Understanding Your Childs Test Scores 
After having your child evaluated by the school district, are you more confused than ever? Do you know what the test scores mean, and how they apply to your child's progress? You will after reading the following article reprinted from Wrightslaw for easier reading.
This article is reprinted from Wrightslaw
http://www.wrightslaw.com/advoc/articles/tests_measurements.html
Introduction
Most parents of special needs
children know that they must understand the law and their rights.
Few parents know that they must also understand the facts. The "facts" of
their child's case are contained in the various tests and evaluations that have
been administered to the child. Changes in test scores over time provide the
means to assess educational benefit or regression.
Important educational decisions, from eligibility to the intensity of
educational services provided, should be based on the results of psychological
and educational achievement testing. Parents who obtain appropriate special
education programs for their children have learned what different tests measure
and what the test results mean.
As an attorney who specializes in representing special education children, many parents consult with me after they decide that their child's special education program is not appropriate. These parents are often right. However, in most cases they do not have the evidence to support their belief, nor do they know how to interpret and use the evidence contained in educational and psychological tests. They need evidence to support their beliefs.
These parents are convinced that a special education program is not providing sufficient help for the child  that under the present special education program, the child is failing to make adequate progress and has fallen further behind. These parents experience a sense of urgency  the child has usually received special education for several years and time is running out.
Critical educational decisions are often based on the subjective beliefs of parents and educators. As a parent, you may believe that your child is not making adequate progress in a special education program. The special education staff may firmly believe that he is doing as well as he can  or that your expectations are too high. Without objective information, both sides take positions that are based on their emotions  and tempered by their hopes and fears. Appropriate educational decisionmaking must be based on objective information and facts, not subjective emotional reactions and beliefs.
Before you can participate in the development of an appropriate special education program, you must have a thorough understanding of the child's strengths and weaknesses. This information is contained in tests that are used to measure the child's abilities and educational achievement.
Tests administered to
children fall into several categories: intellectual or cognitive tests;
educational achievement tests; projective personality tests, questionnaires and
surveys; speech and language tests; and neuropsychological tests.
To successfully advocate for your child, you must also learn about tests and
measurements  statistics. Statistics are ways to measure progress or lack of
progress, using numbers. After you analyze the scores your child obtains when
tested and you know what these numbers mean, you will be able to develop
an appropriate educational program for your child  a program that is tailored
to the child's unique needs and from which the child benefits.
As you read this article, you will learn what tests and evaluations measure, how
this information is reported, and how to use information from tests to measure
and monitor academic progress. You will also learn how to use graphs to visually
demonstrate your child's progress or lack of educational progress in a powerful
and compelling manner.
Wrightslaw Note:
After you read this article three times, you will be able to interpret
and chart your child's test scores and measure educational progress or lack of
progress.
The United
States Supreme Court
Florence County School District Four v. Shannon Carter
(November 9, 1993)
In Florence County School District Four v. Shannon Carter, 510 U. S.7, 114 S. Ct. 361, (1993), the Supreme Court issued a landmark decision. In Carter, the school system defaulted on their obligation to provide a free appropriate education to Shannon Carter, a child with learning disabilities and an Attention Deficit Disorder. Let's look at how the courts viewed the facts and the law in the Carter case.
Background
When Shannon was in the
seventh grade, her parents talked to the public school staff and expressed their
concerns about Shannon's reading and other academic problems. Shannon was
evaluated by a public school psychologist who described her as a "slow learner"
who was lazy, unmotivated and needed to be pressured to try harder. Her parents
pressured her to work harder. In the ninth grade, despite intense pressure,
Shannon failed several subjects.
Shannon's parents had her evaluated by a child psychologist in the private
sector. That evaluator determined that Shannon's intellectual ability was above
average. Educational achievement testing demonstrated that sixteenyearold
Shannon was reading at the fifth grade level (5.4 GE) and doing math at the
sixth grade level (6.4 G.E.). Shannon had dyslexia. She was finally found
eligible for special education. As she prepared to enter tenth grade, she was
also functionally illiterate.
The school district developed an IEP for Shannon's tenth grade year. This IEP proposed that after a year of special education, Shannon would read at the 5.8 grade equivalent level and perform math at the 6.8 grade equivalent level. In other words, after a full year of special education to remediate her learning disabilities, Shannon was expected to make only four months of progress in reading and math. Progress would be measured by her scores on the WoodcockJohnson and KeyMath educational achievement tests. She would progress from the 5.4 to 5.8 grade level in reading and from the 6.4 to 6.8 grade levels in math.
Shannon's parents insisted that their daughter needed a more intensive program so she could learn the necessary reading, writing and math skills. They felt that the proposed program was inadequate, and worried that Shannon would still be functionally illiterate when she graduated from high school three years later. Emory Carter insisted that the school teach his daughter to read, write and do arithmetic at a high school level when she graduated from high school.
Although Emory and Elaine Carter shared their concerns and wishes with the public school officials, the administrators took a "take it or leave it" position. They refused to provide Shannon with a more intensive special education program where she would receive remediation in reading, writing, and arithmetic. The parents requested a special education due process hearing. The Hearing Officer ruled that the public school IEP was appropriate. The parents appealed this decision to a Review Panel. The Review Panel upheld the decision of the Hearing Officer.
At that point, Emory and
Elaine Carter withdrew Shannon from the public school and enrolled her in
Trident Academy in Mt. Pleasant, South Carolina. Trident Academy is a
private school that specializes in educating and remediating children with
learning disabilities, including dyslexia. When Shannon graduated from Trident
Academy three years later, her reading and math scores were on a high school
level.
Shannon's parents then appealed the Review decision to the U. S. District Court.
They asked Judge Houck to award them reimbursement for Shannon's private school
education at Trident.
After hearing testimony and reviewing the transcripts and documents from the Due Process and Review Hearings, Judge Houck found that the school district's IEP was "wholly inadequate" to meet Shannon's needs. He ruled that Shannon had received an appropriate education at Trident and ordered Florence County to reimburse Shannon's parents for the costs of her education. (Read Judge Houck's decision)
On what basis did Judge Houck decide that the IEP proposed by Florence County was inappropriate? What evidence caused him to decide that Shannon received an appropriate education at Trident Academy?
Evidence & Law
The decisions in Shannon's
case, and in most special education cases, are based on the evidence provided by
tests and evaluations of the child. When Judge Houck wrote that Florence
County's IEP was "wholly inadequate" to meet Shannon's needs, he was relying on
test results. Judge Houck knew the importance of accurately interpreting test
scores. He charted Shannon's test scores and included this information in his
decision. (See also Hall v. Vance, 555 EHLR 437, (E.D. NC 1983),
affirmed at 774 F. 2d 629, 557 EHLR 155, (4th Cir. 1985)) in which U. S.
District Court Judge Dupree charted out James Hall's test scores to support his
decision that Vance County, North Carolina did not provide James with an
appropriate education.)
Florence County appealed Judge Houck's decision to the U. S. Circuit Court of
Appeals for the Fourth Circuit. Appeals from the U. S. District Courts in
Maryland, Virginia, West Virginia, North Carolina and South Carolina are heard
in the U. S. Court of Appeals for the Fourth Circuit by a three judge panel.
Appeals from U. S. Circuit Courts of Appeals are filed in the U. S. Supreme
Court. Occasionally a U. S. Court of Appeals will convene all Judges appointed
to the Circuit to hear a case. This is called an en banc review.
A three judge panel of the Fourth Circuit affirmed Judge Houck's decision about the inadequacy of Florence County's proposed IEP. Florence County then appealed to the United States Supreme Court.
On October 6, 1993, Pete Wright argued Shannon's case before the Court. Thirtyfour days later, on November 9, 1993, the Supreme Court issued a unanimous favorable decision on Shannon's behalf. In the Carter decision, written by Justice Sandra Day O'Connor, the Court upheld the lower court decisions, ruled against Florence County School District Four, and ordered them to reimburse Shannon's parents for the costs of her tuition, room and board, and attorney's fees.
Legal Requirements: Measure Progress Objectively
The
Individuals with Disabilities Education Act (IDEA) requires IEPs to include
measurable annual goals and a description of how the child's progress toward
meeting the annual goals will be measured.
(A) Individualized Education Program.
(i) In General. The term 'individualized education program' or IEP means
a written statement for each child with a disability that is developed, reviewed
