NY Learning Disability DefinitionA 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

0.03

40 55 70 85 100 115 130 145 160

Score74 98

0

0.03

40 55 70 85 100 115 130 145 160

Score74 98

Tests with high reliability

Tests with low reliability

Effects of CorrelationRegression 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 Score95

– note: based on IQ score of 90, Kate’s predicted achievement score is “pulled towards the mean”

• Difference between Predicted and Actual Achievement21

• Magnitude of Difference required at .05 level 22

• Kate’s discrepancy does not qualify as a severe discrepancy

0

0.03

40 55 70 85 100 115 130 145 160

Score74 90

Kate’s Measured Achievement (74) and Ability (90)

0

0.03

40 55 70 85 100 115 130 145 160

Score74 90

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 over-identify 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