                       7
                       6
                                                                          Average (median = 4.5)
                       5
                       4
                       3
                       2
                       1
                       0




                                        DATE
                                                                              There is a scientific
                                                                                 explanation
The state expert proposed an
                       Expected WAIS-III IQ (based on
                        WAIS-R IQ) – Actual WAIS-III
                       discrepancy method to support
                           malingering hypothesis




Voodoo psychometrics
WAIS-R IQ 85  Expected WAIS-III 81-83 (will us 82 for discussion)
WAIS-R IQ 85  Expected WAIS-III
 81-83 (will us 82 for discussion)




   Obtained WAIS-III scores lower than
   “expected/predicted” = malingering
        according to state expert
                D

   All other lower scores = malingering
            as per state expert
Major flaws with this method and logic
          (part of commonly stated or implied -- “You can’t fake smart” strategy




• There is no need to estimate WAIS-III scores as actual WAIS-III scores exist

• No scientific or professional evidence or literature suggesting the use or validity of
this method

• The technical manuals do not recommend the use of these tables for this purpose.
The purpose for presenting in TM is to demonstrate concurrent criterion validity. This
information clearly was not presented in the TM to support this type of use

     • If such a procedure were to be used, the study would need to include subjects that had
     WAIS-III 9+ years later than WAIS-R (not average of 4.7 weeks)

     • The tables do not include the standard error of equating (esp. around the cut score of 70)
     which would be required as per the Joint Test Standards if the table was intended to be used
     for this purpose

     • If intended for this purpose, the publisher would have had to conduct a properly designed
     equating study (rectangular distribution; minimum n recommended is 400 to 1,500 – not 192.)

     • etc., etc., etc.
The only scientifically
  accepted method for
predicting one score from
  another is to use the
    correlation and a
    prediction model

    WAIS-R/WAIS-III
correlation of .93 would
 suggest very accurate
       prediction

…..but all prediction has
    error that can be
    quantified as the
   standard error of
     estimate (SEest)
Using WAIS-R IQ scores and standard
prediction model based on WAIR-R/WAIS-
III r = .93, best predicted WAIS-III given
WAIS-R scores is 81

But there is prediction error
    • 1 SEest (68% confidence) = + 5.5
    • 2 SEest (95 % confidence) = +11.0

Thus, given this person’s WAIS-R score, the only
scientifically accepted expected/predicted WAIS-III
score is 81 + 11 pts -- 95 % confidence band of
predicted/expected WAIS-III score of 70 to 92
Only appropriate predicted/expected
   WAIS-III score prediction (95%
confidence) is a range from 72 to 90
                 D
 All actual WAIS-III IQ scores have
     SEM confidence bands that
   overlap with SEest (standard
     error of estimate - error of
 prediction) band based on WAIS-
    R score. Thus, all 3 WAIS-III
       scores are not reliably
     statistically different from
           predicted score
The state expert characterized
                             defendant’s measured
                        achievement (WJ III) as “quite
                         impressive” given his level of
                       measured intelligence – at levels
                          inconsistent with MR/ID Dx

                       The IQ = ACH fallacy argument




Voodoo psychometrics
Problems with “impressive” achievement argument




Defendant’s original WJ III achievement scores were based on
original 2001 norms. Failed to rescore and reinterpret in light of
WJ III 2007 Normative Update (WJ III NU)


Selective “cherry picking” of relatively high scores and failure to
utilize most “real world” score metrics to establish functional
academic skills

    • Ignored cognitive measures on WJ III Ach. Battery consistent
    with MR/ID

IQ = ACH fallacy
Test         State
                                  authors &     expert
                                 pub rec this focused on
                                   as best       these
                                   metric       scores




  Cog
measures




  Cog
measures




           Hardly “quite impressive”
Recall the standard error of the estimate
(SEest) must be used estimate the amount
   of error in the IQ  ACH prediction
The Reality of IQ  Achievement Predicted Scores




IQACH correlation in scientific literature (for adults) reported from .50 to .60

Prediction error (SEest) when r = .50 to .60

     • 1 SEest (68% confidence) = + 12/13
     • 2 SEest (95 % confidence) = + 24/26

State expert used IQ of 73 within the context of his “impressive” conclusion.
Using this score, the scientifically accepted range of expected/predicted
achievement scores is approximately 72 to 98 (68% confidence) and 59 to 111
(95% confidence)

The defendants WJ III NU ach. standard scores are well within these expected
ranges
The IQ  Achievement Fallacy: One cannot
       achieve above your IQ score
The IQ  Achievement Fallacy: One cannot
                 achieve above your IQ score

         (often used as part of “You can’t fake smart” argument)


     IQACH correlations of .50 to .60 indicate that IQ accounts
       for only approximately 25% to 40% of ach. test scores.


