Appendix A A.1: WAIS‐IV Interpretive Worksheet 1 STEP 1. Report the Person’s WAIS-IV Standard Scores (FSIQ and Indexes) and Subtest Scaled Scores. For IQ and indexes, report standard score, confidence interval, percentile rank, and descriptive category. For subtests, report scaled scores and percentile ranks only. (See Rapid Reference 5.2 for descriptive categories.) STEP 2. Determine the Best Way to Summarize Overall Intellectual Ability. Step 2a. To determine whether the FSIQ is interpretable, subtract the Lowest Index from the Highest Index. Highest Lowest Difference Is the difference < 23 points? Index Standard Scores: – = Y or N Step 2b. To determine whether the General Ability Index (GAI) may be used to summarize overall intellectual ability, calculate the difference between the VCI and PRI. VCI PRI Absolute Difference Is the difference < 23 points? Index Standard Scores: – = Y or N To calculate the GAI, sum 6 subtest scaled scores of the 3 VCI subtests and 3 PRI subtests, and locate the GAI that corresponds to this sum in Table C.1 of the WAIS-IV Technical and Interpretive Manual (Psychological Corporation, 2008, p. 169). Sum of Subtest Scaled Scores VC SI IN MR BD VP GAI Scaled Score + + + + + = = If YES, the FSIQ may be interpreted as a reliable and valid estimate of a person’s overall intellectual ability. Proceed directly to Step 3. If NO, then proceed to Step 2b. If YES, the GAI can be calculated and interpreted as a reliable and valid estimate of the person’s overall intellectual ability. If NO, then proceed to Step 3.
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Appendix A A.1: WAIS‐IV Interpretive Worksheet 1
STEP 1. Report the Person’s WAIS-IV Standard Scores (FSIQ and Indexes) and Subtest Scaled Scores.
For IQ and indexes, report standard score, confidence interval, percentile rank, and descriptive category. For subtests, report scaled scores and percentile ranks only. (See Rapid Reference 5.2 for descriptive categories.)
STEP 2. Determine the Best Way to Summarize Overall Intellectual Ability.
Step 2a. To determine whether the FSIQ is interpretable, subtract the Lowest Index from the Highest Index.
Highest Lowest Difference
Is the difference
< 23 points?
Index Standard Scores: – = Y or N
Step 2b. To determine whether the General Ability Index (GAI) may be used to summarize overall intellectual ability, calculate the difference between the VCI and PRI.
VCI PRI Absolute
Difference
Is the difference
< 23 points?
Index Standard Scores: – = Y or N
To calculate the GAI, sum 6 subtest scaled scores of the 3 VCI subtests and 3 PRI subtests, and locate the GAI that corresponds to this sum in Table C.1 of the WAIS-IV Technical and Interpretive Manual (Psychological Corporation, 2008, p. 169).
Sum of Subtest Scaled Scores
VC SI IN MR BD VP GAI
Scaled Score
+ + + + + = =
If YES, the FSIQ may be interpreted as a reliable and valid estimate of a person’s overall intellectual ability. Proceed directly to
Step 3.
If NO, then proceed to Step 2b.
If YES, the GAI can be calculated and interpreted as a reliable and valid estimate of the person’s overall intellectual ability.
If NO, then proceed to Step 3.
Appendix A A.1: WAIS‐IV Interpretive Worksheet 2
STEP 3. Determine Whether the Difference between the Person’s GAI and Cognitive Proficiency Index (CPI) Is Unusually Large.
Step 3a. Determine whether the GAI and CPI represent unitary abilities or processes.
If you have not already done so in Step 2b, determine whether the GAI represents a unitary ability by calculating the difference between the VCI and PRI. If you completed this calculation in Step 2b, then transfer those results here.
VCI PRI Absolute
Difference
Is the difference
< 23 points?
Index Standard Scores: – = Y or N
Determine whether the CPI represents a unitary ability by calculating the difference between the WMI and the PSI.
WMI PSI Absolute
Difference
Is the difference
< 23 points?
Index Standard Scores: – = Y or N
Step 3b. Calculate the GAI and CPI if they represent unitary abilities or processes. If the GAI has been calculated in Step 2b, use the value for Step 3c. Otherwise use the tables below to calculate the GAI and CPI.
To calculate the GAI, sum 6 subtest scaled scores of the 3 VCI subtests and 3 PRI subtests and locate the GAI that corresponds to this sum in Table C.1 of the WAIS-IV Technical and Interpretive Manual (Psychological Corporation, 2008, p. 169).
Sum of Subtest Scaled Scores
VC SI IN MR BD VP GAI Scaled Score
+ + + + + = =
To calculate the CPI, sum 4 subtest scaled scores of the 2 Core WMI subtests and 2 Core PSI subtests and locate the CPI that corresponds to this sum in Appendix A.2 the CD-ROM.
If YES, then the CPI can be calculated and interpreted as a reliable and valid estimate of the person’s overall ability for proficient information processing, through quick visual speed and good mental control.
If NO, the GAI-CPI comparison cannot be made. Go to Step 4.
If YES, the GAI can be calculated and interpreted as a reliable and valid estimate of the person’s overall intellectual ability. Proceed to the next part of this step to determine whether the CPI can be interpreted.
If NO, the GAI-CPI comparison cannot be made. Go to Step 4.
