Norming

Norms and Norm Groups

To make an appropriate comparison, the background characteristics of the norm group and the individual test taker should be similar. The performance of an 18-year-old cannot be compared with the norm group comprising students of 12–15 years. The student’s math results might look good compared to that norm, but the score could look poor when compared to a group of engineering [Page 1158]professionals. The norm group information (e.g., age, gender, socioeconomic status, location) should appear in the testing manual, so that administrators can make informed decisions about the reliability of the student’s performance. To avoid grouping issues, the score of an individual should be compared with similar test takers taking the assessment at the same time.

Often, several groups of individuals are considered the reference groups. These norms can be based upon developmental time points, such as age or grade in school. Geography can influence norms as well. For national norms, test developers often use nationally representative samples. Less frequently, developers or test administrators report local norms of a smaller population to determine the performance of students in other state districts, for example. A controversial norm called race norming involves the comparison based on race or ethnicity. Smaller, defined groups within the larger sample are broadly referred to as subgroup norms. User norms include the performances of the test takers during one time period. Most tests provide only the user norms for the age, grade, geographic, and/or race or ethnicity reference groups.

Procedures

To construct the norms, test developers must define and identify the specific testing population (e.g., students applying to postsecondary institutions) and decide the statistics to be calculated. These decisions will impact the test developers in drawing a sample from the target population. Once the sample takes the psychological assessment, the group statistics are calculated along with standard errors. These statistics describe the performance of the norm group, the individuals used for comparison, representative of the target population. Based on the desired types of normative scores to be reported, test developers then create conversion charts.

To do this, the test sample is divided into appropriate subgroups, such as age subgroups, and percentiles are identified along the range of year or month time points. The norm group scores are commonly assumed to fall within a normal distribution, allowing the conversion based on the mean and standard deviation. The new score distribution must then be smoothed to the curve to avoid irregularities between the percentile points. This conversion table helps exam administrators transform raw scores, the initial score achieved from the assessment, into interpretable data, frequently called derived or scaled scores. If the data are not normally distributed, test developers may transform the distribution into a normal distribution or include additional computations for interpretation.

...