Thus, for any given IQ score:

    •Half of all individuals will obtain achievement scores at or below
    their IQ score.

    •Half of all students will obtain achievement scores at or above
    their IQ score!
Other “You can’t fake smart” examples I have seen (not exhaustive list)




The use of the National Adult Reading Test (NART), a commonly used measure to
predict “premorbid” intelligence in neuropsych settings, to predict expected IQ
scores against which an existing score is compared

The use of neuropsych “demographically adjusted (Heaton)” norms
Other “You can’t fake smart” examples I have seen (not exhaustive list)




Use of group aptitude measures (ASVAB; AFQT) as convergent validity
evidence
Proportional CHC broad ability coverage of ASVAB and ASVAB-derived AFQT score




                                                               Major cognitive ability domains sampled across the major         Other human ability domains
                                                              individualized IQ batteries (Wechslers, Stanford-Binet, WJ           (acquired acculturated
                                                           III/BAT III) which are combined to produce general intelligence       knowledge) included in the
                                                                        (g) full-scale global composite IQ score               ASVAB differential aptitude test
                                                                                                                                           battery

                                                    100%
   % CHC broad abilities represented is ASVAB and




                                                    90%

                                                    80%

                                                    70%                      Note. ASVAB Verbal tests
                ASVAB AFQT score




                                                                             (Verbal Comp or VL as per
                                                    60%                     CHC model/theory) also tap
                                                    50%                     Gc abilities, but require the
                                                                                subject to read the
                                                    40%                      items…thus involving Grw
                                                                                       abilities
                                                    30%

                                                    20%

                                                    10%

                                                     0%
                                                               Gf      Gq       Gc     Glr     Ga      Gv     Gsm      Gs    Grw    Gk
                       ASVAB                                  15.0 0.0% 0.0% 0.0% 0.0% 0.0% 0.0% 25.0 30.0 30.0
                       ASVAB AFQT 25.0 0.0% 0.0% 0.0% 0.0% 0.0% 0.0% 0.0% 50.0 25.0
Other “You can’t fake smart” examples I have seen (not exhaustive list)




 Unknown problems with some of the older “gold standards”: Often due
to lack of due diligence and expertise
The 1960 SB was not a renorming (data gathered for item ordering work)

    • 1960 SB norms still based on 1932 norming sample

    • Any 1960 SB score may suffer from extreme Flynn effect (e.g. if tested in 1972 with
    1960 SB, FE of approximately 12 points)

The 1986 SB-IV had serious psychometric problems (Reynolds, 1987 & others)

    • Underepresentative standardization sample (“far below industry standards”)

    • “IQ roulette”

    • “I believe the use of the S-B IV IQs to be logically indefensible, and I certainly would
    not want to defend their accuracy or validity in a court of law” (Reynolds, 1987; p.
    141)
Other “You can’t fake smart” examples I have seen (not exhaustive list)




    Unknown problems with some of the older “gold standards”

           • WAIS-R norm sample for 16 to 19 year olds have been demonstrated
           to be suspect and “soft.”


                 Simply put, the WAIS-R norms for 16-19-year-olds are suspect and examiners
          should interpret [them] with extreme caution. The norms for 16-19-year-olds are
          ‘soft’ or ‘easy’ because the reference group performed more poorly than 16-to-19-
          year-olds really perform in the general population. The surprising result is that the
          IQs of 16- through 19-year-olds tested on the WAIS-R will be spuriously high by 3
          to 5 points” (p. 85, italics added).