Appendix A A.1: WAIS‐IV Interpretive Worksheet 3
Sum of Subtest Scaled Scores
DS AR SS CD CPI Scaled Score
+ + + = =
Step 3c. Record the size of the difference between the GAI and CPI in the table below. If it is 9 points or more, it should be considered statistically different (at the p < .05 level).
Step 3d. Determine whether the size of the difference between the GAI and CPI is uncommonly large. If it is 19 points or more, it should be considered uncommonly large (occurring less than 10% of the time in the standardization sample).
GAI CPI Absolute
Difference
Is the difference
significant? ≥ 9 points
Is the difference
uncommon? ≥ 19 points
Index Standard Scores – = Y or N Y or N
STEP 4. Select the Wechsler Four-Index Model or the Keith Five-Factor Model.
Step 4 is designed to help you determine if use of the Keith Five-Factor model is appropriate or if the Wechsler Four-Index model should be your choice for interpretation. Answering the next three questions will help you select the appropriate model.
Step 4a. Question: Is the person you tested between the ages of 16 and 69?
• If no, proceed to Step 5 to interpret data with the Wechsler Four-Index Model. • If yes, answer the Step 4b question below.
Step 4b. Question: Did you administer the supplementary subtests, Letter-Number Sequencing, and Figure Weights?
• If no, proceed to Step 5 to interpret data with the Wechsler Four-Index Model. • If yes, answer the Step 4c question below.
Step 4c. Question: Considering your personal theoretical and clinical foundations, do you
choose to interpret the WAIS-IV data with the Keith Five-Factor model?
• If no, proceed to Step 5 to interpret data with the Wechsler Four-Index model. • If yes, continue to Step 6 to interpret the data with the Keith Five-Factor model.
STEP 5. Determine Whether Each of the Four Wechsler Indexes Is Unitary, and Thus
Interpretable
Skip this step if you are interpreting the person’s profile via the Keith Five‐Factor Approach. Proceed to Step 6.
Step 5a–5d. Calculate the difference between the highest and lowest subtest scaled scores for the VCI, PRI, WMI, and PSI.
Y or N
Y or N
Y or N
Appendix A A.1: WAIS‐IV Interpretive Worksheet 4
Highest Lowest Difference
Is the difference < 5
points?
5a. VCI Subtest Scores: – = Y or N
5b. PRI Subtest Scores: – = Y or N
5c. WMI Subtest Scores: – = Y or N
5d. PSI Subtest Scores: – = Y or N
STEP 6. Determine Whether Each of the Five Keith Factors Is Unitary, and Thus Interpretable.
Skip this step if you interpreted the person’s profile via the Wechsler Four‐Index method. Proceed to Step 7.
Step 6a. Calculate the standard scores for the five Keith Factors by summing the scaled scores for the two subtests that comprise each cluster and converting the sum to a standard score using the norms in Appendixes A.3–A.6 of the CD-ROM.
Factor Scaled
Score 1
Scaled Score
2
Sum of Scaled Scores
Factor Standard
Score
Gc VC + IN =
Gsm DS + LN =
Gf MR + FW =
Gv BD + VP =
Gs SS + CD =
Step 6b-6f. Calculate the absolute difference among subtest scaled scores within each of the factors, and determine if the size of the difference less than 1.5 standard deviations (< 5 points).
If YES, the ability presumed to underlie the index is unitary and may be interpreted.
If NO, the index cannot be interpreted as representing a unitary ability. Proceed to
Step 7 after completing Step 5d.
Appendix A A.1: WAIS‐IV Interpretive Worksheet 5
Factor
Scaled Score
1
Scaled Score
2 Absolute
Difference
Is the difference < 5 points?
6b. Gc VC – IN = Y or N
6c. Gsm DS – LN = Y or N
6d. Gf MR – FW = Y or N
6e. Gv BD – VP = Y or N
6f. Gs SS – CD = Y or N
Step 6g. Determine how many of Keith’s Five Factors are interpretable by reviewing the results of Steps 6b–6f.
Is the number < 3
Number of interpretable Keith factors: Y or N
STEP 7. Determine Normative Strengths and Normative Weaknesses in the Index or Factor Profile.
Record the standard score for each interpretable index or factor in the table below. Place a check-mark in the box corresponding to the appropriate normative category for each index or factor.
Wechsler Index
Standard Score
Normative Weakness
< 85
Within Normal Limits 85–115
Normative Strength
> 115 VCI PRI WMI
PSI
If YES, the ability presumed to underlie the factor is unitary and can be interpreted.
If NO, the factor cannot be interpreted as representing a unitary ability. Proceed to
Step 6g after completing Steps 6a–6f.
If YES, only one or two of Keith’s factors are interpretable, so we strongly recommend using the Wechsler Four-Index model to interpret the WAIS-IV data. Go back to Step 5 to complete
interpretation of the Wechsler Four-Index model.
If NO, then proceed to Step 7 to interpret the Keith Five Factors.
Appendix A A.1: WAIS‐IV Interpretive Worksheet 6
Keith Factor
Standard Score
Normative Weakness
< 85
Within Normal Limits 85–115
Normative Strength
> 115 Gc
Gsm
Gv
Gf
Gs
STEP 8. Determine Personal Strengths and Personal Weaknesses in the Index Profile.
Step 8a. Compute the mean of the person’s indexes or factors and round to the nearest tenth of a point. Note that all indexes or factors (interpretable and noninter-pretable) are included in the computation of the mean.
