Why Specific Cognitive Processing Weaknesses Are Typically Only Partial

Explanations for Academic Deficits:It Is Hard To Explain

That Which Is (Mostly) Unexplained

W. Joel SchneiderDepartment of Psychology

Assumptions• Perfect multivariate normality• Linear relationships only• Correlations are population parameters.

These assumptions are unlikely to be strictly true but they are

probably not that far from reality.

Difference = 0

Difference = 25

Difference = 25

Cognitive Strength

Cognitive Weakness

Academic Deficit

Gc = 100

Reading Decoding =75

Phonological Awareness =75

Gc = 100

Phonological Awareness =75

Does this weakness explain the academic deficit?

rGc.PA0.68

0.420

0.264

RD = b0 + b1 * Gc + b2 * PA + error

75 = 31.55 + 0.420 * 100 + 0.264 * 75 + -18.4

Ŷ = 93.4Predicted RD when

Gc = 100 and PA = 75

Error~N(0,11.642)

R2 = 0.40

Gc~N(100,152)

PA~N(100,152)

RD~N(100,152)

1

Ŷ ~N(100,9.462)

1

31.55 1.00

RD Gc PA

RD 1 0.60 0.54

Gc 0.60 1 0.68

PA 0.54 0.68 1

b1

b2

b0

RD = b0 + b1Gc + b2PA + error

ErrorError = -18.4

Ŷ = 93.4Ŷ

Ŷ ~N(100,(15R)2)

Error ~N(0,152(1 - R2))

Reading Decoding =75

Gc = 100

Phonological Awareness =75

Multiple R = rŶ.RD

Multiple Regression

Correlationsfrom WJ III NU (ages 9 to 13):

40 50 60 70 80 90 100 110 120 130 140 150 160

Reading Decoding(Gc = 100, PA = 75)

~N(93.4,11.642)

Reading Decoding(Whole Population)

~N(100,152)

Width of 95% CI = 59Width of 95% CI = 46

This is what “40% of the variance explained” looks like.

So, instead of a rangeof nearly 4 SDs, the

95% CI has narrowedto “only” 3 SDs.

Reading Decoding = 75 is somewhat unusual in both distributions.

6.6 points ≈ 0.5 SD

40

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100

110

120

130

140

150

160

40 50 60 70 80 90 100 110 120 130 140 150 160

Reading Decoding

Predicted Reading Decoding (Ŷ)

RD distribution whenGc = 100 and PA = 75

~N(93.4,11.642)

5.7% of kids with Gc = 100 and PA = 75 have RD ≤ 75

Predicted RD = 93.4 when Gc = 100 and PA = 75

40

50

60

70

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90

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110

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140

150

160

40 50 60 70 80 90 100 110 120 130 140 150 160

Reading Decoding

Predicted Reading Decoding (Ŷ)

RD distribution whenGc = 100 and PA = 100

~N(100,11.642)

1.6% of kids with Gc = 100 and PA = 100 have RD ≤ 75

Predicted RD = 100 when Gc = 100 and PA = 100

5.7 %1.6 % ≈3.6 ×  risk   of  𝑅𝐷≤75

Gc = 100PA = 100

Gc = 100PA = 75

The risk of low performance is low for people with either profile, but

the relative risk of low performance is much higher when PA is low. The

relative risk of low performance increases if the threshold for

defining “low performance” is lower.

RD distribution whenGc = 100 and PA = 6

~N(75,11.642)

50% of kids with Gc = 100 and PA = 6 have RD ≤ 75

Predicted RD = 75 when Gc = 100 and PA = 6

PA must be less than 6 before it is typical for a person with Gc = 100 to

have RD ≤ 75.

In a normal distribution, only about 1.2 people in the whole world have a

score 6 or lower!

If Gc = 100, how low does PA have to be

before we have a good explanation of RD = 75?

What about Multiple Deficits?

Gc Gf Gv Ga Glr Gsm Gs70

75

80

85

90

95

100

105

No Deficits 4 Processing DeficitsRD~N(100,11.242)1.3% risk of RD≤75

RD~N(90.5,11.242)8.4% risk of RD≤75

Relative Risk = = 6.4

ConclusionsWe must abandon dichotomous thinking. The question is not whether some ability is relevant to some outcome, but how much. Often, as in the demonstration here, a relevant predictor is merely a risk factor for low performance and is unlikely to be a sufficient explanation.

Current Context

Best Available Data and Models