Kaufman
 (1990)
IQ Score Interpretations in Atkins Cases




            Kevin S. McGrew, PhD

                       Director
      Institute for Applied Psychometrics (IAP)

           www.themindhumb.com

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IQ Score Interpretation in Atkins MR/ID Death Penalty Cases: The Good, Bad and the Ugly

  • 1. IQ Score Interpretations in Atkins Cases Kevin S. McGrew, PhD Director Institute for Applied Psychometrics (IAP)
  • 2. Additional info re: Kevin McGrew and IAP can be found at the MindHub™ web portal www.themindhub.com
  • 3. For additional information and to stay current (ICDP blog) www.atkinsmrdeathpenaltly.com
  • 4. ICDP …. …. ….
  • 8. IQ Score Interpretations in Atkins Cases A recently successful Atkins case (state agreed to LWOP a few weeks prior to evidentiary hearing) is bases of presentation but will be augmented with information from other cases
  • 9. Case involved the Flynn Effect: But we will not be covering today Recommended article (more at ICDP blog) ICDP
  • 10. “Outliers” – why? State expert built argument around the WAIS-R scores being the best estimates of defendants true intelligence (underlying “You can’t fake bad” strategy ) and dismissed other scores as most likely due to malingering—arguments not based on sound and reliable methods of science State expert failed in professional due diligence to consider scientific based explanations of the consistencies and inconsistencies in the complete collection of scores
  • 11. Median of all = 68 It is statistically or mathematically inappropriate to compute the arithmetic average (mean) of IQ scores. The median is Strong acceptable, under certain convergence circumstances of indicators The only way to compute an average (mean) IQ score is to use a complex equation that incorporates the reliabilities of all scores and the intercorrelations among all scores Median is acceptable metric
  • 12. Fundamental Issue: Comparability (Exchangeability) of IQ Scores Intellectual Functioning: Conceptual Issues Kevin S. McGrew and Keith F. Widaman AAIDD Death Penalty Manual Chapter (in preparation)
  • 13. Fundamental Issue: Comparability of IQ Scores “Not all scores obtained on intelligence tests given to the same person will be identical” (AAIDD, 2010, p. 38) The global (full scale) IQ from different tests are frequently similar…Other times the IQ scores will be markedly different…a finding that often produces consternation for examiners and recipients of psychological reports
  • 14. Fundamental Issue: Comparability of IQ Scores Floyd et al. (2008) used generalizability theory methods to evaluate IQ- IQ exchangeability across ten different IQ battery global composite g- score composites (comprised of 6 to 14 individual tests) across approximately 1,000 subjects
  • 15. Fundamental Issue: Comparability of IQ Scores Average (mdn) r = .76 – lets round to .80 Coefficient of determination r2 x 100 = 64 % shared variance Test A Shared .r = .80 common abilities Test B
  • 16. Fundamental Issue: Comparability of IQ Scores Test A Shared .r = .80 common abilities Test B “psychologists can anticipate that 1 in 4 individuals taking an intelligence test battery will receive an IQ more than 10 points higher or lower when taking another battery” Floyd et al. (2008)
  • 17. The standard error of the difference (SEdiff) must be used to ascertain if the scores in question are reliably different SEdiff = 15 x SQRT[2 - r11 - r22] Test A reliability = .95 Test B reliability = .93 1 SEdiff (68 % confidence) = 5.2 points 2 SEdiff (95 % confidence) = 10.4 points Before interpreting the scores from these two IQ tests as being significantly difference, an IQ-IQ difference of at least 10+ points would be required Easier way via use of confidence band rule-of-thumb