Wechsler Index
Standard Score
Keith Factor
Standard Score
Gc
VCI Gsm
PRI Gv
WMI Gf
PSI Gs
Sum of Indexes Sum of Factors
Number of Indexes ÷ 4 Number of Factors ÷ 5
Mean of Indexes Mean of Factors
Step 8b. Fill in the table as follows:
• Record the interpretable index or factor standard score in column (2). • Record the rounded mean of all indexes or factors in column (3) (from Step 5a or 6a). • Record the difference Score (i.e., Standard Score minus Mean) in column (4). • Record the critical value needed for the difference score to be considered significant in
column (5). (See below for p < .05 values, and see Tables 5.4 and 5.5 for p < .01 level of significance.)
• If the difference score equals or exceeds the critical value, record “PS” for a positive (+) difference score or “PW” for a negative (–) difference score.
Appendix A A.1: WAIS‐IV Interpretive Worksheet 7
Step 8c. Determine whether the personal strength/weakness is uncommon (base rate < 10%) in the general population. If the difference score is ≥ 15 points, it is uncommon.
• Record “Uncommon (or U)” in column (7) for difference scores that are ≥ 15 points.
Interpretable Wechsler
Index (1)
Standard Score
(2)
Rounded Mean of
All Indexes
(3)
Difference Score
(4)
Critical Value
Needed for Significance
(5)
Personal Strength
or Personal
Weakness (PS or PW)
(6)
Uncommon (U) or Not
Uncommon (NU) (7)
VCI PRI WMI PSI
Interpretable Keith Factor
(1)
Standard Score
(2)
Rounded Mean of
All Factors
(3)
Difference Score
(4)
Critical Value
Needed for Significance
(5)
Personal Strength
or Personal
Weakness (PS or PW)
(6)
Uncommon (U) or Not
Uncommon (NU) (7)
Gc Gsm Gv Gf Gs
Critical Value Needed for Significance for Ages 16–90
(p <.05 level of significance)
Wechsler Indexes Keith Factors
Age VCI PRI WMI PSI Gc Gf Gv Gsm Gs
16–17 6.5 6.1 6.8 8.3 6.2 7.0 7.0 6.6 8.7
18–19 5.6 6.3 6.3 7.6 6.0 6.8 6.8 6.4 7.8
20–24 5.7 6.4 7.0 7.6 5.6 7.2 7.2 6.8 7.9
25–29 5.5 5.5 5.8 7.5 5.9 6.3 6.3 5.9 7.8
30–34 5.6 5.6 6.0 8.4 5.9 5.9 6.4 5.5 8.8
35–44 5.6 6.0 6.0 8.4 5.6 6.8 6.8 6.4 8.8
45–54 5.1 5.5 5.9 8.3 5.0 6.4 5.9 5.9 8.8
55–64 5.0 5.8 6.2 7.2 4.9 6.7 6.7 6.3 7.4
65–69 5.0 5.8 6.2 7.2 4.9 6.3 6.3 6.3 7.4
70–74 5.1 5.9 6.6 7.2
75–79 5.5 6.2 5.8 6.9
80–84 5.1 6.9 6.3 6.9
85–90 4.6 6.6 6.6 6.9
Appendix A A.1: WAIS‐IV Interpretive Worksheet 8
Step 8d. Determine whether any of the interpretable Wechsler indexes or Keith factors are Key Assets or High-Priority Concerns.
Review your findings from Steps 7, 8b, and 8c. For each relevant index or factor, place a checkmark in the column that accurately describes the findings for that index or factor. Indexes or factors that represent an uncommon, normative, and personal strength should be identified as a “Key Asset.” Indexes that represent an uncommon, normative, and personal weakness should be identified as a “High-Priority Concern.”
Index or Factor
NS (Step 7)
NW (Step 7)
PS (Step 8b)
PW (Step 8b)
Uncommon (Step 8c)
Key Asset
High-Priority Concern
VCI PRI WMI PSI Gc Gsm Gv Gf Gs Notes: NS = Normative Strength; NW = Normative Weakness; PS = Personal Strength; PW = Personal Weakness.
STEP 9. Interpret Fluctuations in the Person’s Index Profile.
Review Rapid Reference 5.10 for a description of all the terms that are used to classify Indexes or Factors. See Rapid Reference 5.11 for examples of how to describe indexes or factors that are classified as strengths. Rapid Reference 5.12 gives examples of how to describe indexes or factors that are classified as weaknesses. Basic definitions of CHC Broad and Narrow Abilities are also summarized in Appendix A.7 on the CD-ROM. An overview of neuropsychological theory and CHC theory related to the interpretation of the Keith Five-Factor model is presented in Rapid Reference 5.7. The information in Rapid Reference 5.7 can also provide a useful outline for neuropsychologically based and CHC-based interpretation of the Wechsler Four-Index model.
STEP 10. Conduct Planned Clinical Comparisons.
There are 8 possible clinical comparisons. Either conduct all comparisons or select those that are most appropriate for a given individual based on the referral questions and assessment results. Step 10a. Determine whether each Clinical Cluster is unitary.
• Using the tables that follow, record the scaled scores for each relevant subtest. • Subtract the lowest from the highest scaled score to compute the difference. • If the difference equals or exceeds 5 points, the Clinical Cluster is not unitary and
cannot be used to conduct clinical comparisons. • If the difference is less than 5 points, the Clinical Cluster is unitary. • Clinical comparisons may be made only if both clusters comprising the comparison
have been determined to be unitary.
