Norms, scales of measurement, standard scores and percentiles
Last reviewed September 2026 by Dr. Andrew Wichterman · Aligned to the current NCE blueprint. Valid for exams through June 30, 2027.
AI-narrated overview made with Google NotebookLM. The written lesson below is by Dr. Andrew Wichterman.
If a client scores 62 on a test, is that good? This lesson explains, from scratch, how test scores get their meaning: the four kinds of numbers, the normal curve, and the one row of equivalent scores that answers almost every conversion item on the exam.
Try to answer each from memory first, even if you have to guess. Guessing before reading makes the answer stick; reveal only after you have tried.
Start here: a score by itself means nothing
A client tells you she got a 62 on a test. Is that good? You have no idea, and neither does she. Sixty-two out of what? Compared to whom? Was 62 the average, or the top of the class? A raw score, the plain number of points someone earned, is meaningless until you know what it is being compared to. This lesson is about the different ways a raw score gets turned into a number that actually says something. It sounds like math, but almost all of it is one picture and one row of numbers you memorize.
Four kinds of numbers
Before you can do anything with a score, you have to know what kind of number it is. Not all numbers behave the same way. A jersey number is a number, but it makes no sense to average jersey numbers. The exam calls these "scales of measurement," and there are four. They stack like stairs: each step can do everything the one below it can, plus one more thing.
Nominal means "name." The numbers are just labels. Diagnosis codes, gender coded 1 and 2, the numbers on football jerseys. You can count how many are in each group, and that is all. Player 12 is not "more" than player 6.
Ordinal means "order." Now the numbers rank things: first, second, third place in a race. But the gaps between them are not equal. First place might have won by a hair; third might have finished ten minutes later. Class rank and "strongly agree to strongly disagree" ratings are ordinal.
Interval adds equal steps. The gap between 90 and 100 is the same size as the gap between 100 and 110. Temperature in Fahrenheit is the classic example. IQ scores and most test scores are treated as interval. What interval scales lack is a true zero: 0 degrees Fahrenheit does not mean "no temperature," and an IQ of 0 does not mean "no intelligence." Because of that, you cannot say 80 degrees is "twice as hot" as 40.
Ratio adds a true zero. Zero dollars means no money. Zero pounds means no weight. Zero seconds means no time. With a true zero, ratios make sense: 40 pounds is twice 20 pounds. Weight, height, age, income, number of sessions attended.
Compared to whom? Norms
Most tests in counseling tell you how a person did compared to other people. The "other people" are the norm group: a large sample who took the test when it was being developed. If a norm group is 2,000 American adults, then a client's score is being compared to those 2,000 people. That is why the norm group matters. Comparing a 70-year-old's memory test to norms built on college students would make her look impaired when she is normal for her age.
A norm-referenced test compares you to other people: "you did better than 84 percent of the norm group." A criterion-referenced test compares you to a fixed standard: "you got 86 percent and the pass mark is 80." A driving test does not care how other people drove that day; you either parallel-parked or you did not.
The one picture that runs the whole lesson
When you measure something like height, weight or test scores in a large group, most people land near the middle and fewer and fewer people land as you move toward either extreme. Plotted, this makes a bell shape called the normal curve. It shows up everywhere because most human traits are a pile-up of many small influences, and pile-ups of small influences produce bells.
The curve has two numbers that describe it. The mean is the average, the peak in the middle. The standard deviation (SD) is how spread out the scores are; think of it as the "typical distance from the average." A small SD means a tall, skinny bell; everyone is close to the mean. A large SD means a low, wide bell.
The 68-95-99.7 rule
Because every normal curve has the same shape, the same percentages always apply. About 68 percent of people are within one standard deviation of the mean (34 percent just below, 34 percent just above). About 95 percent are within two. About 99.7 percent are within three. From those, you can work out anything: if 68 percent are within one SD, then 32 percent are outside it, 16 percent on each side. So a score one SD above the mean beats 84 percent of people (the 50 percent below the mean plus the 34 percent between the mean and +1 SD).