  • 18. e.g., WAIS-R score The higher The standard error of differences represent the difference (SEdiff) WAIS-R reliable differences with confidence band rule- all other obtained IQ scores is a of-thumb scores scientifically based fact in this case. e.g., Not One needs sign. to accept different and to from each explain why. other e.g., None of If 95 % SEM confidence bands these 6 tests for compared scores do not are sign. touch, the difference is likely a different from reliable difference and one another hypotheses about the difference should be enteratined If 95 % SEM confidence bands for compared scores overlap, then the difference is likely not a reliable difference and should not generate significant hypotheses about score differences.
  • 19. IQ-IQ score differences: Scientific hypotheses that warrant exploration • Test administration or scoring errors • Practice effects • Malingering / effort • Norm obsolescence (Flynn effect) Today will focus only • Content differences between different tests on select topics – or different revisions of the same test only those relevant • Little known psychometric problems with to this example case and some of the some of the “gold standards” more unknown or • Individual/situational factors for person misunderstood issues or specific test session
  • 20. Unscientific IQ-IQ score difference hypthoses I have seen or read Will focus only on select topics – esp. those relevant to the Voodoo psychometrics example case and some of the more unknown or misunderstood issues
  • 21. Outliers – why? Most likely scientific explanations in this case Ability content differences between different tests or different revisions of the same test •“Drilling down” further – changes in g- loadings/saturation of subtests included on WAIS-R and WAIS-III/IV
  • 22. High g IQ test battery subtest T1 Intelligence test battery g-loadings or saturation Individual test g (general T2 Intelligence) loadings T3 General intelligence (g) Derived from factor analysis T4 Think of a general intelligence pole that is T5 saturated with more g-ness (like magnetism) at the top T6 and less g-ness at the bottom. T7 Factor analysis orders the T8 tests on the pole based on their saturation of g-ness T9 T10 Low g Subtests
  • 23. WISC/WISC-R/WAIS/WAIS-R MR/ID subtest g-loading pattern research Also astounding is the study-by-study consistency in the subtests that emerge as “easy” (Picture Completion, Object Assembly, Block Design) or “hard” (Arithmetic, Vocabulary, Information) for diverse samples of retarded populations (Kaufman, 1979, p.203) (28 studies)
  • 24. Plot of ________ 1988 and 1993 WAIS-R Subtest Scaled Scores by g (general intelligence) loadings 16 15 1988 WAIS-R 1993 WAIS-R ________ WAIS-R subtest scaled scores 14 High subtest 13 scaled score PicA 12 11 Dig Spn PicC 10 BlkD Dig 9 Sym Arith 8 Cmp 7 Ob Sim Voc Asm 6 Info 5 4 Low subtest 0.55 0.65 0.75 0.85 0.95 scaled score WAIS-R Subtest g (general intelligence loadings (Kaufman, 1990, p. 253) High g: More Low g: less cognitively cognitively abstract/complex (Fair or moderate g) (Good or high g) abstract/complex
  • 25. Plot of _________WAIS-R Subtest Scaled Scores by g (general intelligence) loadings Rank-order correlation of ___ 1993 WAIS-R Rank-order correlation of ___ 1988 WAIS-R subtest scores test g-loadings is -.71. subtest scores test g-loadings is -.68. 16 15 1988 WAIS-R ___________ WAIS-R subtest scaled scores 1993 WAIS-R 14 High subtest 13 scaled score PicA 12 Dig This is a form of internal 11 PicC Spn convergence validity evidence for 10 Dig BlkD MR/ID Dx 9 Sym Arith 8 Cmp 7 Ob Sim Voc Asm 6 Info 5 4 Low subtest 0.55 0.65 0.75 0.85 0.95 scaled score WAIS-R Subtest g (general intelligence loadings (Kaufman, 1990, p. 253) High g: More Low g: less cognitively cognitively abstract/complex (Fair or moderate g) (Good or high g) abstract/complex
  • 26. Plot of _________WAIS-R Subtest Scaled Scores by g (general intelligence) loadings Dropped from battery in WAIS-IV revision Eliminated from FS IQ in WAIS-IV revision (supplemental subtest) 16 15 1988 WAIS-R __________ WAIS-R subtest scaled scores 1993 WAIS-R 14 High subtest 13 scaled score PicA 12 11 Dig Spn PicC 10 BlkD Dig 9 Sym Arith 8 Cmp 7 Ob Sim Voc Asm 6 Info 5 4 Low subtest 0.55 0.65 0.75 0.85 0.95 scaled score WAIS-R Subtest g (general intelligence loadings (Kaufman, 1990, p. 253) High g: More Low g: less cognitively cognitively abstract/complex (Fair or moderate g) (Good or high g) abstract/complex Eliminated from FS IQ in WAIS-III revision (supplemental subtest) & dropped from battery in WAIS-IV revision