Appendix A A.1: WAIS‐IV Interpretive Worksheet 9
CLUSTER
Highest Scaled Score
Lowest Scaled Score
Differ-ence
Is the difference < 5 points?
Visual-Motor Speed Block Design + Coding + Symbol Search
– = Y or N
Problem Solving without Visual-Motor Speed Matrix Reasoning + VIsual Puzzles + Picture Completion +Figure Weights (ages16–69)
–
=
Y or N
Mental Manipulation Letter- Number Sequencing + Digit Span (ages 16–69)
Step 10b. For unitary clusters only, calculate the Clinical Cluster by following the steps below.
• Sum the scaled scores in each column for the subtests that comprise the Clinical Cluster. • Convert the sum of scaled scores to a Clinical Cluster standard score using Appendixes A.9–A.17. • Record the cluster’s percentile Rank and Confidence Interval (also available in Appendixes A.9–A.17).
Subtest
Visual-Motor Speed
Problem Solving without Visual Motor Speed
Mental Manip-ulation
Verbal Fluid
Reason-ing
Lexical Know-ledge
General Infor-
mation
Long-Term
Memory
Short- Term
Memory
Fluid Reason-
ing
Visual Pro-
cessing
BD SI DS MR VC AR SS VP IN CD LN FW CO CA
PCm
Sum of Scaled Scores Cluster
Standard Score
Percent- ile Rank Confid- ence
Interval
Appendix A A.1: WAIS‐IV Interpretive Worksheet 11
Step 10c. Conduct planned clinical comparisons.
• Only interpretable Clinical Clusters may be used in Step 10c. (See Step 10a’s results.) • Calculate the difference between the clusters in the comparison by completing the next table with the
cluster standard scores that were determined in Step 10b. • If the size of the difference is equal to or greater than the value reported in the next table, then the
difference is Uncommon (U). • If the size of the difference between the two clusters in the comparison is less than the table value, then
the difference is Not Uncommon (NU).
Cluster 1 vs. Cluster 2 Score 1
– Score 2
= Differ-ence
Critical Value
Uncommon (U) or Not Uncommon
(NU) Visual-Motor Speed (BD+CD+SS)
vs. Problem Solving w/o Visual-Motor Speed (MR+VP+PC+FW)
–
=
20
Visual-Motor Speed (BD+CD+SS)
vs. Mental Manipulation (LN+DS)
–
=
24
Mental Manipulation (LN+DS)
vs. Problem Solving w/o Visual-Motor Speed (MR+VP+PC+FW)
–
=
22
Fluid Reasoning (MR+FW)
vs. Visual Processing (BD+VP)
–
=
20
Verbal Fluid Reasoning (SI+CO)
vs. Fluid Reasoning (MR+FW)
–
=
22
Lexical Knowledge (VC+SI)
vs. General Information (CO+IN)
–
=
15
Long-Term Memory (VC+IN)
vs. Short-Term Memory (LN+DS)
–
=
24
Verbal Fluid Reasoning (SI+CO)
vs. Long-Term Memory (VC+IN)
–
=
16
Note: Difference scores that exceed the critical value listed in column 3 should be denoted as “Uncommon.”
Step 10d. Describe results of planned clinical comparisons. Regardless of the outcome of Step 10c, review the information in Rapid Reference 5.18 and 5.19 in chapter 5 of this book to help develop interpretive statements that appropriately describe the results of the person’s Clinical Cluster comparisons.
Appendix A A.2: CPI Equivalents of Sums of Scaled Scores 12
Appendix A.2 CPI Equivalents of Sums of Scaled Scores
Appendix ADefi nitions of CHC Abilities and Processes
CHC THEORY AND THE STRUCTURE OF
COGNITIVE ABILITIES AND PROCESSES
In this section, the defi nitions of the broad and some of the narrow abilities in-cluded in CHC theory are presented. These defi nitions are consistent with those presented in Flanagan, Ortiz, and Alfonso (2007). Given the number of narrow abilities and processes comprising the theory (more than 70), it is not practical to include defi nitions of all of them in this text. Practitioners are referred to Carroll (1993), Flanagan, and colleagues (2007), and McGrew (2005) for defi nitions of all CHC narrow abilities and processes.
Fluid Intelligence (Gf )
Fluid Intelligence (Gf) refers to mental operations that an individual uses when faced with a relatively novel task that cannot be performed automatically. These mental operations may include forming and recognizing concepts, perceiving relation-ships among patterns, drawing inferences, comprehending implications, problem solving, extrapolating, and reorganizing or transforming information. Inductive and deductive reasoning are generally considered to be the hallmark narrow-ability indicators of Gf. The WISC-IV provides three distinct reasoning tests: Picture Concepts and Word Reasoning (which involve the use of inductive reasoning) and Matrix Reasoning (which involves the use of general sequential reasoning, i.e., deductive reasoning). Select Gf narrow abilities are defi ned in Table A.1.
Crystallized Intelligence (Gc)
Crystallized Intelligence (Gc) refers to the breadth and depth of a person’s acquired knowledge of a culture and the effective application of this knowledge. This store of primarily verbal or language-based knowledge represents those abilities that have been developed largely through the investment of other abilities during educational and general life experiences (Horn & Blankson, 2005).