and revised ... and that includes 
. . . . . . .
(II) a statement of measurable annual goals, including academic and
functional goals, designed to 
(aa) meet the child's needs that result from the child's disability to enable
the child to be involved in and make progress in the general education
curriculum; and
(bb) meet each of the child's other educational needs that result from the
child's disability;
(III) a description of
how the child's progress toward meeting the annual goals described in
subclause (II) will be measured and when periodic reports on the progress
the child is making toward the annual goals ... will be provided ... (See 20
U.S.C. 1414(d)(1)(A)(i)(II and III; page 99 in
Wrightslaw: Special Education Law, 2nd Edition, page 99. See also the
"Definition of individualized education program" in the federal special
education regulations, Volume 34 of the Code of Federal Regulations, 34 CFR
300.320(a)(2)(i) and (a)(3)(i); page 245 in
Wrightslaw: Special Education Law, 2nd Edition)
Wrightslaw Note:
Shannon's case was decided under an earlier authorization of the Individuals
with Disabilities Education Act.
Shannon's IEP stated that
she "will be able to improve total reading level from the 5.4 grade level to the
5.8 grade level as measured by the Woodcock Reading Mastery Test . . . (and that
she) will improve math skills from the 6.4 grade equivalent to the 6.8 grade
equivalent as measured by the Key Math Diagnostic Test." This IEP complied with
the regulation in existence at that time, (34 C.F.R. § 300.346, since modified),
by including "appropriate objective criteria." The IEP required that the
WoodcockJohnson and KeyMath tests be readministered to measure Shannon's
progress.
The U. S. District Court and the Fourth Circuit found that the proposed gain of four months after a full year of special education was "wholly inadequate."
In an effort to avoid Florence County's fate, many school districts around the country develop IEPs that include no objective measures of the child's progress. Instead of developing goals where the child's progress is measured using objective tests, as Florence County did, many schools now devise IEPs that rely subjective teacher observations of the child's progress. Let's see how this works.
Johnny is a child who has a learning disability that is affects his ability to read. In reading, Johnny is below grade level. Instead of developing an IEP that will measure his progress in reading on specific objective tests, the special education staff may write a goal like this: "Johnny will make measurable progress in reading, as measured by teacher observation and teacher made tests at 80% accuracy."
In that case, "objective measurement of progress" becomes the teacher's subjective observation about whether her student made progress in reading, writing, or arithmetic. The criteria for determining progress becomes 80% of a subjective belief or opinion. When parents object and request a more intensive program that includes clear objective scores, they are often rebuffed or criticized.
In many areas, school board counsel and state departments of education advised schools to stop using objective measurements of progress (tests) to measure progress for special education children.
If you believe that the special education your child is receiving is inadequate, you must have evidence to support your position. You will find this evidence in the public school and private sector testing that has been or will be completed on your child.
To master the material in this article, you should expect to read the article at least three times. When you take this step, you will know what tests and evaluations measure and how test results are reported. You will know how to convert scores on different tests into numbers that are easily understood. And, you will know how to measure a child's educational progress or lack of progress, i.e. regression.
Michael
Three years ago, your eightyearold son Mike began to have serious difficulties in school. By the time he entered third grade, you were deeply concerned about his difficulties in learning to read. His handwriting was nearly illegible. Homework was a nightmare. You consulted with Mike's teacher about these problems several times. Eventually, the teacher sent Mike's "case" to a special education committee. You attended a meeting of this committee. The committee recommended that Mike be evaluated through the school's special education department. Relieved that something would be done to help you child, you consented to these tests.
According to the evaluations, your son has a learning disability. In Mike's case, he has visualperceptual problems and visualmotor problems that negatively affect his ability to read and write. Based on the results of the evaluations, your son was found eligible for special education services at his neighborhood school.
After Mike was found eligible for special education, you attended a meeting to develop his Individualized Education Program (IEP). This IEP provided for Mike to receive one period of special education in an "LD Resource" class every day. It was your understanding that Mike would receive individualized help in reading and writing from a teacher who was specially trained to remediate his learning disability problems.
Three years have passed. Mike hasn't made much progress, despite the special education help. He still has difficulty reading aloud. His spelling is poor, and his handwriting is unreadable. He is behind most of the children in his class. His attitude has changed. He is angry and depressed and says he "hates school."
When you discussed your concerns about Mike's lack of progress with his special education teacher, she reassured you that he was "making progress" and told you to be patient. From your perspective, patience is not the issue. You are worried that your son will never master the basic academic skills. You are worried about his future.
At a recent IEP meeting, you reiterated your concerns about Mike's lack of progress and expressed your belief that he needs more help than he is getting in the school's Resource program. The IEP team disagreed with you. One person said that Mike was getting all the help he needs and that he was really doing quite well. Another member said that your expectations were too high  and if you don't accept Mike's "limitations," you will damage him emotionally.
What should you do?
You know that time in the LD resource class with several other children is not
providing Mike with the individualized help he needs. The school is not teaching
your son how to read, write and do arithmetic. Instead, his IEP team wants to
lower the bar. They suggest more "accommodations" and "modifications." They
propose to reduce his workload, give him untimed tests, and provide him with
"talking books" and a calculator. They do not propose to give him the
individualized help he needs so he can learn to read, write, and do arithmetic.
You believe that Mike's new "emotional problems" are caused by shame and embarrassment because he is not successful in school. How can you, a parent, prove this to the staff at Mike's school so that they will develop an appropriate educational program for him? How will you know when he is getting the help he needs?
Educational DecisionMaking
Many parents assume that interpreting their child's test data is beyond their competence, that this is the responsibility of the school personnel. If parents do not accept the responsibility of learning this information, they leave interpreting the test data to the school psychologist. The school psychologist often has very little information about your child, aside from scores on tests administered years ago.
The basic principles of tests and measurements are not difficult to learn. As you read this article, you will see that you are already familiar with many of the concepts discussed. Statistics and statistical terms are used in many other areas of life, from business and sports to medicine. Newspaper and magazine articles use statistics to inform readers about change or lack of change. You read articles about changes in the population, the climate, the economy. Even public opinion polls include statistical information to inform you or persuade you of a point.
As a parent, you need to expend time and effort to develop a basic understanding of statistics. To accomplish this goal, you should reread parts of this article several times. Underline, make margin notes, and use a highlighter. Be patient and put in the time. The time you spend now will help to change your child's life forever.
As you study this material, you are likely to see some terms and concepts that are confusing at first terms like standard deviation, standard scores, and grade and age equivalents. Other concepts will be familiar  averages, percentages.
When you master this
information, you will understand the educational and psychological tests
administered to your child. You will be able to use this information to make
wise decisions about your child's education. You'll find that your newfound
knowledge and expertise exceeds that of many of the special education staff and
IEP team members.
When you attend your next IEP or Eligibility meeting, you will be glad you did
your homework!
Katie
Katie is fourteen years old and in the ninth grade. She "hates school" and is failing several subjects. As a young child, Katie was bright, happy, and curious. When she entered third grade, her attitude began to change. Now, she locks herself in her room, lies on her bed, and listens to music for hours. She is sullen and angry and says she can't wait to quit school.
In desperation, Katie's parents took her to a child psychologist for testing. At a meeting to interpret the test results to Katie and her parents, the psychologist explained that Katie scored two "standard deviations" above the mean on the Similarities subtest of the Wechsler Intelligence Test for Children, Fourth Edition (WISCIV) and two and a half "standard deviations" below the mean on the spontaneous writing sample of the Test of Written Language, Third Edition (TOWL3).
Wrightslaw
Note: Test
publishers update and revise their tests fairly often. This article does not
focus on any test's strengths or weaknesses, since weaknesses are often
corrected in the next edition of that test.
The Wechsler Intelligence Scale for children was originally known as the WISC.
Later, it was revised and called the WISCR. Several years later, the next
version was published as the WISCIII. The current version is the
Fourth Edition or WISCIV. The first Test of Written Language (TOWL) was
