Putting Assessment Data into Action: Scale Score vs. Percentile Rank — What’s the Difference?

Summary:

• A scale score accounts for the number of items correctly answered and the difficulty of those items, making it possible for educators to directly compare test scores when assessments are of different difficulty.
• A percentile rank compares a student’s score or performance with that of their peers, indicating what percentage of their peers scored the same as or lower than the student. 
• Scale scores can have any range and are often used for criterion-referenced measures.
• Percentile ranks always range from 0 to 99 and are a norm-referenced measure.

Helping Educators Understand Assessment Data

It’s a common question for educators reviewing assessment results:

What’s the difference between a scale score and a percentile rank?

And how can educators use these two metrics to help inform instruction and support student growth?

Let’s explore what these two terms mean and how to interpret them.

What Is a Scale Score?

Technically speaking, a scale score is a score that has been placed onto a standardized scale, often by taking a raw score (the number of items correctly answered), weighting those items by difficulty or another factor, and then using a mathematical formula to place the weighted score on a standardized scale.

But what does that actually mean for educators?

Let’s consider a scenario in which a teacher is using an adaptive diagnostic assessment at the beginning of the school year to determine her students’ current proficiency levels before she plans instruction. 

Adaptive assessments can be especially helpful in classrooms with students at multiple different performance levels, as the assessments will automatically adjust the difficulty of the items shown according to each student’s performance on prior items. However, that means that not all students see the same items — some students will see easier items and some students will see more challenging items.

For example, Elise is a fourth-grade student who has not yet mastered the third-grade math expectations, and so is entering fourth grade with some gaps in her prerequisite skills. When she takes the beginning-of-year adaptive math assessment, she answers 80% of the items correctly. Most of the assessment items she sees represent third- or fourth-grade-level skills and standards.

Meanwhile, Lula is a fourth-grade student who excelled in math last year and had already mastered the fourth-grade math expectations at the end of third grade. On her adaptive math assessment, she answers 75% of the items correctly. Most of the assessment items she sees represent fifth- and sixth-grade-level skills and standards.

How does their teacher compare these two students? It doesn’t seem right to give Lula a lower score because she only answered 75% of her items correctly, since her items were so much more challenging and represented much more complex skills.

Enter the scale score. The scale score helps account for the number of items correctly answered and the difficulty of those items. It places all student’s assessment results on a single range or scale — hence the name, scale score.

With a scale score, it’s possible to directly compare the assessment results for two different students, even if those students saw very different items on the adaptive assessment.

For example, in this scenario, Lula would have a higher scale score than Elise, even though Lula answered fewer items correctly. The scale score allows their teacher to directly compare the two students’ scores.

Scale scores also allow educators to compare performance between two different tests that use the same scale. For example, Lula takes a beginning-of-year diagnostic in the fall and a middle-of-year diagnostic in the winter. Although these are two different tests, they use the same scale. This means Lula’s teacher can directly compare Lula’s beginning-of-year scale score with her middle-of-year scale score to determine how much Lula has grown over the semester.

In fact, as long as the assessments use the same scale, scale scores can even be compared across school years — allowing educators to get a clear snapshot of a student’s year-over-year growth!

Scale Scores Can Inform Criterion-Referenced Measures

Another important thing to know is that scale scores are often the basis for criterion-referenced measures.

What is a criterion-referenced score?

A criterion-referenced measure, such as a criterion-referenced score, compares a student’s performance against an objective standard or expectation, such as fourth-grade math standards.

Although the term may be unfamiliar, most people have encountered criterion-referenced measures in their lives.

For example, have you ever been tested for anemia? For adults, a “healthy” hemoglobin level is typically 13.5 to 17.5 grams per deciliter for men and 12.0 to 15.5 grams per deciliter for women. This is a criterion! If your hemoglobin level is lower than this criterion, your doctor may recommend taking iron supplements or changing your diet.

It’s not so different with student test scores. If a student’s test score is below the criterion, their teacher may want to give them supplemental support (such as additional instruction and personalized practice) or change the amount and/or type of instruction they receive (for example, by providing them with Tier II or Tier III intervention support).

In education, scoring criteria are often organized into different performance categories such as “does not meet expectations,” “partially meets expectations,” “meets expectations,” or “exceeds expectations.” Thresholds or “cut scores” are used to determine which category a student’s scale score falls into.