2 APPENDIX A
Gc includes both declarative (static) and procedural (dynamic) knowledge. Declarative knowledge is held in long-term memory (Glr) and is activated when related information is in working memory (Gsm). Declarative knowledge in-cludes factual information, comprehension, concepts, rules, and relationships, especially when the information is verbal in nature. Procedural knowledge refers to the process of reasoning with previously learned procedures in order to trans-form knowledge. For example, a child’s knowledge of his or her street address would refl ect declarative knowledge, while a child’s ability to fi nd his or her way home from school would require procedural knowledge. Declarative knowledge refers to knowledge “that something is the case, whereas procedural knowledge is knowledge of how to do something” (Gagne, 1985, p. 48). The WISC-IV measures many different aspects of Gc. For example, the WISC-IV Verbal Com-prehension Index (VCI), which is composed of Vocabulary, Similarities, and Comprehension, provides an assessment of several Gc narrow abilities, includ-ing Lexical Knowledge (VL), Language Development (LD), and General Infor-mation (K0). The WISC-IV Information (K0), Word Reasoning (VL), Picture Concepts (K0), and Picture Completion (K0) subtests also involve the use of specifi c Gc narrow abilities. The breadth of Gc is apparent from the number of narrow abilities (i.e., 11) that it subsumes. Select Gc narrow abilities are defi ned in Table A.2.
A rather unique aspect of Gc not seen in the other broad abilities is that it appears to be both a store of acquired knowledge (e.g., lexical knowledge) as well as a col-lection of processing abilities (e.g., oral production and fl uency). Although Gc is probably most often conceptualized much like Gq and Grw as an ability that is highly
Table A.1 Description of Select Gf Narrow Ability Defi nitions
Narrow stratum I name (code) Defi nitionGeneral Sequential Reasoning (RG)
Ability to start with stated rules, premises, or conditions, and to engage in one or more steps to reach a solution to a novel problem.
Induction (I) Ability to discover the underlying characteristic (e.g., rule, concept, process, trend, class membership) that governs a problem or a set of materials.
Quantitative Reasoning (RQ)
Ability to inductively and deductively reason with con-cepts involving mathematical relations and properties.
Note: Narrow ability defi nitions were adapted from McGrew (1997) with permission from Guilford. All rights reserved. Two letter factor codes (e.g., RG) are from Carroll (1993a).
APPENDIX A 3
dependent upon learning experiences (especially formal, classroom-type experi-ences), it also seems to encompass a few narrow constructs that are more process oriented. General Information, as one example of a narrow ability, is clearly a reposi-tory of learned information. Yet, Listening Ability, as another example of a narrow ability under Gc, not only appears to represent learned material but refl ects another ability as well—the ability to comprehend information presented orally. Although comprehension is of course dependent on knowledge of the words being presented, the natures of these abilities are clearly not identical. Assessment of Gc abilities there-fore may require that closer attention be paid to the narrow abilities and processes it subsumes. Despite the interrelatedness of all narrow abilities under Gc, there may well be times when focus on the narrow constructs that are more process oriented as opposed to those that are more knowledge or ability oriented is important.
Quantitative Knowledge (Gq)
Quantitative Knowledge (Gq) represents an individual’s store of acquired quantita-tive, declarative, and procedural knowledge. The Gq store of acquired knowledge represents the ability to use quantitative information and manipulate numeric symbols. Gq abilities are typically measured by achievement tests. For example, most comprehensive tests of achievement include measures of math calculation, applied problems, and general math knowledge. Although intelligence batteries
Table A.2 Description of Select Gc Narrow Ability Defi nitions
Narrow stratum I name (code) Defi nition
Language Development (LD)
General development, or the understanding of words, sentences, and paragraphs (not requiring reading), in spoken native language skills.
Lexical Knowledge (VL)
Extent of vocabulary that can be understood in terms of correct word meanings.
Listening Ability (LS)
Ability to listen and comprehend oral communica-tions.
General (verbal) Information (K0)
Range of general knowledge.
Information About Culture (K2)
Range of cultural knowledge (e.g., music, art).
Note: Narrow ability defi nitions were adapted from McGrew (1997) with permission from Guilford. All rights reserved. Two letter factor codes (e.g., LD) are from Carroll (1993a).
4 APPENDIX A
(e.g., the Wechsler Scales, SB-IV) have measured aspects of Gq, they typically do not measure them comprehensively. The WISC-IV contains one Gq subtest—namely, Arithmetic, which measures primarily Math Achievement (A3).
It is important to understand the difference between Gq and the Quantitative Reasoning (RQ) ability that is subsumed by Gf. On the whole, Gq represents an individual’s store of acquired mathematical knowledge, including the ability to perform mathematical calculations correctly. Quantitative Reasoning represents only the ability to reason inductively and deductively when solving quantitative problems. Recall that RQ is a narrow ability that is typically found to fall under Gf. However, because RQ, as discussed previously, is dependent on possession of ba-sic mathematical concepts and knowledge, it seems to be as much a narrow ability under Gq as it is under Gf. Quantitative Reasoning is most evident when a task requires mathematical skills and general mathematical knowledge (e.g., knowing what the square-root symbol means). Quantitative Reasoning would be required in order to solve for a missing number in a number-series task (e.g., 3, 6, 9, __). Al-though most achievement batteries measure specifi c math skills and general math knowledge, some also require individuals to solve quantitative problems through inductive or deductive reasoning. Therefore, it may be best to conceptualize RQ as being a narrow ability that falls under both Gf and Gq broad abilities. Select Gq narrow abilities are defi ned in Table A.3.
