Types of scoring options

When you are generating a report, you will have a number of scoring options. Below is a list of all the scoring options available to you, with a description for each. For a quick reference guide of each scoring option, click here.

Unstandardized Scores

The unstandardized scores represent the starting point in the scoring process. These values are computed directly from item-level responses and serve as the base inputs from which all subsequent standardized scores are derived. Grade-Based Scores and Age-Based Scores utilize different scoring calculations from these foundational values, each with distinct interpretive considerations as follows.

Grade-Based Scoring: Raw Score

A Raw Score is the sum of the questions answered correctly on a specific test (e.g., the Naglieri–V test). and the starting point for interpretation when using the grade-based scoring method.

How the Raw Score is Calculated

This score is computed by counting all the items answered correctly, up to the point where the discontinue rule is met (i.e., when four consecutive items have been answered incorrectly). A discontinue rule reduces measurement errors that may occur when using a multiple-choice test format. For example, if five response options are provided, there is a 20% chance that a student can choose the correct answer by guessing. The discontinue rule reduces the measurement error caused by guessing on items that are too hard for the student to answer (i.e., those items above the point where the discontinue rule was met). There is no penalty for wrong answers.

Interpreting the Raw Score

Higher Raw Scores indicate better performance on the test. However, Raw Scores have little interpretive value on their own because they do not reflect how a student’s performance compares to the norm sample. The Raw Scores are used to create the various types of standardized scores, including Rank Order, Percentile Rank, Stanine, and Standard Score. These standardized scores should be used for interpretation and decision-making.

Age-Based Scoring: Raw Sum and Age Raw Score

The Raw Sum is simply the total number of questions a student answers correctly on a test. For example, on the Naglieri–Nonverbal (NV) test, a Raw Sum of 20 means the student correctly answered 20 out of the 40 questions on the test.

Raw Sums are shown in Age Based Group Reports (available for both National and Local Norms) for reference only. They should not be used for score interpretation, because the Raw Sum is not used to calculate age-based standardized scores. Instead of using the Raw Sum, age-based scoring relies on an Age Raw Score.

Age Raw Scores are calculated using Item Response Theory (IRT; see Score Creation for Age-Based National Norms in chapter 5, Development, for more details). The values are used to create all age-based standardized scores. Under this approach:

• Each test item contributes information based on its difficulty and grade form.
• A student’s score more precisely reflects their true underlying ability for their age; not just how many questions were answered correctly.

Why can’t the raw sum be interpreted?

The Raw Sum should not be interpreted or compared across students because it is an unstandardized value and does not account for age-related differences in performance. For interpretation and decision making, districts should rely on standardized scores, including Percentile Ranks, Stanines, and Standard Scores. These standardized scores appropriately account for age, item difficulty, and standardized scoring methods. The Raw Sum should be viewed as a reference value only, not as an interpretive score.

Local Rank Order (Grade- and Age-Based Local Norm Scoring Only)

When Local Norms are selected, student performance is reported using a Local Rank Order. This metric ranks a student’s performance relative to other students in the locally defined comparison group, such as a school, subdistrict, or district as specified by the Assessment Coordinator. The Local Rank Order describes the relative standing among same-grade or same-age peers who have taken the same test (e.g., the Naglieri–Q).

How the Local Rank Order is Calculated

The method used to calculate the Local Rank Order depends on whether Grade-Based or Age-Based Local Norms are selected:

• Grade-Based Local Rank Order. Students are ranked based on their Raw Score within the selected local norm sample.
• Age-Based Local Rank Order. Students are ranked based on their Age-Based Local Standard Score within the selected local norm sample.

In both cases, students are ordered from highest to lowest performance, and each student is assigned a rank.

How to Interpret Local Rank Order

• A lower Local Rank Order value indicates better performance relative to a student’s peers.
• Rank values begin at 1, which represents the highest performing score in the local norm sample.
• Rank values extend up to the number of unique scores in the sample.
• Students who earn the same score are assigned the same Local Rank Order.

Local Rank Order Example

Consider a local norm sample of 60 Grade 3 students within the same school who all took the same test. If there are 35 unique scores, the Local Rank Order will range from 1 to 35.

• Grade-Based Local Rank Order. If three students each earned a Raw Score of 30, and 30 is the highest score in the sample, all three students would receive a Local Rank Order of 1.
• Age-Based Local Rank Order. If three students each earned a Standard Score of 130 (reflecting a nationally-normed age-based standard score; see Standard Score later in this topic), which is the highest score in the sample, all three students would receive a Local Rank Order of 1.

