Interpreting the information from assessment should not be a challenge in itself. If we commit the time to choose an assessment with a purpose that matches our information needs and has clearly articulated targets, then we also need to make sure the results are practical and actionable. Sometimes, however, in order to get to actionable insight, there is a need to distill the information to observe trends and patterns in learning. This is the place where data literacy and assessment literacy intersect.

Data literacy is an important endeavor, particularly if your ability to do your job depends upon your expertise in matters of statistical analysis and psychometrics. For teachers, however, assessment data can often be cumbersome to parse and connect back to instructional strategies. Time in the classroom is precious, so understanding a few basic statistical concepts that are often used to describe assessment results can help teachers get back to teaching quickly.

## Measurement Concepts

Below are a few key measurement concepts that can help educators get more comfortable interpreting and communicating the evidence they surface when using larger scale assessments that produce data and reports.

#### Measurement Scale

Measurement scales are often used in assessments to determine how well a student understands a body of content covered on a test. Generally, content from the curriculum standards is assigned a level of difficulty on the scale. Students are given a “scale score” based upon the average difficulty level of the questions they answer. This information can be helpful to teachers when making decisions about instructional needs. For example, a teacher may want to use the assessment results to group students based upon similar instructional needs.

#### Mean and Median

The mean and median are both known as Measures of Central Tendency. The key word there is Central, as the mean and median are used to describe the center of a set of data. The mean is a method of communicating the average of a set of numbers, whereas the median is the middle number in a given set. These pieces of information can help identify trends and shape comparisons between groups of numbers. Relative to assessment, teachers often rely upon the mean and median to inform grading and summaries of student performance towards targets.

#### Standard Error of Measurement

The statistical analysis of learning is not an exact science. All kinds of factors can influence the way a student will perform on an assessment, from confidence in the subject to the weather on test day. If you gave the same student the same exact test on two different days, there is a likelihood that they will perform differently, better or worse, from the first test to the second. In statistics, this variation between the scores on each test is described as the Standard Error of Measure.

In the classroom, having the Standard Error of Measurement associated with a test score can help a teacher determine a level of confidence in that score. For example, if a student uncharacteristically scores poorly on an assessment and the Standard Error of Measurement is high, it’s possible the student wasn’t giving their best effort. Maybe the student had a tough morning and wasn’t feeling well, so he guessed on several questions. A low score and the high Standard Error of Measure may cause the teacher to check in with the student to see if they want to try the test again another day.