Short-Term Memory (Gsm)
Short-Term Memory (Gsm) is the ability to apprehend and hold information in im-mediate awareness and then use it within a few seconds. It is a limited-capacity system, as most individuals can retain only seven chunks of information (plus or minus two chunks) in this system at one time. The ability to remember a telephone number long enough to dial it, or the ability to retain a sequence of spoken direc-tions long enough to complete the tasks specifi ed in the directions, are examples
Table A.3 Description of Select Gq Narrow Ability Defi nitions
Narrow stratum I name (code) Defi nition
Mathematical Knowledge (KM) Range of general knowledge about mathematics.
Note: Narrow ability defi nitions were adapted from McGrew (1997) with permission from Guilford. All rights reserved. Two letter factor codes (e.g., KM) are from Carroll (1993a).
APPENDIX A 5
of Gsm. Given the limited amount of information that can be held in short-term memory, information is typically retained for only a few seconds before it is lost. As most individuals have experienced, it is diffi cult to remember an unfamiliar telephone number for more than a few seconds unless one consciously uses a cog-nitive learning strategy (e.g., continually repeating or rehearsing the numbers) or other mnemonic device. When a new task requires an individual to use his or her Gsm abilities to store new information, the previous information held in short-term memory is either lost or must be stored in the acquired stores of knowledge (i.e., Gc, Gq, Grw) through the use of Glr.
In the CHC model, Gsm subsumes the narrow construct of working memory, which has received considerable attention in the cognitive psychology literature. Working Memory is considered to be the “mechanism responsible for the tempo-rary storage and processing of information” (Richardson, 1996, p. 23). It has been referred to as the “mind’s scratchpad” (Jensen, 1998, p. 220), and most models of working memory postulate a number of subsystems or temporary buf-
fers. The phonological or articulatory loop processes auditory-linguistic informa-tion, while the visuospatial sketch- or scratchpad (Baddeley, 1986, 1992; Logie, 1996) is the temporary buffer for visually processed information. Most working memory models also posit a central executive or processor mechanism that co-ordinates and manages the activities and subsystems in working memory.
Carroll (1993) is skeptical of the working memory construct, as refl ected in his conclusion that “although some evidence supports such a speculation, one must be cautious in accepting it because as yet there has not been suf-fi cient work on measuring working memory, and the validity and generality of the concept have not yet been well established in the individual differ-ences research” (p. 647). Leffard, Miller, Bernstein, DeMann, Mangis, and McCoy (2006) found that many of the cognitive batteries only measure one aspect of working memory—either the phonological loop or the visuospatial sketchpad—but not both. Notwithstanding these issues, the working memory construct has been related empirically to a variety of different outcomes, in-cluding many specifi c reading and math skills. Therefore, despite the questions that have been raised regarding its validity as a measurable construct, Flanagan and colleagues (2000, 2006, 2007), as well as others (e.g., McGrew, 1997, 2005; Woodcock, McGrew, & Mather, 2001), included working memory in the CHC taxonomy in light of the current literature that argues strongly for its predictive utility. Nevertheless, given that Carroll has raised questions about the validity of the construct of working memory, it is important to remember that this con-struct was included in current CHC theory primarily for practical application
6 APPENDIX A
and ease of communication. Additional research is necessary before defi nitive decisions can be reached about the inclusion or exclusion of working memory in CHC theory. Even so, the WISC-IV Letter-Number Sequencing subtest is purported to measure working memory and the WISC-IV Digit Span subtest is purported to measure memory span, in addition to working memory (viz., Digits Backward). Select Gsm narrow abilities are defi ned in Table A.4.
Visual Processing (Gv)
Visual Processing (Gv) is the ability to generate, perceive, analyze, synthesize, store, re-trieve, manipulate, transform, and think with visual patterns and stimuli (Lohman, 1992). These abilities are measured frequently by tasks that require the perception and manipulation of visual shapes and forms, usually of a fi gural or geometric nature (e.g., a standard Block Design task). An individual who can mentally reverse and rotate objects effectively, interpret how objects change as they move through space, perceive and manipulate spatial confi gurations, and maintain spatial orienta-tion would be regarded as having a strength in Gv abilities. The WISC-IV provides two Gv measures, including Block Design, which assesses the Gv narrow ability of Spatial Relations (SR), and the Picture Completion subtest, which assesses primar-ily Flexibility of Closure (CF). Select Gv narrow abilities are defi ned in Table A.5.
Auditory Processing (Ga)
In the broadest sense, auditory abilities “are cognitive abilities that depend on sound as input and on the functioning of our hearing apparatus” (Stankov, 1994, p. 157) and refl ect “the degree to which the individual can cognitively control the
Table A.4 Description of Select Gsm Narrow Ability Defi nitions
Narrow stratum I name (code) Defi nition
Memory Span (MS) Ability to attend to and immediately recall tempo-rally ordered elements in the correct order after a single presentation.
Working Memory (MW) Ability to temporarily store and perform a set of cognitive operations on information that requires divided attention and the management of the lim-ited capacity of short-term memory.
Note: Narrow ability defi nitions were adapted from McGrew (1997) with permission from Guilford. All rights reserved. Two letter factor codes (e.g., MS) are from Carroll (1993a).
