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From Scores to Insights: How to Summarize Assessment Results
Educational Psychology · Chapter 8: Assessment, Testing, and Making Sense of ResultsSection 8.5 · lesson 74 of 1008 min · free with a free account
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In this lesson
Raw scores, percentiles, standard scores, and how to explain them without causing alarm.
- Convert raw scores into derived scores
- Interpret percentile ranks and standard scores correctly
- Explain why grade equivalents mislead
- Communicate results to families in plain language
Transcript
Everything said in the video, section by section (1,200 words). Read along, or search it.
Assessment, Testing, and Making Sense of Results
From Scores to Insights
A parent hears that their child scored at the thirty-second percentile. Most parents will hear that as a failing grade. It is not. It describes performance within the average range. This section is about that gap between a number and its meaning. We start with raw scores, and why they say almost nothing alone. Then percentages, percentile ranks, and standard scores. Then grade and age equivalents, which mislead more than they inform. And finally how to report any of this to a family. Keep one principle in mind throughout. No score is self-interpreting. Every one of them needs a scale and a comparison group attached.
Raw Scores
The Most Direct Data, and the Least Useful
A raw score is simply the number of items a student answered correctly. It is the most direct form of assessment data there is. And it is remarkably difficult to interpret on its own. Suppose a student earned forty-two out of sixty points. What does that tell you? Almost nothing yet. You do not know the difficulty level of the test. You do not know how the other students performed. Without those, the number describes a test more than a student. Which is why raw scores are usually transformed. They become derived scores, which supply context. And which supply comparability, so numbers can be set beside each other.
Percentages
The Simplest Transformation
The simplest transformation is the percentage score. Take the raw score, divide by total possible, then multiply by one hundred. So forty-two out of sixty becomes seventy percent. And seventy percent places the student against a familiar benchmark. Percentage scores are intuitive, which is a genuine advantage. They are easy to communicate to students and to parents. But they carry two real limitations. First, two different tests with a seventy percent score are not equivalent. Not if those tests differ in difficulty, and they usually do. Second, percentages say nothing about how a student compares to peers. Nor to any national norm group. For those comparisons you need norm-referenced derived scores.
Percentile Ranks
Where You Stand in the Line
The most widely used of those is the percentile rank. It indicates the percentage of students in the norm group. Specifically, the percentage who scored at or below a given score. So a student at the seventy-second percentile scored as well as, or better than, seventy-two percent of students in the norm group. Read that carefully, because it is the source of endless confusion. It is not seventy-two percent of the questions answered correctly. It is seventy-two percent of the comparison group outperformed. Percentile ranks are easy to communicate. And they are widely understood by parents and educators alike. That accessibility is exactly why the next limitation matters so much.
The Catch
Percentiles Are Ordinal, Not Interval
Percentile ranks are ordinal data, and not interval data. That distinction has a very practical consequence. Consider the gap between the fiftieth and fifty-fifth percentile. Now consider the gap between the ninetieth and ninety-fifth. Those two gaps are five percentile places each. But they do not represent the same performance gap at all. At the upper end, where the ninetieth and ninety-fifth sit, scores are more compressed than they are near the middle. So equal steps along the percentile scale are not equal distances. Not equal distances in actual performance, which is what you care about. Which is why percentile ranks are poor for tracking growth. Subtraction on ordinal data does not mean what it appears to mean.
Standard Scores
A Scale With a Fixed Mean
Standard scores solve that problem. They are also called scaled scores, and the two terms mean the same thing. They transform raw scores onto a scale you choose in advance. A scale with a predetermined mean and standard deviation. For many assessments the mean is set at one hundred. With a standard deviation of fifteen, as in many IQ tests. Others use a mean of five hundred, with a standard deviation of one hundred. That was the scale used in older SAT scoring. The payoff is comparison across different test forms. And comparison over time, from one year to the next. Which makes standard scores particularly useful for tracking growth.
Equivalents
The Two Scores That Mislead
Two more score types deserve a warning label. Age equivalents and grade equivalents. They express performance in terms of typical performance. The typical performance of students at a given age or grade level. They sound wonderfully intuitive, and that is the trap. They are frequently misunderstood, and must be communicated carefully. Of the six score types in this section, these are the riskiest to report. They are the ones most often read as saying something they do not say. So the safe practice is the one that governs every score here. State the scale. And never let the number travel on its own.
Six Score Types
What Each One Shows, and Hides
Six score types, side by side, with what each one hides. A raw score, like forty-two out of sixty, shows the number correct. Its limitation is that it carries no context and is not comparable. A percentage, like seventy percent, shows the proportion correct. It is easy to grasp, but it is scale-dependent. A percentile rank, like the seventy-second, shows standing versus a norm group. But it is ordinal, without equal intervals. A standard score, like one hundred and seven, sits on a fixed scale. Mean of one hundred, standard deviation of fifteen. It requires explanation. A grade equivalent, like seven point four, gives a typical grade level. An age equivalent does the same for age. Both of those last two are often misunderstood.
Key Idea
No Score Interprets Itself
All of which leads to the central idea of this section. No score is self-interpreting. A raw score of fifty-five means nothing on its own. Not without the maximum, the difficulty, and the comparison group. So educators must always provide context when reporting results. What scale was used. What the average score was. And what the score means in terms of instructional implications. That last one is the part most often left out. Here is the failure that context prevents. A parent hears thirty-second percentile and reads it as failing. When it actually indicates performance within the average range.
Best Practice
Four Rules for Reporting Results
Four best practices govern how results should be communicated. Use plain language, instead of measurement jargon. Contextualize the score with a brief explanation of the scale. Compare performance to relevant benchmarks. Rather than merely comparing it to other students. And focus on growth, as well as on current standing. There is one framing that reliably clears up percentile confusion. Use the out of one hundred students version. If we lined up one hundred students your child's age, your child would score in the middle of that line. Outperforming fifty of them. That sentence removes the confusion with percentage correct entirely.
In Practice
Growth Changes the Whole Story
Here is one teacher doing all of this in a single conference. Ms. Huang shows a parent a reading assessment result. Her son scored at the thirty-eighth percentile. She does not leave the number sitting there alone. First she translates it into people. He read as well as or better than thirty-eight out of one hundred students. Students his own age, in the national sample. Then she locates it. Slightly below average, but within the normal range. And then she adds the piece that changes everything. He grew from the twenty-fourth percentile last year. Which means he made more progress than the average student. Nothing about the score changed. The story did.
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