replaced by the TOWL2, then revised and replaced by the
TOWL3.
The Woodcock Johnson battery of tests was known as the Woodcock Johnson PsychoEducational Battery. The WJPEB included educational achievement testing and cognitive ability testing. The current version is called the WoodcockJohnson III Tests of Achievement (WJIII) measures academic achievement. The WoodcockJohnson III Tests of Cognitive Abilities (WJ III) measures general intellectual ability and specific cognitive abilities. Dr. Woodcock also produced the Woodcock Reading Mastery Test, now called the WoodcockJohnson III Diagnostic Reading Battery (WJ IIIDRB).
Tip: For information about thousands of tests, go to Testlink from the Educational Testing Service (ETS) at http://www.ets.org/testcoll/index.html
Parents are often surprised to learn that tests do not necessarily measure what they purport to measure. As you will see, a child's score on a pushup test can be represented as an overall fitness score, a measure of arm strength, an upper body measurement score, a measure of perseveration and persistence, or a measure of a child's motivation. A score may measure only one variable or it may accurately reflect all of the above.
Let's look at tests that measure reading ability. One test that purports to measure a child's reading ability actually measures the child's ability to correctly read aloud and pronounce isolated words out of context, i.e., a word recognition test. This test includes a list of words, i.e., cat, tree, dog, house, person, etc. It does not measure reading and may be adversely affected by a child's speech or word finding problems.
Another reading test has the
child read a passage of text, then answer a series of multiple choice questions
about the passage. In this case, the score may be a measure of the child's
ability to eliminate certain answers in the multiple choice format, i.e.,
reasoning, not reading. Some very bright children may need to recognize and
interpret only a few words to discern the total context. Others have excellent
word recognition abilities but cannot link or interpret the words in a body of
text or passage.
Another reading test has the child read a passage of text aloud (measuring oral
reading), then answer questions. The accuracy of the words read aloud and the
child's understanding of the passage makes up the reading score.
Tip: You need to know what tests were used and what the tests measure. To learn more about reading tests, read Reading Tests: What They Measure, and Don't Measure by Dr. Melissa Farrall.
When we first discussed Katie, we saw that she scored two "standard deviations" above the mean on the Similarities subtest of the Wechsler Intelligence Test for Children, Fourth Edition (WISCIV) and two and a half "standard deviations" below the mean on the spontaneous writing sample of the Test of Written Language, Third Edition (TOWL3).
Do these test scores explain
the academic problems Katie is having? Do they have anything to do with her
moodiness and her intense dislike of school? (Answers: Yes and Yes.)
When we return to Katie's case later in this article, you will understand the
significance of her test scores. You will also understand why Katie's self
esteem has plummeted.
After you learn the material in this article, you will be able to interpret your child's test scores. You will be able to read the preceding paragraph and understand the significance of Katie's scores. You will have acquired skills that will allow you to answer questions like these:
You will also learn how to include objective measurements in your child's IEP so the child's educational progress can be charted often.
Measuring Change: Rulers, Yardsticks and Other Tools
To clarify these points, let's change the facts. You can measure your child's physical growth with a measuring tape and a bathroom scale. You can measure growth by charting how much height increases, as measured in inches, and how much weight increases, as measured by pounds, over a period of months or years. Using these tools, you can document his physical growth. You don't need to be a doctor to understand that increases in these measurements prove that your child is growing.
Assume that your child's height was five feet, three inches last year. This year, the child is five feet, six inches tall. You can report this information in several ways. You can say that last year, your child was sixtythree inches tall and is now sixtysix inches tall. Or, you can say that your child was 5.25 feet tall and is now five and a half feet tall. You can even say that a year ago, your child was 160 centimeters tall and is now 168 centimeters tall. Or, that your child was 1.75 yards tall and is now 1.83 yards tall!
If you or your child's pediatrician have measured your child's height and weight at regular intervals, you can create a chart or graph that documents changes in height or weight over time. Your child's pediatrician has growth charts you can use to compare your child's growth with the growth of the "average" child.
Academic or educational growth can be measured and charted too. The yardsticks used for measurement are different, but the principles are the same. Measuring educational growth or progress is not much different from measuring physical growth. Instead of a tape measure and scales, you need the psychological and educational achievement test results. Where will you find the information you need? How can you measure change?
Most school districts test their students on standardized educational achievement tests at regular intervals. The results of these tests provide information about how well the school district is accomplishing the mission of educating children. The information contained in group standardized tests can provide you with some basic information.
Standardized educational achievement tests are general measures. The information they provide is similar to that provided by medical screening tests. Medical screening tests can suggest that a problem exists. In most cases, additional testing is necessary before the problem can be accurately identified and a treatment plan developed. Children's learning problems are identified in a similar manner. In most schools, individual ability and achievement tests that identify academic or functional problems are administered by school psychologists and educational diagnosticians.
What Do Evaluations Tell You?
As you continue on your
advocacy journey, you need to understand the exact nature of your child's
disabling condition(s). How does the disability affect her? In what areas? How
serious is it? What are her strengths and weaknesses? Does she need special
education? What educational issues need to be addressed? How will you know if
she is making progress? How much progress is sufficient?
The answers to these questions will be found in the evaluations and tests that
are administered to children and adolescents.
Many parents believe they cannot understand these tests. Usually, their reasoning goes like this:
Gosh. I'm just a parent. I didn't even finish college. I don't have any training in education or special education so I can't understand that stuff!
or
The people who did that testing on my kid went to school for years to learn how to do that. Who am I to think I can understand it? I'm not a psychologist!
If you believe that you "can't" understand your child's testing, it's time to change your beliefs. You may be reading this article because your son or daughter is performing poorly in school  or has been identified with learning problems  and now believes that he or she "can't" read or write or do arithmetic. Your child must overcome these false beliefs about learning new or difficult material. And, so must you.
Statistics: General Principles
Statistics are simply ways to measure things and to describe relationships between things, using numbers. Part of the confusion that many people experience when they begin to learn statistics is because of the terms and concepts are unfamiliar. As we learned in the earlier discussion about measuring physical growth, there are several ways to report the same information (inches, feet, yards, centimeters, etc.) This can be confusing.
First, let's look at a familiar situation that many of us deal with regularly  how to measure our car's gas mileage. Remember: When we use statistics, we can use several terms to describe the same concept. If you want to describe your car's gas mileage, you can make any of the following statements:
All of these statements accurately describe your car's consumption of gas.
When you have this information, you can make decisions. When will you need to buy more gas? You know that your car has a 15 gallon gas tank. According to the gas gauge, your tank is slightly below the halfway mark. You've been driving in the city. You'll be driving on the highway for the rest of your trip. You have used a precise amount of gas and have a precise amount of gas left in your tank. You can describe and define this information in several ways  gallons used, gallons remaining, miles driven, miles to go, percentage full, and so forth. Using this information, you can do some simple math calculations to learn that your car averages between 17 to 23 miles to a gallon of gas, depending on driving conditions.
Using this information or data, you can also measure change. If you compare your car's present or current mileage to the mileage you obtained last month, before you had your car tuned up, you can measure miles per gallon before and after the tuneup. In this way, you can measure the impact of the tuneup on your car's gas consumption. You can also compare your car's mileage performance to that of other vehicles.
Let's look at another common way in which we use tests and measurements. When you last visited your doctor, you mentioned that you were feeling tired and sluggish. Your doctor asked several questions, then recommended that you have some lab work. After reviewing the test results, the doctor explained that your blood glucose level was moderately elevated.
To lower your blood glucose level, the doctor recommended a plan of treatment that included a special diet and a daily program of moderate exercise. After a month, you return for a followup visit. More lab work is completed. If your glucose level has returned to normal, it is unlikely that you will require additional treatment. But, if your glucose level remains high despite the diet and exercise program, you may need more intensive treatment. By measuring change after an intervention with "data based documentation of repeated assessments ... at reasonable intervals, reflecting formal assessment of progress" (34 C.F.R. 300.309(b)(2), you and your doctor can make rational decisions about your medical treatment.