  • 27. The WAIS-III/IV batteries include more complex tests (than the WAIS-R) and are better indicators of general intelligence The state expert would not recognize (continued to ignore) this scientific fact and held on to the WAIS-R scores as the most accurate – the rest of lower scores due to malingering
  • 28. Outliers – why? Most likely scientific explanations in this case • Ability content differences between different tests or different revisions of the same test • Little known psychometric problems with some of the “gold standards”
  • 29.
  • 30. CHC IQ Test Batteries DNA Fingerprints
  • 31. The publisher, in both the WAIS-III/WAIS-IV manuals, describes changes in abilities measured to improve the battery to be consistent with contemporary research The state expert would not recognize (continued to ignore) this scientific fact and held on to the WAIS-R scores as the most accurate – the rest of lower scores due to malingering
  • 32. Recommended article re: CHC theory of intelligence (Many more at ICDP blog)
  • 33. Continuum of Progress: Intelligence Theories and the Evolution of the Wechsler Adult IQ Battery General Dichotomous Multiple Multiple Multiple Ability (g) Abilities Cognitive Abilities Cognitive Abilities Cognitive Abilities (Incomplete; not implicitly (Incomplete; implicitly (“Complete”; implicitly or explicitly CHC-organized or explicitly CHC-organized or explicitly CHC- organized g Broad Abilities Spearman Original Gf-Gc Thurstone PMAs Cattell-Horn-Carroll (CHC) Theory of Cognitive Abilities CHC is now considered to be the consensus W-B (1939; 1946) model of the structure WAIS-R (1981) WAIS-III (1997) WAIS-IV (2008) of intelligence The WAIS-III and WAIS-IV revisions made the battery more consistent with contemporary neurocognitive and intelligence research. They are more valid indicators of general intelligence (supported by WAIS-III/IV tech manuals and independent reviews) than the older WAIS-R. The changes in abilities measured from the WAIS-R to the WAIS-III/IV help explain the WAIS-R “outlier” scores The WAIS-IV should not be considered “the gold standard” as per the consensus CHC model of intelligence.
  • 34. Continuum of Progress: Intelligence Theories and the Wechsler Adult IQ Battery General Dichotomous Multiple Multiple Multiple Ability (g) Abilities Cognitive Abilities Cognitive Abilities Cognitive Abilities (Incomplete; not implicitly (Incomplete; implicitly (“Complete”; implicitly or explicitly CHC-organized or explicitly CHC-organized or explicitly CHC- organized g Broad Abilities Spearman Original Gf-Gc Thurstone PMAs Cattell-Horn-Carroll (CHC) Theory of Cognitive Abilities The revisions made to W-B (1939; 1946) WAIS-R (1981) WAIS-III (1997) WAIS-IV (2008) other IQ batteries (with adult norms SB and WJ) also changed the composition of their composite IQ scores and is Stanford- Binet LM SB-IV (1986) SB-V(2003) a likely source of score (1937; 1960; differences that must be 1972) considered WJ (1977) WJ III (2001) WJ-R (1989) WJ III NU (2005)
  • 35. Continuum of Progress: Intelligence Theories and the Wechsler Adult IQ Battery General Dichotomous Multiple Multiple Multiple Ability (g) Abilities Cognitive Abilities Cognitive Abilities Cognitive Abilities (Incomplete; not implicitly (Incomplete; implicitly (“Complete”; implicitly or explicitly CHC-organized or explicitly CHC-organized or explicitly CHC- organized g Broad Abilities Spearman Original Gf-Gc Thurstone PMAs Cattell-Horn-Carroll (CHC) Theory of Cognitive Abilities W-B (1939; 1946) Knowing the ability WAIS-III (1997) WAIS-IV (2008) WAIS-R (1981) coverage similarities and differences is important when comparing and understanding possible IQ- Stanford- IQ differences between the Binet LM SB-IV (1986) SB-V(2003) latest versions of these (1937; 1960; 1972) batteries WJ (1977) WJ III (2001) WJ-R (1989) WJ III NU (2005)