In the example of Elise and Lula, their teacher sees that Elise’s scale score is in the “does not meet expectations” category and Lula’s scale score is in the “exceeds expectations” category.

In this way, criterion-referenced scale scores can help educators answer the key question: Is this student meeting grade-level expectations?

What Is a Percentile Rank?

Another question an educator might want to answer is: How is this student performing compared to their peers? 

By itself, a scale score will not answer that question. Instead, an educator needs to look at a different measure: the percentile rank.

Let’s go back to our fourth graders, Elise and Lula.

We already know from Elise’s scale score that she’s not meeting grade-level expectations. But her teacher knows that many other fourth-grade students in the district are also not meeting grade-level expectations. Is this “typical”?

Elise’s percentile rank helps to answer this question. A percentile rank compares Elise’s scale score to the scale scores of the norm group — that is, a group of her peers, usually a large group of students that serve as a nationally representative sample of students in the same grade who were tested at the same point or at a similar point in the school year.

Elise’s teacher sees that her percentile rank is 49. This means that Elise scored the same as or higher than 49% of the students in the norm group, and 51% of the students in the norm group scored higher than Elise.

So, although Elise isn’t meeting grade-level expectations, her performance is pretty typical for her same-grade peers. 

Meanwhile, Lula has a very high percentile rank of 86. This means she scored the same as or higher than 86% of the students in the norm group, and only 14% of the students in the norm group scored higher than Lula.

This shows that Lula’s “exceeds expectations” performance is not typical for her peers.

Percentile Ranks Are Norm-Referenced Scores

Another important thing to know is that percentile ranks are always norm-referenced scores.

What is a norm-referenced score?

A norm-referenced score compares a student’s performance against the performance of their peers (the “norm group”).

Much like criterion-referenced scores, although “norm-referenced score” may not be a term most people use frequently, it is something that most people have encountered.

A common example are growth charts for children.

For example, Elise and Lula are both 9 years old at the start of fourth grade. Elise is 4’6”, which puts her at the 75th percentile for height. This means she is as tall as or taller than 75% of 9-year-old girls. Meanwhile, Lula is 4’1”, which puts her at the 10th percentile for height. She is shorter than 90% of the girls her age!

However, what percentile rank doesn’t tell us is whether or not Lula’s family should be worried about her growth. For that, her doctor would need to check her height against a criterion, such as a CDC Growth Chart. This would quickly tell her doctor that, while Lula is short for her age, her height falls within what the CDC considers a “healthy” range and is not a cause for concern in and of itself.

Of course, Lula’s doctor may want to investigate further: she may want to look at Lula’s percentile rank over time to see if it’s trending upwards or downwards, as well as look at other measures, such as weight, blood test results, activity levels, etc.

Similarly, a low percentile rank on an assessment may be a signal for an educator that they need to look more closely at a student’s overall performance. However, the percentile rank by itself cannot tell an educator if a student is meeting grade-level expectations or not.

Differences Between Scale Score and Percentile Rank

There are some other key differences between scale scores and percentile ranks that educators should know when looking at assessment results.

Different Ranges

Scale scores can have a wide variety of ranges depending on the scale used. Scale scores can go from 0 to 100, 200 to 1200, 551 to 664, or any other range. For example, imagine two different college entrance exams. The first exam uses a scale score from 400 to 1600, and the second uses a scale score from 1 to 36.

One very important thing to remember is that you can never compare scale scores from two different tests using two different scales. For example, a 35 on the exam with a 1-36 range is not a “worse” score than a 600 on the exam with a 400-1600 range, even though 35 is a smaller number than 600. These two tests use two different scales and so their scores cannot be directly compared to each other.

Meanwhile, percentile ranks will always range from 0 to 99. This is because percentile ranks are directly tied to percentages. A percentile rank of 40 always means that the individual scored the same as or higher than 40% of the norm group, and lower than 60% of the norm group. It’s not possible for a student to have a percentile rank below 0 or above 99. 

However, it is important to remember that not all assessments measure the same skills or use the same norm group. Therefore, it is possible for a student to have a percentile rank of 40 on one measure and a percentile rank of 75 on a different measure. 

For example, Elise may not have strong math skills, but she might have excellent reading skills. Although her percentile rank was 49 on her math assessment, she has a percentile rank of 76 on her reading assessment.

