Scoring options

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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.

Raw Scores

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 any test interpretation. 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 error 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. The higher the Raw Score, the better the student’s performance on the test. Raw Scores can be used to create other types of scores, including Local Rank Order, Percentile Rank, Stanine, and Standard Score.

Local Rank Order

When the Raw Scores are ranked in comparison to other students in the school or district as specified by the Assessment Coordinator, this metric is referred to as a Local Rank Order. The Local Rank Order is used to describe the relative standing of a student’s Raw Score within a local norm sample that consists of same-grade peers who have taken the same test (e.g., the Naglieri–Q). The lower the Local Rank Order, the better the student’s performance on the test. Each student’s Raw Score is given a rank between 1 (which denotes the highest Raw Score) and a figure indicating the lowest Raw Score based on the number of students within the selected local norm sample. For example, in a local norm sample that consists of 60 Grade 3 students within the same school, each student’s Raw Score would be ranked highest to lowest on a Local Rank Order of 1 to 41. Note that students with the same Raw Score will be given the same Local Rank Order (e.g., if three students have a raw score of 30, and 30 is the highest score in the local norm sample, then all three students will have a Local Rank Order of 1).

Percentile Rank

A Percentile Rank describes a student’s performance relative to that of other students. This score ranges 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”).

  • For Local Norm Scores this indicates the percentage of students in the local norm sample who obtained a Raw Score that was the same or lower than the Raw Score obtained by the student. For example, if a student has a Local Percentile Rank of 90, this score indicates that the student earned a Raw Score that was equal to or greater than 90% of students in the local norm sample.
  • For the National Norm Scores this indicates the percentage of students in the national norm sample who obtained a Standard Score that was the same or lower than the Standard Score obtained by the student. If a student has a National Percentile Rank of 85, this score indicates that the student earned a Standard Score that was equal to or greater than 85% of their grade-peers in the National Norm Sample.

The higher the Percentile Rank, the better the student’s performance on the test.

Stanine

A Stanine categorizes relative ranking into nine broad categories. Similar to the Percentile Rank, Stanines are derived from the norm sample selected (i.e., local or national).

  • For the local norms, Stanines are a direct transformation of the Local Percentile Ranks obtained from students of the same grade within the local norm sample.
  • For the national norms, Stanines are calculated by transforming the National Percentile Rank from students of the same grade within the national norm sample.

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. 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.

Standard Score

A Standard Score describes the distance a student’s score is above or below the average score of the norm sample on the test.

  • For the local norms, this is based on a comparison between a student’s Percentile Rank and the Percentile Ranks obtained from students of the same grade within the local norm sample. The Local Standard Scores are calculated based on a conversion from the empirically derived Local Percentile Ranks. These percentile ranks can be converted to their corresponding theoretical standard scores.
  • For the national norms, this is based on a linear transformation of the national norm sample. The National Standard Scores are calculated based on a conversion from the Raw Score.

For the Naglieri General Ability Tests, the Standard Scores are standardized to a mean of 100 and a standard deviation of 15. The higher the Standard Score, the better the student’s performance on the test.

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

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. 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. True-score 95% confidence level is used for the Naglieri General Ability Tests national norms, with calculations based on each test’s standard error of measurement (SEM; Nunally, 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.

Total Score

The Total Score for the Naglieri General Ability Tests is based on the combination of the Naglieri–V, Naglieri–NV, and 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 can still be computed based on the two-test combination to derive a composite score.

  • For the local norms, a Total Local Standard Score is provided. This score is derived from the distribution of the sum of their constituent Local Standard Scores. The higher the Total Local Standard Score, the better the student’s performance on the test.

For the national norms, a Total Score is 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 upon the location of the student’s Total Standard Score on the normal probability distribution. The Total National Stanine is derived from constituent National Standard Scores. For each Total National Score type, higher scores indicate better test performance.

References

Nunnally, J. C. (1978). Psychometric theory (2nd ed.). McGraw-Hill.
The Naglieri General Ability Tests can be scored using local or national norms. The Local Norms Report  provides the results for a group of students that were  tested in the same grade. The results are a direct comparison of any student in relation to all students in a  specific school, district, or subdistrict. The National  Norms Report provides a comparison to a student’s  grade-peers within a nationally representative sample.  Please note that both norms are grade-based.