APPENDIX A 7
perception of auditory stimulus inputs” (Gustafsson & Undheim, 1996, p. 192). Auditory Processing (Ga) is the ability to perceive, analyze, and synthesize patterns among auditory stimuli and discriminate subtle nuances in patterns of sound (e.g., complex musical structure) and speech when presented under distorted conditions. While Ga abilities do not require the comprehension of language (Gc) per se, they may be very important in the development of language skills. Auditory Processing subsumes most of those abilities referred to as phonological
awareness/processing and, therefore, tests that measure these abilities (viz., pho-netic coding) are found typically on achievement batteries. In fact, the number of tests specifi cally designed to measure phonological processing has increased signifi cantly in recent years, presumably as a result of the consistent fi nding
Table A.5 Description of Select Gv Narrow Ability Defi nitions
Narrow stratum I name (code) Defi nition
Spatial Relations (SR) Ability to rapidly perceive and manipulate relatively simple visual patterns or to maintain orientation with respect to objects in space.
Visual Memory (MV) Ability to form and store a mental representation or image of a visual stimulus and then recognize or recall it later.
Closure Speed (CS) Ability to quickly combine disconnected, vague, or partially obscured visual stimuli or patterns into a meaningful whole, without knowing in advance what the pattern is.
Visualization (Vz) Ability to mentally manipulate objects or visual patterns and to “see” how they would appear under altered conditions.
Flexibility of Closure (CF)
Ability to fi nd, apprehend, and identify a visual fi gure or pattern embedded in a complex visual array, when knowing in advance what the pattern is.
Spatial Scanning (SS) Ability to accurately and quickly survey a spatial fi eld or pattern and identify a path through the visual fi eld or pattern.
Serial Perceptual Integration (PI)
Ability to apprehend and identify a pictorial or visual pattern when parts of the pattern are presented rapidly in serially or successive order.
Note: Narrow ability defi nitions were adapted from McGrew (1997) with permission from Guil-ford. All rights reserved. Two letter factor codes (e.g., SR) are from Carroll (1993a).
8 APPENDIX A
that phonological awareness/processing appears to be the core defi cit in in-dividuals with reading diffi culties (e.g., Fletcher, Lyon, Fuchs, & Barnes, 2007; Fletcher-Janzen & Reynolds, 2008; Morris et al., 1998; Vellutino, Scanlon, & Lyon, 2000). However, the Ga domain is very broad (i.e., it contains many nar-row abilities subsumed by Ga) and, thus, extends far beyond phonetic coding ability (McGrew, 2005).
In CHC theory, Carroll’s Phonetic Coding (PC) narrow ability was split into separate analysis (PC:A) and synthesis (PC:S) abilities. Support for two different PC abilities comes from a growing number of sources. First, in a sample of kindergarten students, Yopp (1988) reported evidence in favor of two phonemic awareness factors: simple phonemic awareness (required one operation to be performed on sounds) and compound phonemic awareness (required holding sounds in memory while performing another operation on them). Second, in what appears to be one of the most comprehensive Ga
factor-analytic studies, Stankov and Horn (1980) presented evidence for seven different auditory abilities, two of which had tests of sound blending (synthe-sis) and incomplete words (analysis) as factor markers. Third, the WJ-R Sound Blending and Incomplete Words tests (which are almost identical in format to the tests used by Stankov & Horn) correlated only moderately (.37 or 13.7% shared or common variance) across the kindergarten to adult WJ-R norm sample—a correlation that suggests that these tests are measuring different aspects of PC. Fourth, using confirmatory factor-analytic methods, Wagner, Torgesen, Laughton, Simmons, and Rashotte (1993) presented a model of phonological processing that included separate auditory analysis and synthesis factors.
Although the features of these different auditory factors across respective studies are not entirely consistent, there are many similarities. For example, Yopp’s (1988) simple phonemic factor appears to be analogous to Wagner and colleagues’ (1993) synthesis factor and the factor Stankov and Horn (1980) identifi ed with the aid of sound-blending tasks. Also, Yopp’s compound phonemic factor bears similarities to Wagner and colleagues’ analysis factor and the Stankov and Horn factor, identifi ed, in part, by an incomplete words task. Presently, it appears that Wagner and colleagues’ analysis/synthesis distinction is likely the most useful. According to Wagner and colleagues, analysis and synthesis can be defi ned as “the ability to segment larger units of speech into smaller units” and “the ability to blend smaller units of speech to form larger units” (p. 87), respectively. The analy-sis/synthesis distinction continues to be empirically supported, as demonstrated by the separate Phonetic Coding: Analysis and Phonetic Coding: Synthesis tests included in the new WJ III (Woodcock et al., 2001). Select Ga narrow abilities are defi ned in Table A.6.
APPENDIX A 9
Long-Term Storage and Retrieval (Glr)
Long-Term Storage and Retrieval (Glr) is the ability to store information in and fl u-ently retrieve new or previously acquired information (e.g., concepts, ideas, items, names) from long-term memory. Glr abilities have been prominent in creativity research, where they have been referred to as idea production, ideational fl uency, or associational fl uency. It is important not to confuse Glr with Gc, Gq, and Grw, an in-dividual’s stores of acquired knowledge: Gc, Gq, and Grw represent what is stored in long-term memory, while Glr is the effi ciency by which this information is initially stored in and later retrieved from long-term memory.
