Scale Scores and Error Band

Results from the summative and interim assessments include scale scores as well as an error band for individuals and groups.

Student-Level Information

Scale Scores for Smarter Balanced ELA and Mathematics Assessments

Each student who completes a Smarter Balanced interim or summative assessment receives an overall scale score. The scale score is the basic unit of reporting. It allows for fair comparisons at both the individual student level and the aggregate or group level. This scale ranges from approximately 2000 to 3000 which includes grades 3-8 and high school.

The Smarter Balanced scale is a vertical scale, which means that student performance in all grades is reported on the same scale. This allows educators to compare a student’s scale score from a test in one grade to that student’s scale score from a test in another grade. However, this comparison should be done with caution, especially when interpreting or predicting scores for non-adjacent grade levels. An important aspect of a vertical scale is that the overall score range for each grade steadily increases, and the threshold scores between each level increase across grade levels. Figure 1 below shows the range of scaled scores for each grade and content area.

Scale scores provide information about overall student performance and can be used to evaluate student progress.

Figure 1. Smarter Balanced Vertical Scale

Scale Scores for CAST Interim Assessments

All reporting is based on scale scores. A scale score for each California Science Test (CAST) Interim Assessment is displayed within CERS along with the achievement level corresponding to the earned scale score.

Scale scores offer a more precise way to determine students’ performance on the computer-based assessments than achievement levels. CAST Interim Assessment scores are on the same scale as scores for the corresponding summative CAST. Given the shorter length of the CAST Interim Assessments, the scale scores may be less reliable than the scores on the summative assessments, and it is important to consider the measurement error when interpreting the scale scores. CAST Interim Assessments are not designed to be a predictive measure of summative assessment performance or for accountability and should not be used for such purposes.

Scale score ranges for all grade levels and grade bands are provided in table 1.

Scale Scores for ELPAC Interim Assessments

All reporting is based on scale scores. A scale score for each English Language Proficiency Assessments for California (ELPAC) Interim Assessment is displayed within the California Educator Reporting System (CERS) along with the performance level corresponding to the earned scale score.

ELPAC Interim Assessment scores are on the same scale as scores for the corresponding Summative ELPAC. The ranges of possible scores are identical for assessments associated with the two ELPAC assessment programs. Each of these assessments has a minimum possible scale score of 1150 and a maximum possible scale score that varies depending on the grade level associated with each assessment. These maximum values are provided in table 2.

ELPAC Interim Assessments are optional resources that provide teachers with helpful information about student progress and are designed to be given at locally determined points during the school year. The ELPAC Interim Assessments can help teachers, students, and parents/guardians gauge student progress toward English language proficiency (ELP) and identify strengths and areas for support in relation to the state standards. ELPAC Interim Assessments are not designed to be a predictive measure of summative assessment performance or for reclassification and should not be used for such purposes.

Error Band

Assessments provide the most precise scores possible, but no assessment can be 100 percent accurate. Each test score reflects a combination of both student skill and factors unrelated to that skill. Unrelated factors can include the sample of items included on the assessment, the student’s mental or emotional state on the testing day, the student’s luck in choosing more correct answers than incorrect answers when guessing, the conditions under which the student took the assessment, and many others.

Each time a student takes an assessment a scale score and the standard error of measurement is calculated for the student’s score. The standard error of measurement (SEM) is an evaluation of the degree to which a student’s test score is expected to change across administrations of parallel test forms because of unrelated factors. The SEM is useful in describing a range for which a student’s actual level of skill is likely. The SEM is accounted for in the student test results by the error bands. The error band indicates a statistical range of scores that the student would likely achieve if they were to take the assessment multiple times. This range represents one standard error of measurement above and below the student’s scale score.

An example of student scale score with the error band can be found in Appendix B of this document. For more examples on measurement error, please refer to the Tests Results are Not Perfect Measures of Student Performance section of this document.

Group-Level Information

Average Scale Scores and Standard Error of the Mean

For group-level reports, an average scale score and error band based on the Standard Error of the Mean for that score are displayed. The average scale score is an average of the scale scores for each individual student in the group. The average scale score is not assigned to an associated achievement level. Instead, a Student Score Distribution displays the percentage of students who performed at each achievement level. The standard error is a statistical term that measures the accuracy with which a sample distribution represents a population by using standard deviation. In statistics, the average mean deviates from the actual mean of the population—this deviation is called the Standard Error of the Mean.