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Understanding the Highly Capable Score Report

How to Understand Your Student’s Highly Capable Scores

(Also known as the Technical Appendix for Matrix Scores)

 

The Issaquah School District reports scores for Highly Capable testing as a single holistic matrix score. This technical appendix defines key terms, explains how the matrix score is determined using a z-score formula and provides examples of score reports.

ISD uses three assessments to determine Highly Capable Program eligibility:

  1. CogAT: Cognitive Abilities Test (K-12)
  2. i-Ready Reading and Math (grades K-5) or the IOWA Achievement Test (grades 6-12)
  3. TTCT: Torrance Test of Creative Thinking (grades 2 - 12)

The Matrix Score At-A-Glance:

The District uses a z-score formula to convert the standard scores from each test to a common scale. Scores from the three assessments can then be combined for each student into a single holistic matrix score. This approach allows the District to be more precise and equitable in its decisions and supports students who might have a somewhat uneven profile.

Step 1:  Use Standard Scores

Step 2: Each score is converted to a z-score and assigned a matrix score 1-8

Step 3: Calculate weightings to get a total weighted matrix score

Step 4: Use the total matrix score to determine eligibility for various Highly Capable Program services

The Matrix Score in Detail

Step 1: Use the standard score

The Standard Score (SS) is based on the student’s raw score, which has been adjusted for age or grade and placed on a scale that makes a comparison with a representative sample of students of the same age or grade. The CogAT uses age based standard scores and the Iowa Achievement Test and Torrance Test of Creative Thinking use grade based standard scores. Standard scores are used to determine the matrix score instead of percentile ranks because standard scores can be normalized. Normalization is a process of adjusting values measured on different scales to a common scale. 

The standard score is used for making the comparisons necessary in the identification process. There is wide-range of standard scores with the 99th percentile.

Percentile Rank   Standard Score
99 160
99 159
99 158
99 157
99 156
99 155
99 154
99 153
99 152
99 151
99 150
99 149
99 148
99 147
99 146
99 145
99 144
99 143
99 142
99 141
99 140
99 139
99 138
99 137
99 136
99 135

 

 

Step 2:  Each score is converted to a z-score and assigned a matrix score 1-8

What is a Z-score?
 

Z-scores are standard scores which are calculated by a formula that includes the mean (average) of all students in the norm group and the standard deviation (distance from the mean) to create a statistic that is consistent across all tests. 

What is a standard deviation?

The Standard Deviation (SD) tells us how far a score is from the average score for a group. A score that is very close to the average score will have a very small standard deviation. A score that is far above the average score will have a large positive standard deviation. A score that is far below the average score will have a large negative standard deviation. A standard deviation ranges from -4.0 to +4.0. 

 

 

How are Z-scores calculated?

The formula for calculating Z-scores is the student’s standard score minus the mean of the norm group divided by the standard deviation.  The mean of the norm group and the standard deviation are statistics provided by the test vendors. 

Z-scores help to identify students significantly above the average while reducing the risk of a student being eliminated because of one individual criteria.          

Examples:

Standard Score Minus

Mean Standard Score*

Divided by the Standard Deviation*

Equals the z-score

Matrix Score

155 -

100

/16

= 3.43

8

240 -

185

/21.6

= 2.59

7

121 -

111.3

/15.6

= .62

3

*These are sample numbers for the purpose of understanding the formula only.

 

Step 3: Calculate weightings to get a total weighted matrix score

 

 Z-scores are converted to a matrix score to determine which students are significantly above the average.  (See the Z-score Conversion Matrix below). The Final Matrix Scores are totaled to determine the appropriate services.

Z-score Conversion Matrix Table

Z-score

Relation to the Mean of all Scores

Matrix Score Conversion

3.00 and above

A score that is at least 3 standard deviations (SD) above the mean

8

2.5 - 2.99

A score that is between 2.5 SDs above the mean and 3 SDs above the mean

7

2.0 - 2.49

A score that is between 2 SDs above the mean and 2.5 SDs above the mean

6

1.5 - 1.99

A score that is between  1.5 SDs above the mean and 2 SDs above the mean 

5

1.0 - 1.49

A score that is between 1 SD above the mean and 1.5 SDs above the mean 

4

0.5 - .99

A score that is between ½ SD above the mean and 1 SD above the mean

3

0 - .49

A score that is between the mean and ½ SD above the mean

2

-.01 and below

A score that is below the mean

1

 

 

 

 

 

 

 

 

 

 

 

Are the Scores Weighted?

The scores are weighted to balance priorities in ability and achievement for success in the services offered. Weightings are given to the measures according to their value in predicting success in the Highly Capable Program. The CogAT is weighted X3 and the i-Ready or Iowa X2 and the TTCT X1. The CogAT is weighted higher (X3) than the IOWA Achievement Test (X2) because this test is intentionally designed to identify students who will be successful in a highly capable program.  Weighting the achievement test slightly less attempts to equitably balance the range of educational experiences of the students. Note that the TTCT assessment is used for grades 2 through 12 only.