Here’s another example: Lula’s percentile rank on her school math assessment was 86. However, when Lula joins a competitive math club, she takes another math assessment — and this time her percentile rank is only 51. That’s because the norm group for her school math assessment consisted of a group of fourth-grade students that were representative of fourth-grade students across the entire country. However, the norm group for her math club assessment was a group of high-achieving students who ranged from fourth to sixth grade.

So even though Lula’s skills haven’t changed, her percentile rank changed because the norm group she was being compared to changed.

This is why it’s important to remember to not directly compare percentile ranks from different assessments, even if all percentile ranks use the same 0-99 range.

One Test Can Provide Multiple Measures

What kind of measures will an educator get from assessment?

Some assessments only provide criterion-referenced measures like a scale score. Rarely, an assessment will only provide a percentile rank. However, many assessments provide both a scale score and a percentile rank.

When looking at assessment results, be sure you know what kind of results you’re getting: scale score, percentile rank, or both.

Certain assessments — such as diagnostic or benchmark assessments — usually provide a performance level in addition to a scale score and a percentile rank for each student. Often, a student will have an overall performance level that represents their overall performance, plus a performance level for each skill domain assessed.

For example, on a math assessment, Lula’s teacher may see that, overall, she is exceeding grade-level expectations. However, when her teacher looks more closely, she sees that Lula is exceeding expectations in the Geometric Reasoning and Algebraic Reasoning domains, meeting expectations in the Measurement domain, and not meeting expectations in the Data & Probability domain. That means that, although overall Lula is exceeding grade-level expectations overall, she may need additional support in Data and Probability to continue growing her math skills.

Some assessments will also provide additional measures, such as a Lexile® or Quantile® measure. Both Lexile measures (for reading) and Quantile measures (for math) are scale scores that use their own unique scale to measure a student’s reading or math ability. Additional scores like a Lexile or Quantile measure can help give educators additional insight into student performance.

Changes Mean Different Things

Because a scale score and a percentile rank are different measures, changes in these measures mean different things.

Over time, a student receiving appropriate instruction and support should see an increase in their scale score. An increase in scale score indicates an improvement in skill level and proficiency — in other words, it’s an indication that the student is learning and growing.

In contrast, a student receiving appropriate instruction and support may not see an increase in their percentile rank. If a student’s percentile rank stays the same over time, this does not indicate that the student is not learning. Instead, it indicates that the student is learning at the same rate as their peers. An increase in percentile rank may indicate that a student is learning at an accelerated rate (faster than their peers) and a decrease in percentile rank may indicate that a student is learning at a decelerated rate (slower than their peers).

However, an educator should never rely on percentile rank alone to make instructional decisions about a student. Other factors, such as the student’s scale score and performance category, should also be taken into consideration.

One Point in Time vs. Trends Over Time

Although knowing a student’s scale score and percentile rank at a single point in time can be very helpful for informing instruction, being able to see the change over time in a student’s scale score and percentile rank can provide even deeper insight into a student’s performance and growth.

Changes in scale score can help a teacher see how much a student has learned over a set period of time, whereas changes in percentile rank can help the teacher see if a student is learning at the same rate as their peers. 

For more information on how to interpret changes in scale score and percentile rank over time, be sure to subscribe to Savvas Insights to be notified when our upcoming blog on this topic is published.

Scores Are Numbers, Not Whole Students

The most important thing to remember when looking at scale scores and percentile ranks is that they are just numbers — they’re a numerical approximation of a student’s performance on the day they took the assessment, but they are not a holistic representation of that student.

Numbers alone can’t capture a complete picture of each student. Whenever educators are making instructional decisions, they should consider assessment data in addition to their knowledge of the student, their professional experience and expertise, best practices based on research, their school or district’s standards and expectations, insights and shared learnings from their colleagues, and the many other factors that can help inform the best course of action for each student.

Ultimately, the goal is to make sure each student has the opportunity to learn, grow, and achieve their full potential. That requires more than just assessments: it also requires high-quality instructional materials, research-based instructional approaches, clear learning expectations, effective classroom management strategies, and a supportive learning environment.

Most importantly, it requires great educators. At the end of the day, it’s educators who teach students and guide them at every stage of their academic learning journeys, from kindergarten all the way to graduation — and often beyond.

Assessment scores are simply one tool among many to help educators do their best work as they help students build the skills and knowledge they need to be successful in school and in life.

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