Remember: The principles that allow you to compute your car's gas mileage and make medical decisions will also allow you to measure and monitor educational progress. When you measure educational progress (as when you measure your gas mileage and blood levels), the test scores can be reported and compared in several different ways.
Because educational test scores are often reported in different formats and compared in different ways, it is essential for parents and advocates to understand all of the scoring methods used in measuring and evaluating educational progress, including:
Knowledge about statistics will enable you to assess your child's progress or lack of progress in a particular educational program. Lack of progress is usually referred to as regression. Unfortunately, regression is a common educational problem that we will discuss in more detail later. You must learn how to recognize regression and reverse the downward spiral before your child is further damaged.
Applied Statistics
Let's look at the performance of a group of children. You need to understand how an individual child scores when compared with other children who are his age or in his grade  and what this means.
First, we'll examine a single component of physical fitness in a group of elementary school students. Our group or sample consists of 100 fifth grade students. These children are enrolled in a physical fitness class to prepare them to take the President's Physical Fitness Challenge. We will assume that the average chronological age (CA) of these children is exactly ten years, zero months. (CA=100) The children are tested in September, at the beginning of the school year.
To qualify as "physically fit," each child must meet several goals. Pushups are one measure of upper body strength. Each child must complete as many pushups as possible in a period of time. Each child's raw score is the number of pushups completed. The term raw score is simply another way of describing the number of items correctly answered or performed.
After all of the fifth grade students complete the pushup test, their scores are listed. The results are as follows:
As we continue to analyze the children's scores, we see patterns:
Again, twothirds of the children in this fifth grade class were able to complete between 7 and 13 pushups. The remaining third of the children did fewer than 7 or more than 13 pushups. Nearly all of the children  98 out of 100  were able to complete between 4 and 16 pushups. Click here to view the bell curve chart.
The test results provide us with a sample of data. As we analyze the data in our sample, we can compare the performance of any individual child with that of the entire group. As we make these comparisons, the data will enable us to recognize any child's strengths and weaknesses when compared with the peer group of similar youngsters.
If we conduct an identical pushup test with children in other grades, we can compare our original group of 100 fifth grade children with other groups of youngsters  children who are older, younger, in different grades, in different schools. If we gather enough information or data from other sources, we can compare our original group of fifth graders  or an individual child within our group  to a national population of children who are being tested for their upper body strength as measured by their ability to do pushups.
Using the Bell Curve to Measure Progress
In nature, traits and characteristics distribute themselves along theoretical curves. For our purposes, the most important curve is called the normal frequency distribution or bell curve. Because the percentages along the bell curve are wellknown and thoroughly researched, they become our frame of reference.
By using the bell curve, we can develop a diagram or graph of the children's pushup scores. This map  on the bell curve  provides us with additional information. We can see what percentage of children were able to complete specific numbers of pushups. When we use the bell curve, we can visually demonstrate where any particular child scores, when compared with other children who are the same age or in the same grade. Likewise, with educational test scores, we can visually demonstrate scores and change over time.
If we compare the pushup scores obtained by children who attend different schools, we can determine whether the physical fitness of children, as measured by their ability to do pushups, varies in different schools, neighborhoods, states, or countries.
We can also measure progress over time  with pushups and with improvement in reading skills. Let's look at our class of fifth graders again. We want to gather information as to whether the physical fitness class is effective  whether the children's fitness levels improve. How can we answer this question?
To measure the effectiveness of the fitness class, we will measure the children's number of pushups before they take the class and compare this score with their score after they take the class. If the class is effective, we should see individual improvement and group improvement. Some children will have minimal improvement  these children will fall further behind the peer group. Other children who performed below their peers may show significant improvement. Some children will improve so much that they now perform as well or better than the "average" youngster.
We will measure the children's progress on one or more occasions as they progress through the class. If the fitness class is "working," that is, if the children's' fitness levels are improving, their ability to perform fitness skills should improve measurably over time. In our example, physical fitness improvement is being measured with "technically sound instruments" that "are valid and reliable" (34 C.F.R. §300.404(b)(c)) and use "Databased documentation of repeated assessments of achievement at reasonable intervals, reflecting formal assessment of student progress ..." (34 C.F.R. §300.309(b)(2))
Because of its value and usefulness in measuring educational progress, we will return to the subject of the bell curve repeatedly throughout this article.
The Bell Curve: Basic Concepts
On all bell curves, the
bottom or horizontal line is called the X axis. In our sample of fifth
graders, the X axis represents "number of pushups." And, on all bell curves,
the up and down vertical line is called the Y axis. In our sample, the
Y axis represents the number of children who earned a specific score (number of
pushups completed).
As you can see in the diagram above, the highest point of the bell curve on the X axis is equal to a score of 10 pushups. You recall that more children completed 10 pushups than any other number. Thus, the highest point on this bell curve represents a score of 10. The next most frequently obtained scores were 9 and 11, followed by 8 and 12. This pattern continues out toward the far ends of the bell curve. In our example, the ends occurred at 1 and 19 pushups.
Using the bell curve, we can
now chart each child's score and compare it to the score achieved by all 100
students in the class. Look at the bell curve above, and find 10 pushups. We
know that Amy completed 10 pushups so her raw score was 10. Ten pushups placed
her squarely in the middle of the class. Half of the youngsters in Amy's class
earned a score of 10 or more; half of the children scored 10 or less. If you
look at the bell curve diagram (below), you see that Amy's score of 10 placed
her at the 50% level. The individual's percent level is referred to as their
percentile rank (PR). Amy's percentile rank is 50 (PR=50).
Erik completed 13 pushups. Looking at the bell curve above, you see that his score of 13 placed him at the 84th percent level. Erik's percentile rank is 84 (PR=84). Erik's ability to do pushups placed him in the 84th position out of the 100 fifth grade children tested on upper body strength.
Sam completed 7 pushups. His raw score of 7 placed him at the (bottom) 16 percent. Sam's percentile rank was 16 (PR=16). Out of our sample of 100 fifth grade children, 84 children earned a higher score than Sam.
Larry completed 6 pushups. We can convert his raw score of 6 to a percentile rank of 9 (PR=9). 91 children scored higher and 8 children scored lower than Larry in upper body strength as measured by the ability to do pushups.
Oscar completed 2 pushups. His raw score of 2 placed him in the bottom 1 percent of fifth graders tested (PR=1).
Nancy's raw score of 17 placed her at the upper 99 percent. We say that Nancy scored at the 99th percentile rank (PR=99).
You can see the relationship between the number of pushups completed and the child's percentile rank (PR) reproduced in the table below: Click here to see the table
The bell curve is a powerful tool. When you use the bell curve, you can objectively compare any child's percentile rank to that of a group of children. You can also compare a single child's progress or regression when compared to the group.
Using the bell curve, you can compare a single child's score to the scores obtained by other children who are older or younger or in different grades.
Let's see how this works. Again, we will measure the children's upper body strength by the number of pushups they can perform. In this case, we decide to evaluate all children in all the elementary grades, from Kindergarten through fifth grade. We will assume that the average chronological age of these elementary school children is exactly eight years (CA=80 years).
After we test the third graders, we find that the average or mean score of our sample of 100 eight year old third graders is 6 pushups. This means that the "average" third grade child (who is 8 years old) can do 6 pushups. We can also compare an individual child's score on arithmetic problems answered correctly with the average number answered correctly by children the same age.
How can we compare children from different groups? Let's look at Larry who was a member of our original group of fifth graders. Although the average fifth grader performed 10 pushups, Larry only completed 6 pushups. His raw score of 6 converts to a percentile rank of nine (PR=9).
When we compare Larry's
performance to all elementary school students, we learn that Larry (a fifth
grader) is functioning at the level of the average third grader  who
is also eight years old  in the ability to do pushups. Therefore, we see
that Larry's age equivalent score is 8 years (AE=80) and his grade
equivalent score is at the third grade level (GE=30).
Fifth Grade Students: Push Up Scores 