Step 4: Use the total matrix score to determine eligibility for various Highly Capable Program services

Highly Capable Program Selection Criteria

Program

Assessments Used

Matrix Score for Eligibility

PEP

i-Ready Math and Reading

CogAT Full Battery

80 or greater

SAGE Reading

i-Ready Achievement - Reading

CogAT Nonverbal

CogAT Verbal

TTCT Creativity Index

47 or greater

SAGE Math

i-Ready Achievement - Math

CogAT Nonverbal

CogAT Quantitative

TTCT Creativity Index

49 or greater

MERLIN

CogAT Verbal

CogAT Nonverbal

CogAT Quantitative

i-Ready Achievement Math

i-Ready Achievement Reading

TTCT Creativity Index

84 or greater

 

Sample Score Reports

 

Sample Score Report ~ CogAT Screener

Below is a sample score report. See the steps listed below to understand how the Weighted Matrix Score is derived.

Test Given

Standard  Score (SS)

Matrix Score

Weighting

Weighted Matrix Score

 

 

 

 

 

CogAT Screener

132

6

x3

18

 

 

 

 

 

Total Matrix Score Required for Highly Capable Full Testing Eligibility = 20 or greater

Total Matrix Score: 18

 

 

 

 

Step 1: Standard Score is reported from the test vendor

Step 2: The score is converted to a Z-score and assigned a matrix score

Step 3: The weighting is calculated to get a final weighted matrix score

Step 4: The total matrix score is used to determine eligibility for full testing

Sample Score Report for Full Testing ~ PEP (K-2)

 

Below is a sample score report. See the steps listed below to understand how the Weighted Matrix Score is derived. 

Test Given

Standard  Score (SS)

Matrix Score

Weighting

Weighted Matrix Score

 

 

 

 

 

CogAT Verbal

148

8

x3

24

CogAT Quantitative

135

6

x3

18

CogAT Nonverbal

139

6

x3

18

i-Ready Reading

154

8

x2

16

i-Ready Math

150

8

x2

16

 

 

 

 

 

Total Matrix Score Required for Highly Capable Eligibility with services in PEP= 80

Total of all tests.

Total Matrix Score:

92

 

 

 

 

 

 

 

 

 Step 1: Standard Scores are reported from the test vendor

Step 2: Each score is converted to a z-score and assigned a matrix score

Step 3: Weightings are calculated and the final matrix scores are added together to get a total weighted matrix score

Step 4: The total matrix score is used to determine eligibility for HCP services

 

Sample Score Report ~ SAGE and MERLIN

Below is a sample score report for a student who qualified for SAGE Math. See the steps listed below to understand how the Matrix Scores for MERLIN, SAGE Reading and SAGE Math are derived.

Test Given

Standard  Score (SS)

Matrix Score

Weighting

Weighted Matrix Score

 

CogAT Verbal

121

4

x3

12

CogAT Quantitative

140

7

x3

21

CogAT Nonverbal

146

7

x3

21

i-Ready Reading 198 4 x2 8
i-Ready Math 207 7 x2 14

Torrance Test of Creative Thinking (TTCT)

116

2

x1

2

 

 

 

Total matrix score required for HCP eligibility with services in MERLIN is 84.

 

This is the sum of all tests.

 

MERLIN Matrix

 

Score: 78

 

 

 

 

Total matrix score required for HCP eligibility with services in SAGE Reading is 47.

 

This is the sum of the CogAT Verbal, CogAT Nonverbal, Iowa Reading and TTCT.

 

SAGE Reading Matrix

 

Score: 43

 

 

 

Total matrix score required for HCP eligibility with services in SAGE Math is 49.

 

This is the sum of the CogAT Quantitative, CogAT Nonverbal, Iowa Math and TTCT.

 

SAGE Math Matrix

 

Score: 58

 Step 1: Standard Scores are reported from the test vendor

Step 2: Each score is converted to a Z-score and assigned a matrix score

Step 3: Weightings are calculated and the final matrix scores are added together to get a total weighted matrix score

Step 4: The total matrix score is used to determine eligibility for HCP services

Explanation of the Score Report ~ Secondary

Below is a sample score report for a student who qualified for identification in the area of Math. See the steps listed below to understand how the Matrix Scores for secondary qualification in Reading, Math or both areas are derived.

Test Given

Standard Score (SS)

Matrix Score

Weighting

Final Matrix Score

 

CogAT Verbal

121

4

x3

12

CogAT Quantitative

140

7

x3

21

CogAT Nonverbal

146

7

x3

21

 

Iowa: Total Reading* (Two parts)

 

IOWA: Reading

198

 

4

 

x2

 

8

 

IOWA: Vocabulary

194

Iowa Achievement Test:  Total Math

207

7

x2

14

 

Torrance Test of Creative Thinking (TTCT)

116

2

x1

2

 

 

 

 

Total matrix score required for HCP eligibility in Reading is 47.

 

This is the sum of the CogAT Verbal, CogAT Nonverbal, IOWA Reading and TTCT.

 

Secondary Reading Matrix

 

Score: 43

 

 

 

Total matrix score required for HCP eligibility with services in Math is 49.

 

This is the sum of the CogAT Quantitative, CogAT Nonverbal, IOWA Math and TTCT.

 

Secondary Math Matrix

 

Score: 58

 Step 1: Standard Scores are reported from the test vendor

Step 2: Each score is converted to a Z-score and assigned a matrix score

Step 3: Weightings are calculated and the final matrix scores are added together to get a total weighted matrix score

Step 4: The total matrix score is used to determine eligibility for HCP services

* For IOWA Total Reading the standard scores are reported separately for reading and vocabulary. The converted Z-scores are then averaged to determine the matrix score.