## How Should Educators Interpret Value-Added Scores?

### Highlights

- Each teacher, in principle, possesses one true value-added score each year, but we never see that "true" score. Instead, we see a single estimate within a range of plausible scores.
- The range of plausible value-added scores -; the confidence interval -; can overlap considerably for many teachers. Consequently, for many teachers we cannot readily distinguish between them with respect to their true value-added scores.
- Two conditions would enable us to achieve value-added estimates with high reliability: first, if teachers' value-added measurements were more precise, and second, if teachers’ true value-added scores varied more dramatically than they do.
- Two kinds of errors of interpretation are possible when classifying teachers based on value-added: a) “false identifications” of teachers who are actually above a certain percentile but who are mistakenly classified as below it; and b) “false non-identifications” of teachers who are actually below a certain percentile but who are classified as above it. Falsely identifying teachers as being below a threshold poses risk to teachers, but failing to identify teachers who are truly ineffective poses risks to students.
- Districts can conduct a procedure to identify how uncertainty about true value-added scores contributes to potential errors of classification. First, specify the group of teachers you wish to identify. Then, specify the fraction of false identifications you are willing to tolerate. Finally, specify the likely correlation between value-added score this year and next year. In most real-world settings, the degree of uncertainty will lead to considerable rates of misclassification of teachers.

### Introduction

A teacher's value-added score is intended to convey how much that teacher has contributed to student learning in a particular subject in a particular year. Different school districts define and compute value-added scores in different ways. But all of them share the idea that teachers who are particularly successful will help their students make large learning gains, that these gains can be measured by students' performance on achievement tests, and that the value-added score isolates the teacher's contribution to these gains.

A variety of people may see value-added estimates, and each group may use them for different purposes. Teachers themselves may want to compare their scores with those of others and use them to improve their work. Administrators may use them to make decisions about teaching assignments, professional development, pay, or promotion. Parents, if they see the scores, may use them to request particular teachers for their children. And, finally, researchers may use the estimates for studies on improving instruction.

Using value-added scores in any of these ways can be controversial. Some people doubt the validity of the achievement tests on which the scores are based, some question the emphasis on test scores to begin with, and others challenge the very idea that student learning gains reflect how well teachers do their jobs.

**In order to sensibly interpret value-added scores, it is important to do two things: understand the sources of uncertainty and quantify its extent.**

Our purpose is not to settle these controversies, but, rather, to answer a more limited, but essential, question: How might educators reasonably interpret value-added scores? Social science has yet to come up with a perfect measure of teacher effectiveness, so anyone who makes decisions on the basis of value-added estimates will be doing so in the midst of uncertainty. Making choices in the face of doubt is hardly unusual – we routinely contend with projected weather forecasts, financial predictions, medical diagnoses, and election polls. But as in these other areas, in order to sensibly interpret value-added scores, it is important to do two things: understand the sources of uncertainty and quantify its extent. Our aim is to identify possible errors of interpretation, to consider how likely these errors are to arise, and to help educators assess how consequential they are for different decisions.

We'll begin by asking how value-added scores are defined and computed. Next, we'll consider two sources of error: statistical bias and statistical imprecision.

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