Introduction

Maybe you've noticed that there is something around called a "standard score," really an adapted standard score. Maybe you've heard someone in your state office talk about it. Maybe you've tried to convert your own final test scores to standard units. Maybe your state office converted all the scores on your final report for you and returned a score report to you. Just what is this standard score, anyway?

The standard score is actually an adapted version of the standard score many of you learned about in your graduate statistics class. It's a number that very simply represents any score quantity (e.g., percentile rank, percent, raw score) in terms of standard deviations, or a fraction of a standard deviation, in a normal distribution.

If you've seen any of these standard scores from school final reports, you've probably noticed that they tend to look small, such as .17, or .25, or.39, but looks can be deceiving. For example, .25SU (standard units) means a quarter of a standard deviation on the normal curve scale. That's equivalent to 10 percentile rank points in the middle of the normal distribution—an appreciable magnitude for a school to change its student achievement. In fact, based on the distribution of student achievement change in approximately 600 schools that had already completed their first improvement cycle, the following descriptive scale was developed to assist school personnel in interpreting their own student's achievement:

Why Standard Units Are Used

As you know, there are more tests and more ways to assess student achievement than you could list on a large billboard, and these assessment results come in many different forms. To name a few, we get results in percents, percentile rank, raw scores, levels of attainment (rubric scales), grade‑equivalents, tallies (e.g., percent of students achieving some level), and others. We use standard units so that our public (supporters and critics) can make sense of what we've accomplished. Using standard units puts our student achievement results into a single simple numerical language that all can understand.

NCA COS schools normally select three or more goals for a school improvement effort, and they are required to use more than one assessment to document student performance on any one goal. Further, all schools are answerable to our public. Therefore, there are a number of reasons why conversion of student change in achievement scores to standard units is useful. Among them are:

• Public reviewers (supporters and critics) can make sense of what they read.
• The results of two or more assessments on the same goal can be compared, and it may be easier to interpret conflicting results.
• The results on different goals in the school or in the entire region can be compared.
• Educators can make sense of the magnitude of the results (see previous section).
• It isn't necessary for a school to have a statistician or psychometrician on staff to interpret or even convert the scores. The system is user friendly.

With standard scores, faculty within any school can compare the achievement gain on a goal to that of any other goal. State committee members, almost at a glance, can make informed evaluations regarding the progress of the schools that have completed an improvement cycle. The published results of school improvement efforts can inform our critics, our supporters, the profession, and the public at large in terms that make many kinds of internal and external com­parisons possible.

Anyone who has read the early reports on the progress of our schools in the endorsement pro­cess (Wick 1997; Armstrong 1998; Armstrong 2000) may have noticed that the reports were written using adapted standard units as the basic data. If you haven't read these reports, you should. Doing so will not only help to familiarize you with the numbers, it will illustrate the importance of using these standard units to report all our achievement results.

Converting to Standard Units

How is the conversion of assessment scores to standard units accomplished? In any case in which the test score is not already in percent or percentile rank form, that score is converted to a percent. The percent can then be transformed to the standard score in one step. To do so, the assumption is made that if the particular test were given to all appropriate students in the NCA region, the results would approximate a normal distribution over the test mid‑score range. This transformation can change almost all test results, however different they may appear to be from each other, into equivalent, comparable numbers.  Note:  There are two or three assessment result types that for technical reasons cannot or should not be converted to standard units.

In doing this, our adapted standard scores become in essence the numerical universal lan­guage of our reporting and comparisons. Without such a common language we might be char­acterized as a statistical "Tower of Babel," or "babble," as the case may be. With such a lang­uage we have the means to talk to each other and make comparisons, goal to goal, school to school, state to state, and to the region and nation.

If you would like to learn more about NCA COS adapted standard units, contact Bob Arm­strong at the regional office (1-800-525-9517) and ask for a copy of "Standard Score Explanation for Schools," a page‑and‑a‑half description that is only slightly technical. Still more can be learned, including how to convert scores by hand, from Score Conversion Handbook, 2nd Edition. You can con­tact Mr. Armstrong at the regional office for a copy of this, also, or download it on the Internet at http://www.nca.asu.edu/ssw/handbook/. If you want to try converting your own scores but don't want to do so by hand, you can use the conversion algorithms in NCA's software Data Analysis or Data Analysis 2, or by using the Score Wizard on the Internet at http://www.nca.edu/ssw/.

When you become familiar with the NCA COS adapted standard score system, you will find it easy to understand and easy to use. You will wonder how we ever compared and contrasted our achievement results before.

References

Wick, J. (1997). Does the outcomes endorsement really work? NCA Quarterly, 71 (3), 406‑410.

Armstrong, R. (1998). The outcomes endorsement: An update. NCA Quarterly, 72(3), 384‑389.

Armstrong, R. (2000). Change of achievement in outcomes endorsed schools: A second up­date. Journal of School Improvement, 1(1), 23‑29.