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NY Learning Disability Definition
A student with a disorder in one or more of the basic
psychological processes involved in understanding or in using
language, spoken or written, which manifests itself in an
imperfect ability to listen, think, speak, read, write, spell, or
to do mathematical calculations. The term includes such
conditions as perceptual handicaps, brain injury, neurological
impairment, minimal brain dysfunction, dyslexia and
developmental aphasia. The term does not include students
who have learning problems which are primarily the result of
visual, hearing or motor handicaps, of mental retardation, of
emotional disturbance, or of environmental, cultural or
economic disadvantage. A student who exhibits a discrepancy
of 50 percent or more between expected achievement and
actual achievement determined on an individual basis shall be
deemed to have a learning disability
IDEA's Definition of Learning Disability
". . . a disorder in one or more of the basic psychological
processes involved in understanding or in using language,
spoken or written, that may manifest itself in an imperfect
ability to listen, think, speak, read, write, spell, or do
mathematical calculations, including conditions such as
perceptual disabilities, brain injury, minimal brain
dysfunction, dyslexia, and developmental aphasia."
However, learning disabilities do not include, "…learning
problems that are primarily the result of visual, hearing, or
motor disabilities, of mental retardation, of emotional
disturbance, or of environmental, cultural, or economic
disadvantage."
Example of State Requirements for LD Diagnosis
Achievement Intelligence
Discrepancy
Severe Discrepancy Determination by Formula
Kate obtains an IQ score of 90 and an achievement score of 74. Is
this 16-point difference large enough to be considered a ‘significant
difference’ between ability and achievement?
Data:
Ability Score ………………………………………………... 90
Reliability of Ability Score ……………………………. … 0.91
Achievement Score ……………………………………….. 74
Achievement Reliability ………………………………….. 0.91
Correlation Between Ability and Achievement Scores .. 0.47
Methods for Determining Severe Discrepancy
•
•
•
•
Deviation from Grade Level
Standard Deviation from the Mean
Standard Score Comparison
Regression Formula
Deviation from Grade Level
• difference between grade level functioning and
placement
• “Is a student’s measure of grade level functioning
significantly different than his or her grade
placement?”
• For example:
– Kate is in grade 6 and is achieving at a 3rd grade level
– the 50% discrepancy would be considered a severe
discrepancy
Deviation from Grade Level (continued)
• Problems:
– grade equivalent scores are not based on equal units
– learning is not linear
– example: a third grader two years behind is not
comparable to an 11th grader two years behind
– least psychometrically sound method
Standard Deviation from the Mean
• Difference between obtained achievement and normed
averages
• Compares an individual to a group
• “Is a student’s score on an achievement test discrepant
from the test mean by a standard value”
• To calculate:
– change achievement score to z-score
– compare the z-score to some predefined discrepancy (e.g., 1.5sd or
1.75 sd)
Standard Deviation from the Mean
(continued)
• Example of Kate
– if a severe discrepancy is defined as 1.5 sd
– Kate’s achievement score of 74 would transform to a z-score of
(74-100)/15=-1.73
– Kate’s discrepancy does qualify as a severe discrepancy
• Problems:
– conceptually different from measures of intrapersonal
discrepancies & would qualify all low performing individuals
– would not identify many students who would be expected to
perform better than the average
– does not consider measurement error
Standard Score Comparison
• Difference between standard scores from ability
and achievement tests
• Compares an individual to himself or herself
• To calculate:
– obtain measures of achievement and ability
– change scores to z-scores
– subtract achievement z-score from ability z-score and
divide by standard error of the difference
– compare to predefined severe discrepancy score
Standard Score Comparison (continued)
• Example of Kate
– if a severe discrepancy is defined as 1.5 sd
– Kate’s achievement score of 74 would transform to a z-score of
(74-100)/15=-1.73
– Kate’s ability score of 90 would transform to a z-score of
(90-100)/15=-0.66
– use formula (Zach-Zability)/((1-rxx) + (1-ryy))1/2
= (-1.73+.66)/.42
= -2.5
– compare -2.5 to 1.5 (note the severe discrepancy cutoff point is
expressed as a positive value but think of it as a discrepancy
between achievement and ability that would be a negative value
when used to define ld)
– because Kate’s discrepancy is larger than the predefined severe
discrepancy
– Kate’s discrepancy does qualify as a severe discrepancy
Standard Score Comparison (continued)
• Problems:
– assumes that measures of ability perfectly correlate with measures
of achievement
– e.g., assumes that Kate’s measured IQ of 90 would mean that we
expect her achievement score to be 90
– does not consider measurement error
Regression Formula
• Difference between standard scores from ability
and achievement tests using regression formulas
– use regression to predict an individual’s achievement
score from his or her ability score
– includes corrections for measurement error and
regression to the mean
Regression Formula (continued)
• Example regression formula:
y’ = rxy(Sy/Sx)(IQ - `x) + `y
where:
y’ = predicted achievement score
rxy = correlation between IQ and achievement test
Sy = standard deviation of achievement test
Sx = standard deviation of IQ test
`x = mean of IQ test
`y = mean of achievement test
Effects of Test Reliability or Error of Measurement
0.03
0
40
55
70
85
74
100
98
115
130
145
160
130
145
160
Score
Tests with high reliability
0.03
0
40
55
70
85
74
100
98
115
Score
Tests with low reliability
Effects of Correlation
Regression to the Mean
Regression Formula (continued)
• After predicting achievement based on IQ
– discrepancy is formed by calculating difference
between actual and predicted achievement
– the calculated discrepancy is tested for
significance
– is the discrepancy so large that we would
consider it not likely due to chance?
• Determination is made
Regression Formula (continued)
• Calculation discrepancy using a severe discrepancy
calculator:
• Kate’s Ability Score
90
• Achievement Score
74
• Reliability of Ability Score.91
• Achievement Reliability
.91
• Correlation Between Ability and Achievement Scores
.47
Regression Formula (continued)
• Predicted Achievement Score
95
– note: based on IQ score of 90, Kate’s predicted achievement score
is “pulled towards the mean”
• Difference between Predicted and Actual Achievement
21
• Magnitude of Difference required at .05 level
• Kate’s discrepancy does not qualify as a severe
discrepancy
22
0.03
0
40
55
70
74
85
90
100
115
130
Score
Kate’s Measured Achievement (74) and Ability (90)
145
160
0.03
0
40
55
70
74
85
90
100
115
130
145
160
Score
95
Predicted Achievement Score (95) Based on IQ of 90
Regression Formula (continued)
• Problems:
– complex calculations
– excludes many students in lower ability range
who would be included using simple
discrepancy method
• Benefit:
– most psychometrically sound method
Summary
• Determination of LD Diagnosis is based in
part on:
– State determinations of severe discrepancy
– method of calculating severe discrepancy
• Different methods of calculating a
discrepancy will result in different students
being severely discrepant
Summary
• Regression models appear to produce proportional
racial representation (Braden & Weiss, 1988)
• Standard score comparison methods may overidentify high ability students and under-identify
minority students (Braden & Weiss, 1988)
• Deviation from grade level or test mean will
under-identify high performing students.
Questions
• Is LD a Valid diagnosis?
– can you make inferences based on LD?
– Can you make predictions about LD individuals
that differ from “low achievement”?
• Is your method of determining LD
consistent with your conception of LD?
– e.g., intrapersonal construct vs. interpersonal
construct