Child's Name 
Raw Score 
Percentile Rank 
Oscar 
3 
1 
Larry 
6 
9 
Sam 
7 
16 
Amy 
10 
50 
Erik 
13 
84 
Frank 
15 
95 
Nancy 
17 
99 
Look at the table above and find Amy. At the time of testing, Amy was 100 years
old and in the fifth grade. She scored at the mean for her peers, i.e.,
10 pushups. Her grade equivalent score was fifth grade (GE=50) and her
age equivalent score was 10.0 years (AE=100). If we tested a 20 year old
person and found that this person was able to do 10 pushups, then the 20 year
old has an age equivalent score of 100 and a grade equivalent score of 5.0,
i.e., the same score as Amy.
Look again at the table of scores above and find Frank's name. You see that Frank earned a raw score of 15 pushups which converts to a percentile rank of 95 (PR=95). Frank's score looks great  until we remember that Frank was "held back" three times. Although he is in the fifth grade, Frank is 13 years old!
With this new information, let's take another look at Franks' performance. The average score for 8th graders (who are 13 years old) is 15. Frank scored 15. Frank had a grade equivalent score of 8th grade (GE = 8.0) and an age equivalent score of 13 years (AE = 130). When we compare Frank with other children in his expected grade, we see that his achievement is in the average range. Frank is in the 95th percentile level when compared to fifth graders, not when compared to eighth graders.
Frank's case brings up some additional questions. Frank (age 13) was included in our sample of 5 th graders who had an average age of 10. When compared to this group of children who were younger than him, Frank scored at the 95% percentile rank (PR) level. Question: If we compare Frank's performance to that of children who are three years younger than him, will this comparison provide us with an accurate picture of his physical fitness? Answer: No.
In Frank's case, statistics inform us of two facts. First, we see that Frank performs at a superior level when compared with other children in his grade. Second, we see that he performs at an average level when compared with children who are his age.
When you evaluate the significance of data from tests, you must know how the scores are being reported. Test scores can be reported using percentile ranks, age equivalents, grade equivalents, raw scores, scale scores, subtest scores, or standard scores.
Remember: Although Frank's performance was superior for his grade, it was average for his age. If you did not know Frank's age and grade, you would have been misled as to Frank's actual achievement. But  if Frank was an 8 year old 3rd grader, his scores would be in the superior range, using both age equivalent and grade equivalent measures.
The number of pushups each child completed was his or her raw score. Let's assume that we want to obtain an overall fitness score. To obtain an overall or composite score, we will measure three skills (situps, pushups, a timed 50 yard dash) and obtain scores on each of these skills. In educational testing, the child's overall score (in reading, math, etc.) is often a composite of several subtest scores.
Next, we will develop a weighting system that will convert each child's raw score to a scale score. After we convert the raw scores to scale scores, we will be able to compare each of the three scores to each other (number of pushups, number of situps, seconds to complete the 50 yard dash). How do we convert raw scores into scale scores?
One way to convert scores is by developing a rank order system. In rank order scoring, the child who scores highest in an event (most pushups, most situps, fastest run) receives a scale score of 100; the lowest receives a score of 1. The other 98 children receive their respective "rank" as their scale score.
After each child's raw scores are converted to scale scores, we can easily compare an individual child to the group and to all children who are the same age or in the same grade. We can also compare an individual child's performance at different times, i.e. before and after completing the fitness course. Was the child able to do significantly more pushups after taking the fitness course? Was the child reading better after receiving reading remediation?
Composite Scores
You can see that after we develop a global composite score, the individual child's raw scores on each of the three fitness subtests have less significance. This is exactly what happens with educational achievement and psychological tests. Most educational tests are composites of several subtests; the subtest scores are combined to develop composite scores. More about this shortly.
Let's look at how composite scores can be used and some of the problems that arise when we rely on them.
John is a member of our original group of 100 fifth graders. He has good muscular strength (he scored at the 70% PR level in pushups and at the 78% PR in situps). But, John is very slow and uncoordinated. In the 50 yard dash, he finished 2nd from the last out of the 100 children (PR=2).
How will John's composite fitness score be derived? In this example, we will average John's percentile rank scores on the three events. John's composite score is determined as follows: Add the percentile ranks of each event (70 + 78 + 2 = 150), then divide this score by the number of events (3). In John's case, 150 / 3 = 50. (Note: actually it is improper to average the percentile rank scores, you must use the standard scores or scale / subtest scores.)
John's composite score is 50. This composite percentile rank score of 50 places him squarely in the "average" range. Is John an "average" child? His individual scores demonstrated a significant amount of subtest scatter. When you analyze his three subtest scores, you see that he has specific strengths and a very severe deficiency. Despite his average composite score, John is not an average child! (Note: As noted above, the proper calculation is to use the standard scores. Thus the same analysis of John's composite score by using standard scores, is calculated to a standard score of 96.5 and percentile rank of 41  again, John appears to be an average child).
Let's look at another example of composite scores to see how they can mislead us. Oscar was at the 1 percent level in pushups. But when the other fitness subtests were given, Oscar was the fastest child in the class scoring at the 99% level. He was average in situps, scoring at the 50% level. Oscar's composite fitness score, using percentile ranking, is 50%. Is Oscar really an average child? Would he benefit from remediation to improve his upper body strength, as measured by pushups? Oscar also a great deal of subtest scatter, i.e., from extremely weak upper body strength to superior speed.
Subtest Scatter
When subtest scores vary a great deal, this is called subtest scatter. If significant scatter exists, this suggests that the child has areas of strength and weakness that need to be explored.
How can you determine if significant subtest scatter is present? Most subtests have a mean score of 10. Most children will score + or  3 points away from the mean of 10, i.e. most children will score between 7 and 13.
If the mean on a subtest is 10 (and most children score between 7 and 13), then scores between 9 and 11 will represent minimal subtest scatter. Lets assume that Child A is given a test that is composed of 10 subtests. The child's scores on the 10 subtests are as follows: on 4 subtests, the child scores 10, on 3 subtests, the child scores 9, and on 3 subtests, the child scores 11. In this case, the overall composite score is 10 and the scatter is very minimal. This child scored in the average range in all 10 subtests.
In our next example, we will assume that Child B earns 4 subtest scores of 10, 3 scores of 4, and 3 scores of 16. The child did extremely well on 3 tests, very poorly on 3 tests, and average on 4 subtests. Again, the child's composite score would be 10. Subtest scatter is the difference between the highest and lowest scores. In this case, subtest scatter would be 12 (164 = 12) Is this an "average" child? Because the child's scores demonstrate very significant subtest scatter, we need to know more about these weak and strong areas.
In educational situations, it is essential that parents understand the nature of the weak areas, what skills need to be learned to strengthen those areas, and how the strong areas can be used to help remediate the child's weak areas. The spread or variability between the subtest scores is called subtest scatter.
Apply Your
Knowledge: Composite Scores & Subtest Scatter
in the Wechsler Intelligence Scale for ChildrenIV (WISCIV)
How do composite scores and
subtest scatter relate to the information contained in your child's evaluations?
The results of educational tests given to children are often provided in
composite scores.
The Wechsler Intelligence Scale for Children, Fourth Edition (WISCIV) is
the mostly commonly administered test of ability. The WISCIV includes ten core
subtests and five supplementary subtests. Each subtest measures a different
ability.
Psychologists typically provide five scores: a Full Scale IQ (FSIQ) and
four Index Scores  a Verbal Comprehension Index (VCI), a Perceptual
Reasoning Index (PRI), a Working Memory Index (WMI), and a Processing Speed
Index (PSI). Index Scores are composites of two or three subtest scores. The
Full Scale IQ is a composite score that includes ten of the fifteen WISCIV
subtests.
IQ and Index Scores between 90 and 110 are considered within the "average
range." If there is a significant difference between Index scores or if there is
significant scatter between subtests, the Full Scale IQ may not accurately
represent the child's level of functioning.
Katie is the 14 year old youngster whose situation was outlined earlier in this
article. Let's look at her scores on the subtests.
On the Wechsler Intelligence Scale for ChildrenIV, Katie achieved a Full Scale
IQ of 101. If the only number you had was her Full Scale IQ score, you would
probably assume that an IQ of 101 placed her squarely in the "average range" of
intellectual functioning.
Is Katie an "average" child?
Katie's Subtest Scores on the Wechsler Intelligence Scale 

