# Understanding the Highly Capable Score Report

### How to Understand Your Student’s Highly Capable 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)
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  2-8

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. Example below using CogAT:

 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 2-8

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.

Test Standard Score Mean Standard Score Standard Deviation Z-score Matrix Score
CogAT Nonverbal 160 100 16 3.75 8
CogAT Quantitative 150 100 16 3.13 8
CogAT Verbal 139 100 16 2.44 6
i-Ready Math 515 82.28 24.41 4.00 8
TTCT 111 110.2 15.4 0.05 2

*Means and Standard Deviations in the above table are provided by the test vendor.

#### 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 0

### 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 50 or greater SAGE Math i-Ready Achievement - Math* CogAT Nonverbal CogAT Quantitative TTCT Creativity Index 50 or greater MERLIN CogAT Verbal CogAT Nonverbal CogAT Quantitative i-Ready Achievement Math* i-Ready Achievement Reading* TTCT Creativity Index 85 or greater

* Similar to the CogAT and the TTCT, the Standard Score and Mean provided by the test vendor, which is i-Ready.

#### Sample Score Reports

##### Sample Score Reports ~ CogAT Screener - Kindergarten

Below is a sample score report. Total Matrix Score required on the CogAT Screener for Highly Capable Full Testing is 7 or greater. See the steps listed below to understand how the Matrix Score is derived.

Sample 1:

 Test Given Student's Standard  Score (SS) Mean Standard Score Standard Deviation Matrix Score Eligibility CogAT Screener 139 100 16 6 Not eligible

Sample 2:

 Test Given Student's Standard  Score (SS) Mean Standard Score Standard Deviation Matrix Score Eligibility CogAT Screener 147 100 16 7 Eligible

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 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 145 7 x3 21 CogAT Quantitative 114 3 x3 9 CogAT Nonverbal 148 8 x3 24 i-Ready Reading 510 8 x2 16 i-Ready Math 406 5 x2 10 Total Matrix Score Required for Highly Capable Eligibility with services in PEP= 80 Total of all tests. Total Matrix Score: 80

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 565 5 x2 10 i-Ready Math 515 8 x2 16 Torrance Test of Creative Thinking (TTCT) 116 2 x1 2

 Total matrix score required for HCP eligibility with services in MERLIN is 85.   This is the sum of all tests. MERLIN Matrix   Score: 82 Total matrix score required for HCP eligibility with services in SAGE Reading is 50.   This is the sum of the CogAT Verbal, CogAT Nonverbal, Iowa Reading and TTCT. SAGE Reading Matrix   Score: 45 Total matrix score required for HCP eligibility with services in SAGE Math is 50.   This is the sum of the CogAT Quantitative, CogAT Nonverbal, Iowa Math and TTCT. SAGE Math Matrix   Score: 60

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 50.   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 50.   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.