Understanding Norms

By: Rachel Brown, Ph.D., NCSP

For an assessment to be helpful, it needs a basis for comparison. This is true whether the assessment is school-based or related to other aspects of life. For example, health care providers routinely measure blood pressure at medical appointments. Knowing one’s blood pressure numbers can be helpful, but only if one also knows what numbers are healthy and what numbers are unhealthy. The same is true for school-based assessments. For scores on any test to be useful, there must be a basis of comparison. Schools often use norms to evaluate students’ scores on assessments. This posting will review how norms are developed and how they can assist teachers with instructional decision making.

What Are Norms?

The term “norms” is short for normative scores. Normative scores are ones collected from large numbers of students with diverse backgrounds for the purpose of showing “normal” performance on a specific assessment. Normal performance refers to what scores are typically observed on an assessment by students in different grades. For example, students in lower grades are not expected to know as much as students in higher grades. If students in all grade levels completed the exact same test, younger students would be expected to obtain lower scores than older students on the test. Such a score distribution would be considered “normal” in relation to student grade levels. Norms represent the typical or “normal” scores of students at different grades or learning levels. In addition to scores being different for younger and older students, they can also vary among students in the same grade because of differences in prior learning and general ability.

Importantly, norms can only be developed for tests that are standardized. Standardized tests are ones that have specific directions that are used in the same way every time the test is given. This is because test scores can only be compared when the test is identical for all students who take it, including both the items and the testing instructions. Comparing scores from tests with different items and directions is not helpful because the students did not complete the same tasks; score differences are probably due to the different questions on the tests. Standardized tests allow score comparisons because the students all answered the same questions under the same conditions.

How Are Norms Developed?

In order to understand the differences in students’ scores within and between grade levels, test developers develop and try out test questions many times before the final test is complete. Once the test is complete, the developers then give the test to what is a called a “normative sample.” This sample includes a selection of students from all of the grades and locations where the final test will be used. The sample is designed to allow collection of scores from a smaller number of students than the entire group that will eventually take the test. But, the sample needs to be representative of all the grade levels and backgrounds of students who will later take the test. This is important because if the normative sample includes only students from a certain grade level or part of the country, the scores will not be similar to all other student grades levels and backgrounds.

In order to make sure that the normative sample is representative, a certain number of students from each grade as well as from applicable geographic regions are selected. For example, in gathering a normative sample for a state assessment a certain number of students from each grade level in each county or school district could be selected. In addition to selecting students based on grade and location, normative samples need to consider other student background features. For this reason, students with disabilities, who are learning English, and from different socioeconomic backgrounds need to be included. One of the ways that test publishers decide how many students to recruit for a normative sample is to use data from the U.S. Census. The U.S. government conducts a survey of all the people in the country every 10 years. This census provides information about how many people of what backgrounds live in each state. Such data can help test publishers know the backgrounds of the students who attend schools in different regions.

After identifying the backgrounds representative of students needed for the sample, the test publisher will recruit students and have them complete the assessment according to the standardized rules. Once all of the sample participants have completed the assessment, the scores are organized so that they can be analyzed. One of the major ways that the scores are organized is to put them into sets by grade levels and then rank order them. Rank ordering means to list them from lowest to highest. The rank orders by grade level can then be converted to percentile rankings. Percentiles provide a way for teachers to know which scores are below, average, or above expectations for each grade level. Percentile ranks group the scores in relation to the number of students whose scores were similar or different to other students. Percentile ranks range from 1% to 99% and can be used to understand what scores are typical — or average — for students in each grade.

How Do Norms Assist Teachers?

Scores collected as part of a normative sample that represents all of the types of students who will later take a certain test offer a way for teachers to know which scores are typical and which ones are not typical. To determine if a score is typical, the teacher compares it to the available norms. For example, if a teacher wanted to know if a score of 52 on a standardized and normed test is in the average range, he or she can consult the norms for that test. If the test has a range of scores from 0 through 100, and the average score is 50, then a score of 52 would be considered normal. But if the test has a range of scores from 0 through 200 and the average score is 100, 52 would be considered a low score. The teacher could then look and see the percentile ranking for a score of 52. The percentile ranking would indicate what percentage of students in the normative sample scored below and above 52. Such information would help the teacher to know how far below average the score is. The teacher could also identify how many points the student needs to gain in order to reach the average range of scores.

In any class there will always be a range of student abilities and scores. If teachers can learn how each student’s score compares to the norms, they can develop instruction that matches each student’s learning needs. It is important to note that norms can be used to identify both lower-achieving and higher-achieving students. In some classes, there might be many students who are well above the average score. In such cases, the teacher needs to develop lessons that help students advance to even higher levels. Unlike benchmarks, norms provide information related to all students’ current skills. Benchmarks show which students have met a single specific goal but norms indicate all students’ standing compared to the distribution of scores from a normative sample.

Summary

Norms — short for normative scores — are scores from standardized tests given to representative samples of students who will later take the same test. Norms provide a way for teachers to know what scores are typical (or average) for students in a given grade. Norms also show the range of all possible scores on the test at each grade level and the percentile ranks matched to each score. Unlike benchmarks, norms provide information about all students’ relative performance on a test, whether at the low, middle or high levels. Teachers can use norms to identify each student’s current proficiency as compared to other students, as well as to identify which students need remedial, typical, or accelerated instruction.

Dr. Rachel Brown is FastBridge Learning’s Senior Academic Officer. She previously served as Associate Professor of Educational Psychology at the University of Southern Maine. Her research focuses on effective academic assessment and intervention, including multi-tier systems of support, and she has authored several books on Response to Intervention and MTSS.

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