  • 36. Continuum of Progress: Intelligence Theories and the Wechsler Adult IQ Battery General Dichotomous Multiple Multiple Multiple Ability (g) Abilities Cognitive Abilities Cognitive Abilities Cognitive Abilities (Incomplete; not implicitly (Incomplete; implicitly (“Complete”; implicitly or explicitly CHC-organized or explicitly CHC-organized or explicitly CHC- organized g Broad Abilities Spearman Original Gf-Gc Thurstone PMAs Cattell-Horn-Carroll (CHC) Theory of Cognitive Abilities W-B (1939; 1946) IQ-IQ score difference WAIS-R (1981) WAIS-III (1997) WAIS-IV (2008) explanations may require knowledge of across and within battery revision ability coverage understanding. There are many possible scenarios Stanford- when there is a history of IQ Binet LM SB-IV (1986) SB-V(2003) testing within the same battery (1937; 1960; 1972) system or across battery systems WJ (1977) WJ III (2001) WJ-R (1989) WJ III NU (2005)
  • 37. Continuum of Progress: Intelligence Theories and Test Batteries General Dichotomous Multiple Multiple Multiple Ability (g) Abilities Cognitive Abilities Cognitive Abilities Cognitive Abilities (Incomplete; not implicitly (Incomplete; implicitly (“Complete”; implicitly or explicitly CHC-organized or explicitly CHC-organized or explicitly CHC-organized g Broad Abilities (Neuropsych. Psychometric) Primary Theories Spearman Original Gf-Gc Thurstone PMAs Cattell-Horn Carroll (CHC) Theory of Cognitive Abilities Simultaneous- PASS Successive (Planning, Attention, Simultaneous, Successive) WJ (1977) WJ-R (1989) WJ III (2001) WJ III NU (2005) Stanford- SB-IV (1986) SB-V(2003) Applied IQ Batteries Binet LM (1937; 1960; 1972) WPPSI-R (1989) WPPSI-III (2002) When childhood and adult WISC-IV (2003) WISC-R (1974) WISC-III 1991) battery scores are available the W-B (1939; 1946) WAIS-IV (2008) WAIS-III (1997) interpretation of IQ-IQ WAIS-R (1981) differences due to ability coverage differences becomes even more complex K-ABC (1983) KABC-II (2004) KAIT (1993) CAS (1997) DAS (1990) DAS-II (2007)
  • 38.
  • 39. Knowledge of CHC ability coverage critical TONI-2/ when brief special purpose Ravens/ 100% Gf (e.g., nonverbaI) IQ scores are reported
  • 40. The state expert argued that some of the lower subtest scores (after the WAIS-R’s) was further evidence of malingering Voodoo psychometrics
  • 41. State expert argued that variability in Wechsler subtest scores, esp. lower scores post-Atkins were obvious sign of malingering …thus supporting the conclusion that the WAIS-R scores were the best estimate of general intelligence The implied “You can’t fake smart” strategy or interpretation
  • 42. There is an EXTREME amount of variability in the professional expertise in IQ subtest profile interpretation: Scientific/psychometric vs. “clinical” lore-based interpretation VS
  • 43. Recall the standard error of the difference (SEdiff) must be used to ascertain if the scores in question are reliably different
  • 44. Plot of ___________WAIS-R & WAIS-III Similarities scores (+- 95 SEM) - Range of 4 20 19 18 17 16 15 14 Scaled score 13 95% SEM band (median = +- 1.7) 12 11 10 9 8 7 6 Average (median = 5.0) 5 4 3 2 1 0 6 8 0 2 4 6 8 0 2 4 6 8 0 98 98 99 99 99 99 99 00 00 00 00 00 01 1, 1, 1, 1, 1, 1, 1, 2, 2, 2, 2, 2, 2, Date No statistically reliable difference across all scores
  • 45. Plot of ______________WAIS-R & WAIS-III Comprehension scores (+- 95 SEM) - Range of 4 20 19 18 17 16 15 14 Scaled score 13 95% SEM band (median = +- 2.3) 12 11 10 9 8 7 6 Average (median = 5.5) 5 4 3 2 1 0 6 8 0 2 4 6 8 0 2 4 6 8 0 98 98 99 99 99 99 99 00 00 00 00 00 01 1, 1, 1, 1, 1, 1, 1, 2, 2, 2, 2, 2, 2, Date No statistically reliable difference across all scores
  • 46. Plot of __________ WAIS-R, WAIS-III & WAIS-IV Digit Span scores (+- 95 SEM) – Range of 7 20 19 18 As reported in WAIS-R tech. manual, DS has poor 17 16 reliability (mdn = .81) – 4th weakest in battery. Thus 15 some variability to be expected. And, the WAIS-IV 14 DS is a three-component and not two component Scaled score 13 12 test—so they are not measuring the SEM band (median = +- 1.9) 95% exact same 11 10 construct 9 8 7 6 Average (median = 5.5) 5 4 3 2 1 0 6 8 0 2 4 6 8 0 2 4 6 8 0 98 98 99 99 99 99 99 00 00 00 00 00 01 1, 1, 1, 1, 1, 1, 1, 2, 2, 2, 2, 2, 2, Date 7 point difference There is a scientific explanation
  • 47.