Standard Score or

Standard Score or


WISCIV Full Scale IQ 
101 






Verbal Comprehension Index 
124 
Perceptual Reasoning Index 
88 
Similarities 
16 
Block Design 
11 
Vocabulary 
14 
Picture Concepts 
7 
Comprehension 
12 
Matrix Reasoning 
6 
Information 
(13) 
Picture Completion 
(8) 
Word Reasoning 
(12) 






Working Memory Index 
110 
Processing Speed Index 
75 
Digit Span 
14 
Coding 
4 
LetterNumber Sequencing 
10 
Symbol Search 
7 
Arithmetic 
(8) 
Cancellation 
(8) 




Remember:
A Full Scale IQ score is a composite of four Index Scores (VCI, PRI, WMI, and
PSI). When you look at Katie's scores, you see that she has significant subtest
scatter, from a high of 16 on the Similarities subtest (98th percentile) to a
low score of 4 on Coding (2nd percentile). By using the
Conversion Table below, you can convert the rest of her subtest scores.
There are also significant differences between Katie's Index Scores. Her Verbal
Comprehension Index Score (VCI) is 124 (95th percentile), while her Perceptual
Reasoning Index Score (PRI) is 88 (21st percentile). When you subtract Katie's
Perceptual Reasoning Index Score (PRI) of 124 from her Verbal Comprehension
Index Score (VCI) of 88, you find a 36 point difference between these Index
Scores.
And, when you subtract her score on the Perceptual Reasoning Index  21st
percentile from her score on the Verbal Comprehension Index  95th percentile.
you see that a difference of 74 points in her percentile ranks (9521=74) on the
Index Scores.
If we rely on composite Index
Scores or Full Scale IQ scores, we may easily be misled, with serious
consequences. If we did not examine the subtest scores and Index Scores, we
might view Katie as an "average" child  and we would be mistaken.
We will look at more of Katie's test scores shortly.
WoodcockJohnson Tests of Achievement (WJIII ACH)
One of the most commonly
administered individual educational achievement tests is the Woodcock
Johnson III Tests of Achievement (WJIII ACH). The WoodcockJohnson III
Tests of Achievement include two batteries, a standard battery and an extended
battery. Subtests are organized into clusters.
Because the WJIII subtests are short, many do not provide good qualitative
information about what a child knows, can do, and where the child needs
continued work. For example, the WJIII does not measure the child's ability to
write a paragraph or an essay; it only examines the ability to formulate brief
responses.
The WJIII is scored by computer. The results obtained are organized into
cluster scores. Cluster scores must be considered with caution when there is
a significant difference between individual subtest scores. Relying on composite
or 'cluster' scores can lead to faulty educational decisionmaking that have
tragic consequences for children.
Tip:
Parents must obtain all subtest scores on the tests that have been
administered on their child and examine subtest scores and Index Scores.
When Apparent Progress Means Actual Regression
One concern that many parents share is the belief that their child is not making adequate progress in a special education program. How can parents know if their perception is accurate? How can parents persuade school officials that the special education program being provided needs to be changed?
Earlier in this article, we discussed how statistics are used in medical treatment planning. We demonstrated how a medical problem is identified and the efficacy of treatment is measured by the use of objective tests. In our example, the patient had pre and post testing to determine if the intervention was working. Based on post test results, more medical decisions would be made  to continue, terminate, or change the treatment plan.
This practice of measuring
change, called pre and post testing, is essential to educational planning. The
child's levels of performance are measured. An educational plan (IEP) is
developed and implemented. The child is retested at set intervals to determine
if the child is progressing, regressing, or maintaining the same position
within the group (stagnating).
When we use pre and posttesting, we can measure educational benefit (or lack
of educational benefit). We can use scores from pre and post testing to create
graphs to visually demonstrate the child's progress or lack of progress in any
academic area.
To see how this works, let's visit our fifth grade fitness class. According to earlier testing in September, Erik completed 13 pushups which placed him in the 84th percentile of all youngsters in his class. After a year of fitness training, fifth graders were retested. When Erik was retested, he completed 14 pushups.
Question:
Did Erik progress?
Answer: Yes and no.
The average performance of the fifth grade class improved by 2 pushups, from an average raw score of 10 to 12. Erik's raw score increased by 1 pushup, from 13 to 14. We see that while Erik's age equivalent and grade equivalent scores increased slightly from earlier testing, his actual position in the group dropped from the 84th percentile to the 75th percentile. While Eric is still ahead of his peers, he regressed.
What about Sam? Sam's performance also improved, from a raw score of 7 to 8. Although Sam's age equivalent and grade equivalent scores increased slightly, he also regressed. He dropped from the 16th percentile to the 9th percentile. Sam continues to fall further behind the peer group.
Assume that we test Sam again, when he reenters school in the fall. Now, we have three sets of test data (beginning 5th grade, end 5th grade, beginning 6th grade). Did Sam's score change? If his percentile continues to fall, Sam continues to regress. We need to know how long will it take for Sam to recoup the skills he lost during the summer. Regression and recoupment are two of the issues considered when determining if the child needs Extended School Year (ESY) services during the summer.
Norm Referenced and Criterion Referenced Tests
Most standardized tests are norm referenced or criterion referenced.
When we evaluated our group of fifth graders, we compared each child's performance to the norm group of fifth graders. Both Erik (raw score of 13, percentile rank of 84) and Sam (raw score of 7, percentile rank of 16) were compared to this norm group of fifth graders. To evaluate benefit, we looked at the norm group and the individual child's position in that group when we administered the first and second tests. We computed each child's change in position to determine progress or regression.
In our example, we also referenced the criteria of number of pushups completed. A criterion reference analysis determines whether or not a child meets certain criteria (without reference to a norm group.) For example, at the beginning of the year, Sam completed 7 pushups. If the criteria for success was 8 pushups, Sam failed to reach that goal. Assume that Sam received a year of physical fitness remediation. After that year, Sam completed 8 pushups. Does Sam met the criteria for success? The answer to this question depends on whether the criteria increased because Sam is a year older.
Another factor complicates this picture. We know that Sam's' peer group completed 10 pushups at the beginning of the year and 12 pushups at the end of the year. Definitions of success are affected by the passage of time. If we rely on criterion referenced measures, we can be misled as to whether the child is falling further behind the peer group. We need to know exactly what the criterion is and what this means when the child is compared to a norm group.
Standard Deviation
Percentile ranks are computed by determining the mean score and the amount of variation of all scores around the mean score. Are the scores bunched around the number 10 in a tight uniform distribution? Are the scores evenly distributed? Do they peak and taper slowly, or do they bunch at the ends, without few or no scores in the middle? Is there a great variance, with the scores spread over a wide range, with two or more peaks? Is there a normal bell curve distribution of scores?
On our pushup test, most of the 5th graders earned scores around 10 pushups, with an even distribution above and below 10 pushups. If onehalf of the children completed 5 pushups, onefourth completed 14 pushups, and onefourth completed 16 pushups, the average or mean number of pushups would still be 10! Onehalf of the children scored above 10 and onehalf below 10.
In this case, the scores are
not evenly distributed in a smooth curve above and below the mean score of 10.
The variance is very large and would present a very unusual curve with a peak at
5, a drop to zero between 6 and 13, a jump at 14, a drop at 15, another jump at
16. This distribution of scores would not present a normal bell curve
distribution.
Educational and psychological tests are designed to present normal bell curve
distributions with predictable patterns of scores. We need to know the mean and
standard deviation of the test. In most educational and psychological tests, the
mean is 100 and the standard deviation is 15. (Mean = 100, SD =
15) On most subtests, the mean is 10; the standard deviation is
3. (Mean = 10, SD = 3) Average scores do not deviate far from the mean. When
a score falls significantly above or below the mean, it is referred to as being
a distance from the mean, e.g., 1 or 2 standard deviations from the mean.
In all tests, the mean is 0 (zero) standard deviations from the mean. The next marker on the bell curve is +1 and 1 standard deviations from the mean, followed by 2 standard deviations from the mean. To interpret your child's test scores, you need to know the mean and standard deviation.
Using our original pushup example, the mean was 10 pushups. The standard deviation (SD) was 3 pushups. This pushup example is identical to the subtest scores in almost all standardized educational and psychological testing.
One standard deviation
above the mean is 10 plus 3, i.e. 10 + 3 = 13. One standard deviation
below the mean is 10 minus 3; i.e. 10  3 = 7. One standard deviation above
the mean always falls at the 84 percentile (PR = 84); one standard deviation
below the mean is always at the 16 percentile (PR = 16). Two SD's above the mean
is always at the 98 percentile (PR = 98); and two SD's below the mean are always
at the 2nd percentile(PR = 2).
When we look at actual test scores, we see that the child scored "one standard deviation below the mean" on a particular test or subtest. If the score is one standard deviation below the mean, the child's percentile rank is 16.
REMEMBER: Most subtests have a mean of 10 and standard deviation of 3. If a child scores 7 on a subtest, this score is at the 16th percentile. A subtest score of 13 is at the 84th percentile.
Standard Scores
One of the most difficult concepts for most people to grasp is standard scores. Since educational test scores are usually provided in standard scores, parents must know what they mean.
At an IEP meeting, a parent is told that the child earned a standard score of 85 in one area, a standard score of 70 in another area. Most parents are relieved to hear this news. Why? Most parents believe these numbers are similar to grades, with 100 as the highest score and 0 as the lowest. Standard scores are NOT like grades.
With standard scores, the average score or mean is 100. The standard deviation is 15. The average child earns a standard score of 100. If a child scores 1 standard deviation above the mean, the standard score is 100 plus 15; i.e. 100 + 15 = 115. If the child scores 1 standard deviation below the mean, this is 100 minus 15, i.e. 100  15 = 85.
A standard score of 115 is 1 standard deviation above the mean so it is always at the 84th percentile. A standard score of 85 is 1 standard deviation below the mean so it is always at the 16th percentile. A standard score of 130 (+2 SD) is always at the 98th percentile. A standard score of 70 (2 SD) is always at the 2nd percentile.
Remember Katie? Earlier, we learned that on the Wechsler Intelligence Scale, Katie earned a Full Scale IQ of 101. Later, we realized that this score was misleading because Katie's Verbal Comprehension Index Score (VCI) was 124, while her Perceptual Reasoning Index Score (PRI) was 86. The psychologist found that Katie scored 2 standard deviations above the mean on the Similarities subtest of the Wechsler Intelligence Scale for Children, 4th Edition (WISCIV). What does this mean?
You learned that a score of 2 standard deviations above the mean places the child at the 98th percentile in the area being measured. Since the Similarities subtest of the WISCIV measures verbal reasoning ability, Katie's verbal reasoning power is at the 98 percentile.
The psychologist also found that Katie had a standard score of 68, 2.5 standard deviations below the mean, on the spontaneous writing sample of the Test of Written Language (TOWL3). Two SD's below the mean is at the 2nd percentile. With your new knowledge, you know that Katie's ability to produce spontaneous writing samples was actually below the 1st percentile.
When we first introduced Katie, we posed two questions:
1. Do these two test scores help to explain the academic problems Katie is having?
2. Do her test scores tell us anything about her moodiness and her intense dislike of school?
Katie's verbal reasoning ability places her at the 98th percentile of youngsters her age. However, her ability to convey her thoughts in writing is below the 1st percentile. Katie is very bright but she is unable to convey her knowledge to her teachers on written assignments and tests. Would you expect her to feel frustrated and stupid? Do you question why, after years of frustration, Katie is angry, depressed and now wants to quit school?
Wrightslaw Quick Rules of Tests
All educational and psychological tests that report scores using percentile ranks or standard scores are based on the bell curve. To interpret tests results, you must know the mean and the standard deviation. Most standardized tests use a mean of 100 and a standard deviation of 15.
The results of most educational tests are reported as standard scores. Parents must learn how to convert standard scores into percentile ranks. By using the conversion table and the bell curve, you can convert any standard score into a percentile rank. The earlier pushup example used standard scores. Click here to view the table
Means and Standard Deviations of Other Tests
With some tests, scores are reported differently. For example, test scores may be reported as "z scores." Z scores are have a mean of 0 (zero) and and standard deviation of 1 (Mean = 0, SD = 1)
If you know that a child earned a z score of 1, you know that the child scored one standard deviation below the mean. One standard deviation below the mean is at the 16th percentile. If you convert this score into the standard score format, with a mean of 100 and a standard deviation of 15, a z score of 1 is the same as a standard score of 85.
Other tests report results as T Scores. T scores have a mean of 50 and a standard deviation of 10 (Mean =50; SD=10). A T score of 60 is the same as a z score of +1. A child who has a T score of 60 or a Z score of +1 scored at the 84th percentile rank. A T score of 70 is the same as a z score of +2, a standard score of 130, and a percentile rank of 98.
A few tests report results in Stanines. In Stanine tests, the mean is five and the standard deviation is 2 (Mean = 5; SD=2).
Applying Your Knowledge to Subtests
Since tests are always in a state of change with new editions being published, we will not attempt to review and describe tests in this article. Please check the links at the end of this article for test information.
Earlier, you learned that Index Scores are actually composites or averages of two or three different subtests. Each subtest measures different abilities. Let's take look at Katie's subtest scores to see what we can learn from them.
Katie's Subtest Scores on the Wechsler Intelligence Scale 