Percentile Rank

A Percentile Rank describes a student’s performance relative to that of other students. Percentile Ranks indicate the percentage of students in the sample who obtained a score that was the same or lower than the score obtained by the student.

How Percentile Ranks are Calculated

• Grade-Based Local Norm Scores. Grade-Based Local Percentile Ranks are calculated using the student’s Raw Score relative to other students in the same grade within the selected local norm sample. For example, if a student has a Grade-Based Local Percentile Rank of 90, this score indicates that the student earned a Raw Score that was equal to or greater than 90% of the students in the local norm sample.
• Age-Based Local Norm Scores. Age-Based Local Percentile Ranks are calculated using the student’s Age-Based Standard Score relative to other students in the selected local norm sample. For example, if a student has an Age-Based Local Percentile Rank of 95, this score indicates that the student earned an Age-Based Standard Score that was equal to or greater than 95% of the students in the local norm sample.
• Grade-Based National Norm Scores. Grade-Based National Percentile Ranks are calculated using the student’s Standard Score relative to grade-level peers in the Grade-Based national norm sample. For example, if a student has a Grade-Based National Percentile Rank of 85, this score indicates that the student earned a Grade-Based Standard Score that was equal to or greater than 85% of their grade-peers in the national norm sample.
• Age-Based National Norm Scores. Age-Based National Percentile Ranks are calculated using the student’s Standard Age Score relative to other same-age peers in the Age-Based national norm sample. For example, if a student has an Age-Based National Percentile Rank of 92, this score indicates that the student earned an Age-Based Standard Score that was equal to or greater than 92% of the students in the national norm sample.

How to Interpret Percentile Ranks

• The higher the Percentile Rank, the better the student’s performance on the test.
• Scores range from 1 to 99 (note that in order to differentiate the very top of the distribution, scores of 99.0 to 99.4 are denoted as 99, while scores ≥ 99.5 are denoted as “>99”).

Stanine

A Stanine indicates how far a student's score is above or below the average score of the norm sample using nine broad categories of relative ranking. Similar to the Percentile Rank, Stanines are derived from the norm sample selected (i.e., local or national).

How Stanines Are Calculated

• Grade-Based Local Norm Scores. Grade-Based Local Stanines are a direct transformation of the Grade-Based Local Percentile Ranks obtained from students of the same grade within the local norm sample.
• Age-Based Local Norm Scores. Age-Based Local Stanines are a direct transformation of the Age-Based Local Percentile Ranks obtained from students of the same age within the local norm sample.
• Grade-Based National Norm Scores. Grade-Based National Stanines are calculated by transforming the Grade-Based National Percentile Ranks from students of the same grade within the national norm sample.
• Age-Based National Norm Scores. Age-Based National Stanines are a direct transformation of the Age-Based National Percentile Ranks obtained from students of the same age within the national norm sample.

How to Interpret Stanines

• Stanines, while not as granular as Percentile Ranks or Standard Scores, can be used as simple categories to broadly classify students. The higher the Stanine, the better the student’s performance on the test. Stanines have a mean of 5 and a standard deviation of 2.
• Stanines between 4 and 6 are considered within the average range, while scores as low as 1 or as high as 9 occur more rarely and denote extremely low or high performance, respectively.

Standard Score

A Standard Score indicates how far a student's score is above or below the average score of the norm sample. Standard Scores represent a more granular unit of measure compared to Stanines.

How Standard Scores Are Calculated

• Grade-Based Local Norm Scores. Grade-Based Local Standard Scores are derived from the student’s Local Grade Percentile Rank, which reflects performance relative to other students in the same grade within the local norm sample. Empirically derived Local Percentile Ranks are converted to their corresponding theoretical Standard Scores to produce the Local Grade Standard Score.
• Age-Based Local Norm Scores. Age-Based Local Standard Scores are derived using a continuous norming transformation of Age Raw Scores. National Age Standard Scores are first calculated from empirically derived Local Age Percentile Ranks. These scores are then referenced against students in the selected local sample to produce the Local Age Standard Scores.
• Grade-Based National Norm Scores. Grade-Based National Standard Scores are calculated by converting the student’s Raw Score using a linear transformation based on the Grade-Based National Norm sample. This produces the National Grade Standard Scores.
• Age-Based National Norm Scores. Age-Based National Standard Scores are calculated using continuous norming transformations of Age Raw Scores within the Age-Based National Norm sample.