  • 48. Plot of ________WAIS-R, WAIS-III & WAIS-IV Picture Completion scores (+- 95 SEM) - Range of 6 On the WAIS-RWAIS-III revision. “Only 50% of the content of Picture Completion and Picture Arrangement was retained from the WAIS-R, and only 20 19 60 % of the Object Assembly items were retained. In addition, the correlations 18 between WAIS-R and WAIS-III version of these subtests are relatively low (r’s of 17 .59 - .63)” ------ 35 – 40 % shared variance 16 15 14 13 (Kaufman & 12 95% SEM band (median = +- 2.5 ) Lichtenberger, 20 PICC 11 02, p. 91) 10 9 8 7 6 Average (median = 4.5) 5 4 3 2 1 0 DATE There is a scientific explanation
  • 49. The state expert proposed an Expected WAIS-III IQ (based on WAIS-R IQ) – Actual WAIS-III discrepancy method to support malingering hypothesis Voodoo psychometrics
  • 50. WAIS-R IQ 85  Expected WAIS-III 81-83 (will us 82 for discussion)
  • 51. WAIS-R IQ 85  Expected WAIS-III 81-83 (will us 82 for discussion) Obtained WAIS-III scores lower than “expected/predicted” = malingering according to state expert D All other lower scores = malingering as per state expert
  • 52. Major flaws with this method and logic (part of commonly stated or implied -- “You can’t fake smart” strategy • There is no need to estimate WAIS-III scores as actual WAIS-III scores exist • No scientific or professional evidence or literature suggesting the use or validity of this method • The technical manuals do not recommend the use of these tables for this purpose. The purpose for presenting in TM is to demonstrate concurrent criterion validity. This information clearly was not presented in the TM to support this type of use • If such a procedure were to be used, the study would need to include subjects that had WAIS-III 9+ years later than WAIS-R (not average of 4.7 weeks) • The tables do not include the standard error of equating (esp. around the cut score of 70) which would be required as per the Joint Test Standards if the table was intended to be used for this purpose • If intended for this purpose, the publisher would have had to conduct a properly designed equating study (rectangular distribution; minimum n recommended is 400 to 1,500 – not 192.) • etc., etc., etc.
  • 53. The only scientifically accepted method for predicting one score from another is to use the correlation and a prediction model WAIS-R/WAIS-III correlation of .93 would suggest very accurate prediction …..but all prediction has error that can be quantified as the standard error of estimate (SEest)
  • 54. Using WAIS-R IQ scores and standard prediction model based on WAIR-R/WAIS- III r = .93, best predicted WAIS-III given WAIS-R scores is 81 But there is prediction error • 1 SEest (68% confidence) = + 5.5 • 2 SEest (95 % confidence) = +11.0 Thus, given this person’s WAIS-R score, the only scientifically accepted expected/predicted WAIS-III score is 81 + 11 pts -- 95 % confidence band of predicted/expected WAIS-III score of 70 to 92
  • 55. Only appropriate predicted/expected WAIS-III score prediction (95% confidence) is a range from 72 to 90 D All actual WAIS-III IQ scores have SEM confidence bands that overlap with SEest (standard error of estimate - error of prediction) band based on WAIS- R score. Thus, all 3 WAIS-III scores are not reliably statistically different from predicted score
  • 56. The state expert characterized defendant’s measured achievement (WJ III) as “quite impressive” given his level of measured intelligence – at levels inconsistent with MR/ID Dx The IQ = ACH fallacy argument Voodoo psychometrics
  • 57. Problems with “impressive” achievement argument Defendant’s original WJ III achievement scores were based on original 2001 norms. Failed to rescore and reinterpret in light of WJ III 2007 Normative Update (WJ III NU) Selective “cherry picking” of relatively high scores and failure to utilize most “real world” score metrics to establish functional academic skills • Ignored cognitive measures on WJ III Ach. Battery consistent with MR/ID IQ = ACH fallacy
  • 58. Test State authors & expert pub rec this focused on as best these metric scores Cog measures Cog measures Hardly “quite impressive”