It is important to note that different processes are involved in Glr and Gsm. Al-though the expression long-term frequently carries with it the connotation of days, weeks, months, and years in the clinical literature, long-term storage processes can begin within a few minutes or hours of performing a task. Therefore, the time lapse between the initial task performance and the recall of information related to that task is not necessarily of critical importance in defi ning Glr. More impor-tant is the occurrence of an intervening task that engages short-term memory before the attempted recall of the stored information (e.g., Gc; Woodcock, 1993;
Table A.6 Description of Select Ga Narrow Ability Defi nitions
Narrow stratum I name (code) Defi nition
Phonetic Coding: Analysis (PC:A)
Ability to segment larger units of speech sounds into smaller units of speech sounds.
Phonetic Coding: Synthesis (PC:S)
Ability to blend smaller units of speech together into larger units of speech.
Speech Sound Discrimination (US)
Ability to detect differences in speech sounds under conditions of little distraction or distor-tion.
Resistance to Auditory Stimulus Distortion (UR)
Ability to understand speech and language that has been distorted or masked in one or more ways.
Memory for Sound Patterns (UM)
Ability to retain on a short-term basis auditory events such as tones, tonal patterns, and voices.
General Sound Discrimination (U3)
Ability to discriminate tones, tone patterns, or musical materials with regard to pitch, intensity, duration, and rhythm.
Note: Narrow ability defi nitions were adapted from McGrew (1997) with permission from Guilford. All rights reserved. Two letter factor codes (e.g., PC:A) are from Carroll (1993a).
10 APPENDIX A
Woodcock, McGrew, & Mather, 2001). Although Glr is measured directly by sev-eral major intelligence batteries, the WISC-IV does not assess Glr. In the present CHC model, 13 narrow memory and fl uency abilities are included under Glr. Select Glr narrow abilities are defi ned in Table A.7.
Table A.7 Description of Select Glr Narrow Ability Defi nitions
Narrow stratum I name (code) Defi nition
Associative Memory (MA) Ability to recall one part of a previously learned but unrelated pair of items when the other part is presented (i.e., paired-associative learning).
Meaningful Memory (MM) Ability to recall a set of items where there is a meaningful relation between items or the items comprise a meaningful story or con-nected discourse.
Free Recall Memory (M6) Ability to recall as many unrelated items as possible, in any order, after a large collection of items is presented.
Ideational Fluency (FI) Ability to rapidly produce a series of ideas, words, or phrases related to a specifi c con-dition or object. Quantity not quality is emphasized.
Associational Fluency (FA) Ability to rapidly produce words or phrases as-sociated in meaning (semantically associated) with a given word or concept.
Expressional Fluency (FE) Ability to rapidly think of and organize words or phrases into meaningful complex ideas under high general or more specifi c cueing conditions.
Naming Facility (NA) Ability to rapidly produce names for concepts when presented with a pictorial or verbal cue.
Word Fluency (FW) Ability to rapidly produce words that have specifi c phonemic, structural, or orthographic characteristics (independent of word meanings).
Figural Fluency (FF) Ability to rapidly draw or sketch several ex-amples or elaborations when given a starting visual or descriptive stimulus.
Note: Narrow ability defi nitions were adapted from McGrew (1997) with permission from Guilford. All rights reserved. Two letter factor codes (e.g., MA) are from Carroll (1993a).
APPENDIX A 11
Processing Speed (Gs)
Processing Speed (Gs), or mental quickness, is often mentioned when one is talking about intelligent behavior (Nettelbeck, 1992). Processing speed is the ability to fl u-ently and automatically perform cognitive tasks, especially when under pressure to maintain focused attention and concentration. Attentive speediness encapsulates the essence of Gs, which is measured typically by fi xed-interval, timed tasks that require little in the way of complex thinking or mental processing. The WISC-IV provides three Gs tasks—namely, Coding, Symbol Search, and Cancellation.
Recent interest in information-processing models of cognitive functioning has resulted in a renewed focus on Gs (Kail, 1991; Lohman, 1989; Woodcock et al., 2001). A central construct in information-processing models is the idea of lim-ited processing resources (e.g., the limited capacities of short-term or working memory). That is, “many cognitive activities require a person’s deliberate efforts and . . . people are limited in the amount of effort they can allocate. In the face of limited processing resources, the speed of processing is critical because it deter-mines in part how rapidly limited resources can be reallocated to other cognitive tasks” (Kail, p. 152). Woodcock (1993) likens Gs to a valve in a water pipe. The rate in which water fl ows in the pipe (i.e., Gs) increases when the valve is opened wide and decreases when the valve is partially closed. Three different narrow speed-of-processing abilities are subsumed by Gs in the present CHC model. Select Gs narrow abilities are defi ned in Table A.8.
Table A.8 Description of Select Gs Narrow Ability Defi nitions
Narrow stratum I name (code) Defi nition
Perceptual Speed (P) Ability to rapidly search for and compare known visual symbols or patterns presented side-by-side or separated in a visual fi eld.
Rate-of-Test-Taking (R9) Ability to rapidly perform tests which are relatively easy or that require very simple decisions.
Number Facility (N) Ability to rapidly and accurately manipulate and deal with numbers, from elementary skills of counting and recognizing numbers to advanced skills of adding, subtracting, multiplying, and di-viding numbers.
Note: Narrow ability defi nitions were adapted from McGrew (1997) with permission from Guilford. All rights reserved. Two letter factor codes (e.g., R9) are from Carroll (1993a).
Appendix A A.8: Visual-Motor Speed Cluster Equivalents of Sums of Scaled Scores 29
Appendix A. 8 Visual-Motor Speed Cluster Equivalents of Sums of Scaled Scores