Standard scores: the same position, written different ways
A standard score tells you where a raw score sits on the normal curve. Different tests use different number systems for this, the way temperature can be written in Fahrenheit or Celsius. The position is the same; only the numbering changes.
| Score type | Mean | SD | Where you see it | What "one SD above average" looks like |
|---|---|---|---|---|
| z-score | 0 | 1 | The raw building block; statistics courses | +1.0 |
| T-score | 50 | 10 | MMPI and most personality inventories | 60 |
| Deviation IQ | 100 | 15 | Wechsler scales, Stanford-Binet (SD 16 on older Binet) | 115 |
| Stanine | 5 | 2 | Some achievement tests; whole numbers 1 to 9 | 7 |
| SAT / GRE (per section, older form) | 500 | 100 | College admissions | 600 |
| Percentile rank | median = 50 | not equal steps | Score reports for parents and clients | 84th |
A z-score is the simplest: it just counts how many SDs a score is from the mean. A z of +1 means one SD above average; a z of −2 means two SDs below. Every other standard score is a z-score dressed up to avoid negatives and decimals. A T-score is z × 10 + 50. A deviation IQ is z × 15 + 100.
A percentile rank is different from the others: it tells you the percentage of people who scored at or below you. The 84th percentile means you beat 84 percent of the norm group. It is the easiest score for clients to understand and the one the exam most often asks you to convert to. One caution: percentiles are ordinal, not interval. The distance from the 50th to the 60th percentile is a small change in raw score (lots of people are bunched near the middle), while the distance from the 90th to the 99th is a big one. Never average percentiles.
Doing the conversions in your head
The exam will give you one score and ask for another. You do not need a calculator; you need the row in the figure above and the ability to step from it.
| If the item says… | Think… | Answer |
|---|---|---|
| A client's T-score on the MMPI is 70. What percentile? | T 70 is two SDs above the mean (50 + 10 + 10). Two SDs above is the 98th percentile. | 98th percentile (and "clinically significant" on the MMPI, whose cutoff is T 65) |
| A child's WISC IQ is 85. What z-score? | 85 is 15 below 100, and the SD is 15, so one SD below. | z = −1 (16th percentile) |
| A score is at the 50th percentile. What T-score? | 50th percentile is the mean. | T = 50 (z = 0, IQ = 100) |
| A z-score of +2 on a test with mean 500 and SD 100? | Two SDs above 500. | 700 |
| About what percentage of people have an IQ between 85 and 115? | That is −1 to +1 SD. | About 68% |
A few more score words the exam uses
| Term | Plain meaning |
|---|---|
| Raw score | The plain number of points earned. Meaningless until compared to something. |
| Age equivalent / grade equivalent | "Reads like a typical 4th grader." Easy to misunderstand: a 2nd grader with a grade equivalent of 4.0 did as well as a 4th grader would on 2nd-grade material, not that they can do 4th-grade work. |
| Cut score (cutoff) | The line for a decision: pass/fail, refer/don't refer. Setting it is a judgment, not a statistic. |
| Ceiling effect | The test is too easy; many people get the top score, so it cannot tell high scorers apart. |
| Floor effect | The test is too hard; many people score at the bottom, so it cannot tell low scorers apart. |
| Standardization | Everyone takes the test the same way (same instructions, time, scoring) so that comparisons to the norm group are fair. |
How the exam asks about this
Three kinds of items cover this lesson. Which scale? A short description of a variable, and you name it nominal, ordinal, interval or ratio. Look for order (ordinal), equal steps (interval) and a true zero (ratio). Convert this score. Given a T, IQ, z or percentile, produce another. Use the memorized row. What does this score mean? "A client at the 16th percentile is how far from the mean?" One SD below. "What percent of the population falls between one and two SDs above the mean?" About 13.5 percent.
The most common trap is the percentile: students confuse "percentile" with "percent correct." The 84th percentile does not mean the client got 84 percent of the questions right. It means 84 percent of people scored at or below her.
Report a problem with this lessonWithout scrolling up, write everything you remember from this lesson. Then check yourself against the key terms. Recalling the whole lesson once, right after reading it, does more than reading it twice.
Ten more questions from the whole domain, with an explanation after each answer.
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