  • 59. Recall the standard error of the estimate (SEest) must be used estimate the amount of error in the IQ  ACH prediction
  • 60. The Reality of IQ  Achievement Predicted Scores IQACH correlation in scientific literature (for adults) reported from .50 to .60 Prediction error (SEest) when r = .50 to .60 • 1 SEest (68% confidence) = + 12/13 • 2 SEest (95 % confidence) = + 24/26 State expert used IQ of 73 within the context of his “impressive” conclusion. Using this score, the scientifically accepted range of expected/predicted achievement scores is approximately 72 to 98 (68% confidence) and 59 to 111 (95% confidence) The defendants WJ III NU ach. standard scores are well within these expected ranges
  • 61. The IQ  Achievement Fallacy: One cannot achieve above your IQ score
  • 62. The IQ  Achievement Fallacy: One cannot achieve above your IQ score (often used as part of “You can’t fake smart” argument) IQACH correlations of .50 to .60 indicate that IQ accounts for only approximately 25% to 40% of ach. test scores. Thus, for any given IQ score: •Half of all individuals will obtain achievement scores at or below their IQ score. •Half of all students will obtain achievement scores at or above their IQ score!
  • 63. Other “You can’t fake smart” examples I have seen (not exhaustive list) The use of the National Adult Reading Test (NART), a commonly used measure to predict “premorbid” intelligence in neuropsych settings, to predict expected IQ scores against which an existing score is compared The use of neuropsych “demographically adjusted (Heaton)” norms
  • 64. Other “You can’t fake smart” examples I have seen (not exhaustive list) Use of group aptitude measures (ASVAB; AFQT) as convergent validity evidence
  • 65. Proportional CHC broad ability coverage of ASVAB and ASVAB-derived AFQT score Major cognitive ability domains sampled across the major Other human ability domains individualized IQ batteries (Wechslers, Stanford-Binet, WJ (acquired acculturated III/BAT III) which are combined to produce general intelligence knowledge) included in the (g) full-scale global composite IQ score ASVAB differential aptitude test battery 100% % CHC broad abilities represented is ASVAB and 90% 80% 70% Note. ASVAB Verbal tests ASVAB AFQT score (Verbal Comp or VL as per 60% CHC model/theory) also tap 50% Gc abilities, but require the subject to read the 40% items…thus involving Grw abilities 30% 20% 10% 0% Gf Gq Gc Glr Ga Gv Gsm Gs Grw Gk ASVAB 15.0 0.0% 0.0% 0.0% 0.0% 0.0% 0.0% 25.0 30.0 30.0 ASVAB AFQT 25.0 0.0% 0.0% 0.0% 0.0% 0.0% 0.0% 0.0% 50.0 25.0
  • 66. Other “You can’t fake smart” examples I have seen (not exhaustive list) Unknown problems with some of the older “gold standards”: Often due to lack of due diligence and expertise
  • 67. The 1960 SB was not a renorming (data gathered for item ordering work) • 1960 SB norms still based on 1932 norming sample • Any 1960 SB score may suffer from extreme Flynn effect (e.g. if tested in 1972 with 1960 SB, FE of approximately 12 points) The 1986 SB-IV had serious psychometric problems (Reynolds, 1987 & others) • Underepresentative standardization sample (“far below industry standards”) • “IQ roulette” • “I believe the use of the S-B IV IQs to be logically indefensible, and I certainly would not want to defend their accuracy or validity in a court of law” (Reynolds, 1987; p. 141)
  • 68. Other “You can’t fake smart” examples I have seen (not exhaustive list) Unknown problems with some of the older “gold standards” • WAIS-R norm sample for 16 to 19 year olds have been demonstrated to be suspect and “soft.” Simply put, the WAIS-R norms for 16-19-year-olds are suspect and examiners should interpret [them] with extreme caution. The norms for 16-19-year-olds are ‘soft’ or ‘easy’ because the reference group performed more poorly than 16-to-19- year-olds really perform in the general population. The surprising result is that the IQs of 16- through 19-year-olds tested on the WAIS-R will be spuriously high by 3 to 5 points” (p. 85, italics added). Kaufman (1990)
  • 69.
  • 70. IQ Score Interpretations in Atkins Cases Kevin S. McGrew, PhD Director Institute for Applied Psychometrics (IAP) www.themindhumb.com