Standard Score or

Standard Score or


WISCIV Full Scale IQ 
101 






Verbal Comprehension Index 
124 
Perceptual Reasoning Index 
88 
Similarities 
16 
Block Design 
11 
Vocabulary 
14 
Picture Concepts 
7 
Comprehension 
12 
Matrix Reasoning 
6 
Information 
(13) 
Picture Completion 
(8) 
Word Reasoning 
(12) 






Working Memory Index 
110 
Processing Speed Index 
75 
Digit Span 
14 
Coding 
4 
LetterNumber Sequencing 
10 
Symbol Search 
7 
Arithmetic 
(8) 
Cancellation 
(8) 




* Wrightslaw Note: Scores in Brackets ( ) are supplementary subtests. They are not used to calculate the Full Scale IQ or Index Scores.
When we presented Katie's test results, you learned that variation among subtest scores (subtest scatter) is a valuable source of information. Look at Katie's WISCIV Index and subtest scores in the table above. You can see that she has significant subtest scatter, from a high score of 16 on Similarities (98th percentile) to a low score of 4 on Coding (2nd percentile).
Subtests of the WISCIV range
from a low score of 1 to a high score of 19. WISCIV subtest scores have a mean
of 10 and a standard deviation of 3. A subtest score of 7 is one standard
deviation below the mean (1 SD). By using the Conversion Table, you can convert
the subtest score of 7 to a percentile rank of 16 (PR = 16). You can also
convert the subtest score of 7 to a standard score of 85.
When you look at Katie's subtest scores, you see that she has significant
subtest scatter, from a high score of 16 on the Similarities subtest (98th
percentile) to a low score of 4 on the Coding subtest (2nd percentile). You know
that subtest scatter is the difference between the highest and lowest subtest
scores. Subtract the lowest score of 4 (Coding) from her highest score of 16
(Similarities). Katie's subtest scatter is 12 (16  4 = 12). The WISCIV manual
tells us that scatter this great is unusual.
You need to understand what
subtests measure. When we first discussed Katie's test scores, you learned that
Similarities subtest is highly correlated with abstract reasoning. The Coding
subtest measures
visualperceptual mechanics. Assessment experts Jerome Sattler and Ron Dumont
(information is at the end of this article) describe the Coding subtest as "an
information processing task that involves the discrimination and memory of
visual pattern symbols."
If you find that a child has a visual, hearing, attentional, or motor problem
that may interfere with his or her ability to take one or more of the subtests,
do not use these subtests in computing Index scores or a Full Scale IQ score. A
left handed child may be penalized on the Coding subtest because the child will
"have to lift his hand repeatedly during the task to view" the test items.
Katie's scores are evidence that she could excel in discussions of complex
literature in an honors English class because of her reasoning abilities, but
she is unable to write what she knows. Since Katie cannot write what she knew,
she was placed in slowpaced remedial classes. Because her abilities were
untapped, Katie concluded that she was stupid and wanted to quit school.
When you look at Katie's subtest scores, you see that several scores are in
parentheses. On the WISCIV, Information, Word Reasoning, Arithmetic, Picture
Completion, and Cancellation are not included in the Full Scale IQ or the Index
Scores. These subtests are used to provide additional data about how a child
learns.
Subtests of the Wechsler Intelligence Scale for ChildrenIV (WISCIV)
The WISCIV Technical and Interpretive Manual describes the WISCIV subtests as follows:
WISCIV Subtests 