How to Interpret Standard Scores

• The higher the Standard Score, the better the student’s performance on the test.
• For the Naglieri General Ability Tests, Standard Scores are standardized to a mean of 100 and a standard deviation of 15. Therefore, a score of 130 represents a student whose ability is two standard deviations higher than typical for their peers.
• Standard Scores are better suited for comparing performance across Naglieri–V, Naglieri–NV, and Naglieri–Q test scores than Percentile Ranks. In general, Percentile Ranks are useful for comparing an individual student to other students of the same grade in the norm sample. However, although Percentile Ranks are often used in education, it is important to understand that these scores should not be used in any mathematical calculations because differences in Percentile Ranks are not equivalent across the full range of scores. For example, the 20-point difference between a 50th and 70th Percentile Rank corresponds to Standard Scores of 100 and 108, while the 20-point difference between a 70th and 90th Percentile Rank corresponds to Standard Scores of 108 and 119.

Confidence Intervals (Grade- and Age-Based National Norm Scoring Only)

All measurements contain some error. Measurement error in the Naglieri General Ability Tests is described in terms of the Confidence Interval. Confidence intervals take measurement error into account, providing, at a specific level of probability (usually 90% or 95%), a range of scores within which the true Naglieri General Ability Tests score is expected to fall (Harvill, 1991). That is, if an individual was evaluated 100 times and a 95% confidence interval was created each time, then 95 of those 100 confidence intervals would be expected to contain their true score. Note that confidence intervals are provided when using the National Norms scoring option, but not with Local Norms.

The width of the confidence interval indicates the precision of the estimate; more confidence can be placed in estimates with narrow confidence intervals than in those with wide confidence intervals (Morris & Lobsenz, 2000). A less reliable standard score (i.e., one with a greater error in measurement) will have a wider confidence interval than more reliable scores. A true-score 95% confidence level is used for the Naglieri General Ability Tests (Grade-Based National Norms, and Age-Based National Norms only), with calculations based on each test’s standard error of measurement (SEM; Nunnally, 1978). For example, if a Grade 2 student’s standard score was 90 on the Naglieri–V, the Assessment Coordinator can be quite confident that the student’s true Standard Score falls within the range of 82–100. See chapter 8, Practical Applications of Standard Error of Measurement: Confidence Intervals, for more information about Confidence Intervals.

Total Score

The Total Score for the Naglieri General Ability Tests is based on the combination of the Naglieri–V, Naglieri–NV, and/or Naglieri–Q test scores. When a student has completed all three tests, a Total Score based on all three tests can be computed. When a student has completed only two tests, a Total Score is computed based on the two-test combination to derive a composite score.

How the Total Score is Calculated

• Grade-Based Local Norm Scores. Grade-Based Total Local Standard Scores are derived from the distribution of the sum of their constituent Local Standard Scores.
• Age-Based Local Norm Scores. Age-Based Total Local Scores are provided as a Standard Score, Percentile Rank, and Stanine. The Age-Based Total Local Standard Score is calculated based on the student's responses to all three tests combined, and it accounts for the grade form, correctness of their responses, and relationships between the tests. To obtain the Local Total Score, the score derived from the national comparison is then normally distributed within the locally selected sample. The Age-Based Total Local Percentile Rank and Stanine are based on the location of the student’s Age-Based Total Local Standard Score on the normal probability distribution.
• Grade-Based National Norms Scores. Grade-Based Total National Scores are provided as a Standard Score, Percentile Rank, and Stanine. The Total National Standard Score is derived from the distribution of the sum of their constituent National Standard Scores. The Total National Percentile Rank is based on the location of the student’s Total Standard Score on the normal probability distribution. The Total National Stanine is derived from the constituent National Standard Scores.
• Age-Based National Norm Scores. Age-Based Total National Scores are provided as a Standard Score, Percentile Rank, and Stanine. The Total National Age Standard Score is calculated based on the student's responses to any combination of two or three tests, and it accounts for the grade form, correctness of their responses, and relationships between the tests.

How to Interpret the Total Score

• For each Total Score type (Total Percentile Ranks, Total Stanines, and Total Standard Scores), higher scores indicate better test performance.

References