Indexes & Subtests 
Ability Measured 


Verbal Comprehension Index 

Similarities 
Abstract reasoning, verbal categories and concepts 
Vocabulary 
Language development, word knowledge, verbal fluency 
Comprehension 
Social and practical judgment, common sense 
Information (supplementary) 
Factual knowledge, longterm memory, recall 
Word Reasoning (supplementary) 
Verbal comprehension, general reasoning ability 


Working Memory Index 

Digit Span 
Shortterm auditory memory, mental manipulation 
LetterNumber Sequencing 
Sequencing, mental manipulation, attention 
Arithmetic (supplementary) 
Attention and concentration, numerical reasoning 


Perceptual Reasoning Index 

Block Design 
Spatial analysis, abstract visual problem solving 
Picture Concepts 
Abstract, categorical reasoning 
Matrix Reasoning 
Pattern recognition, classification, analogical reasoning 
Picture Completion (supplementary) 
Alertness to detail, visual discrimination 


Processing Speed Index 

Coding 
Visualmotor coordination, speed, concentration 
Symbol Search 
Visualmotor quickness, concentration, persistence 
Cancellation (supplementary) 
Processing speed, visual selective attention, vigilance 


PsychoEducational Evaluations by Evaluators in the Private Sector
We find that public school evaluators are often limited in the tests that are available for their use. Heavy workloads may prevent them from completing a comprehensive evaluation of a child. As a result, we do not rely on testing by public school employees. Instead, we have the child evaluated by a child psychologist, school psychologist, speech language pathologist, and/or educational diagnostician in the private sector.
A Word About Individualized Education Programs (IEPs)
When you use this article and Wrightslaw: Special Education Law, Second Edition, you will be able to write IEP's that include measurable goals.
After you master the
information in this article, you will be able to convert test scores into easily
understood numbers. You will be able to measure and monitor your child's
educational progress. The feelings of helplessness and confusion you have
experienced at school meetings will dissipate. You will be knowledgeable about
your child's test scores and the significance of the data.
As Susan Bruce learned, "the numbers don't lie." To learn how Susan used
information from this article and
Wrightslaw: Special Education Law to get quality special education programs
for her children, read
Success Story: From Victim to a Mighty Force.
The Parent's "ToDo List"
1. After you complete this article, make a list of all the times when your child has been tested. Arrange your list in chronological order. Include the names, dates, and scores of each test that has been administered to your child more than once.
2. Begin your list with the test or tests that have been administered most frequently. In many cases, that will be the Wechsler Intelligence Test and the WoodcockJohnson and/or Kaufmann Educational Achievement Tests.
3. Write down all of the scores from the first administration of a test battery. Convert these scores to percentile ranks. Complete the same process with the most recent testing of the same battery. Compare the results. You should be able to determine whether your child is being remediated (catching up), staying in the same position, or falling further behind the peer group.
4. Dig for the standard scores or percentile rank scores in your child's file. You may find that some scores are only reported in "ranges" (i.e., high average, lowaverage) or in grade equivalent or age equivalent scores. If the standard scores are not available, you should ask for them. When you request the data in standard score format, the school staff may be surprised but they should be able to comply with your request.
5.
Take the most glaring
deficiencies where your child has shown minimal progress or even regression and
chart out the test results. If you do not have a computer, use graph paper.
Software programs like Excel and PowerPoint allow for dramatic visual
presentations of test data. If this is too difficult or confusing, consult with
an expert.
Gather your material  your bell curve chart and standard score / percentile
rank chart, your list of test scores, and your child's evaluations, and consult
with a private sector psychologist or educational diagnostician who can explain
the significance of the scores using percentile ranks.
6. Ask the professional to use the bell curve chart that includes standard scores, standard deviations and percentile ranks. Be sure that you have a photocopy of the bell curve so you can take it home to study. If the professional is willing, it may be helpful to tape record this portion of the session so that you can go back over it at home with the test scores in front of you.
7. Contact your state's Department of Education and request all publications about special education and IEPs, along with your state regulations.
8. Download our companion article, "Your Child's IEP: Practical and Legal Guidance for Parents and Advocates."
A short video on how to make graphs on Excel.
http://www.expertvillage.com/video/161712_makedoublebargraph.htm
Resources about Testing
For information about
thousands of tests, go to
Testlink from the Educational Testing Service (ETS) at
www.ets.org/testcoll/index.html
For unparalleled
expertise and wit on testing, visit the
website published by John Willis and Ron Dumont at
http://alpha.fdu.edu/psychology. The site includes includes
Test Reviews and Commentary and
PsychoEducational Reports and Report Critiques.
Reading Tests: What They Measure, and Don't Measure by Dr. Melissa Farrall

"There are two important
realities in testing. Tests do not always measure what they appear to measure,
and not all tests measure reading, writing, and math skills comprehensively."
Bell Curve
Charts & Percentile Rank / Standard Scores Conversion Charts
Download and print bell curve charts and a list of standard scores, scale /
subtest scores, standard deviation and percentile ranks:
http://www.wrightslaw.com/bellcurvepicture.pdf and
http://www.wrightslaw.com/bellcurveandstandardscore.pdf
Print several copies of both. You will be surprised at how often you refer to
them. Make copies for your friends.
Don't forget to download
Your Child's IEP: Practical and Legal Guidance for Parents and Advocates.
Books
Wrightslaw: From Emotions to Advocacy, 2nd Edition
 Chapters 10 and 11 teach you
about tests and measurements and how to measure progress objectively.
From Emotions to Advocacy includes bell curves, charts, graphs, and
other visual aides to help you master this subject.
Chapter 12 about SMART IEPs teaches you how to draft IEPs that are Specific,
Measurable, use Action words, are Realistic, and Time
Specific.
Assessment of Children: Cognitive Applications (4th edition) by Jerome M. Sattler. Excellent book about assessments and tests for the professional, attorney, and the curious parent. Dr. Sattler's book includes a Bell Curve with percentile ranks for the Wechsler IQ tests, subtest scores, and most other tests that are used with children who receive special education services.
Assessment of Children: WISCIV and WPPSIIII Supplement by Jerome M.
Sattler.
You can order Dr. Sattler's books from his
publishing site, or from the
Advocate's Bookstore at Wrightslaw.
Back to Top
About
the Authors
Pete Wright represented Shannon Carter before the United States Supreme Court in
Florence County School District Four v. Shannon Carter, 510 U.S. 7,
(1993). In Carter, the Court issued a unanimous decision on November 9,
1993, just thirtyfour days after oral argument.
Transcript of oral argument in Florence County School District Four v.
Shannon Carter.
All decisions in the Carter case.
Pam Wright is a psychotherapist who has worked with children and families since the early 1970’s. Her training and experience in clinical psychology and clinical social work give her a unique perspective on parentchildschool dynamics, problems, and solutions. She is the coauthor of Wrightslaw: Special Education Law, 2nd Edition (1999,2007), Wrightslaw: No Child Left Behind (2003), Wrightslaw: IDEA 2004, (2005) and Wrightslaw: From Emotions to Advocacy, 2nd Edition (2001, 2005). Pam is also the editor of The Special Ed Advocate newsletter.