In Part 1, I wrote about the different kinds of test scores. In Part 2, I'll explain how to interpret those scores. As I said in Part 1, I prefer to use standard scores to gauge progress because they’re on an equal interval scale. But what do they mean? To assist with this discussion, consult the diagram below from Part 1:
The Average Range. To review, about 68 percent of the people who take a standardized test will obtain scores within plus or minus one standard deviation (explained in Part 1). The Wechsler and Stanford-Binet intelligence tests designate the middle 50 percent of the area between plus or minus one standard deviation as the Average range--or 90 to 109 for tests with a mean of 100 and standard deviation of 15. That's the area that many evaluators consider Average, including me. In other words, half the students taking the test will have scores within the Average range and half will have scores that are above or below Average.
However, some researchers and clinicians consider the full 68 percent to be in the Average range, or scores between 85 and 115. Neither interpretation is right or wrong because there isn't agreement in the field. In my opinion, it makes more sense to use the 50 percent figure; it doesn't seem to me that the scores of almost two-thirds of the population are in the Average range.
If 90 to 109 is Average, 80 to 89 is Below Average and 110 to 119 is Above Average. (FYI, psychologists use the terms Low Average and High Average for Below and Above Average.) It might help you keep track if you make a simple chart of these scores. For example:
Confidence Bands. Moving on from the scores themselves, have you heard people talking about confidence bands? That's an important concept to understand because a single testing may not demonstrate a student's true score, his or her actual ability. The true score is a statistical concept and too complicated to explain here, but the point to understand is that there is some error, some uncertainty in all testing--in the test itself, in the testing conditions, in the student's performance, and so on. To account for this uncertainty, a confidence band is constructed to indicate the region in which a student's true score probably falls. Evaluators can select different levels of confidence for the bands; I use 90 percent. Therefore, I provide a confidence band that indicates the region in which a student's true score probably falls 90 times out of 100. Test publishers usually compute these for users.
Here's an example. Mary obtained a standard score of 97 on a reading test, which is solidly in the Average range (90 to 109). However, although the obtained score on a test gives the best single estimate of a student's ability, a single testing may not necessarily demonstrate the true score. Mary's standard score confidence band is 91 to 104.
Subtests and Scaled Scores. Many tests measure different parts of a domain with component tests called subtests. Sometimes the subtests yield scaled scores, which are standard scores that range from 1 to 19 points with a mean of 10 and a standard deviation of 3. Scaled scores between 8 and 12 are considered Average.
Composite Scores. If they have high statistical reliability, subtest scores may stand alone. If not, they should only be reported as part of a composite score. A composite score is computed by combining related subtests--for example, subtests that assess word recognition and reading comprehension or math computation and applications.
Because composite scores are generally more statistically reliable than subtest scores, they are sometimes the only score that should be considered. However, it is better to use tests with highly reliable subtests when they are available because composite scores can mask the differences among the subtest scores. For example, Richard obtained these subtest scores on a recent reading test: Word Recognition, 73; Pseudoword Decoding, 78; and Reading Comprehension, 107. The 73 and 78 scores were in the Borderline range (70-79), and the 107 was in the Average range. The composite score was 82, in the Below Average range. However, none of the three subtests was Below Average. Because of the variability between the word recognition and decoding scores on the one hand and the comprehension score on the other, it would have been more accurate to not provide a composite score in this case.
Here's another example. Nalia obtained two math scores recently: 100 in Math Applications (Average range) and 84 in Math Computation (Below Average) with a composite score of 90, which is at the bottom of the Average range. However, there was a 16-point difference between the two subtest scores, and it would be incorrect to say that Nalia's math performance was in the Average range when she was struggling with computation. Yet sometimes this kind of difference isn't explained in an evaluation report, so you'll need to read carefully and critically.
I've presented quite a bit of technical information in this blog post. Please let me know in the Comments below if you have any questions! And feel free to share any ideas you have for future posts.
In Part 1, I discuss the different kinds of test scores and what they mean and don't mean. In Part 2, I'll address how to interpret scores--what's considered average, confidence bands, the differences between composite and subtest scores, and so on.
The array of test scores in an evaluation report can be confusing. On standardized tests, the number correct is called the raw score. A raw score by itself is meaningless because it’s not the percentage correct; it’s just the number correct, and different tests have a different number of items. So publishers convert the raw scores into derived scores to compare a student’s performance to that of other students his age in the norm group—the people the test was standardized on. There are several kinds of derived scores. Before I discuss a few of them, I need to introduce some statistics. I know this is technical, but bear with me because it will help in the end!
Most psychological and educational test results fall within the normal or bell shaped curve. The normal curve is divided into standard deviations that measure the distance from the mean (the average score). In the diagram below, you can see that about 68 percent of the population will have scores between plus and minus one standard deviation (pink area). An additional 27 percent will have scores between plus/minus two standard deviations (about 95 percent; pink and blue areas). And 4 percent more will have scores between plus/minus three standard deviations (about 99 percent; pink, blue, and yellow areas). Now pat yourself on the back for getting through this section!
I worry a lot about the difficulties of administering standardized tests. That might sound a little strange, but assessment data are essential to my work with children, and it concerns me when tests are invalidated, usually by mistake. A standardized test compares a student to a "norm," or the average performance of similar students, generally in a national sample. Part of the process of producing such a test involves "norming," or administering it to a sample of children considered representative of the national population. During norming, the test is administered under specific conditions with very specific instructions to the students in the normative group, and the publishers expect users to later replicate those same conditions and use those same instructions. Otherwise, the results are invalid. It's as simple as that. If test administrators allow extra time or ask leading questions that are not in the test manual or give students advanced preparation or permit multiple attempts beyond those allowed or in many other ways give students advantages that the children in the normative sample did not have--or conversely make the test more difficult--they are invalidating the test results.
I often need to read other professionals' evaluation reports, and sometimes the test scores appear to be an extreme over-estimate of the student's ability. I can only guess at the reasons for this because there's no way to know what occurred during test administration. Still, it makes me wonder how carefully the tests were administered. Admittedly this can be confusing because tests can have different administration and scoring rules even when they measure the same task. For example, some oral reading tests count all self-corrected errors, whereas others suggest that we note these corrections but do not count them in the scoring. Some tests have time limits per item administered and some do not. And so on. Yet while this is indeed confusing, it is also the evaluator's responsibility to understand and apply the rules appropriately. I frequently review the test manuals before giving some tests even though I've administered them dozens of times. I just consider it part of the job.
But there are other ways to invalidate a standardized test. Some evaluators' reports provide examples of items that students answered incorrectly. At first glance this might seem to make sense; after all, it can be part of an in-depth error analysis. The problem is that this practice can weaken the security and integrity of the test items. I sometimes describe the type of item with sample words that are not part of the actual tests. However, when real test items are shared, there is the possibility that they will become known by teachers or parents, or both, and ultimately by students, which invalidates the test. Parents or teachers may even see these errors and teach them to students--which makes the test useless for re-evaluation at a future time. If the items are directly instructed to a class, this test can be invalidated for all the students in that class. Now you may assume that in the course of a school year, some of these items would naturally be part of the curriculum anyway, and you are certainly correct. Tests are meant to sample the entire domain, e.g., of word meanings or high-frequency words or spelling. But inadvertently teaching some of the items is not the same thing as purposely teaching specific test items.
Ultimately what's important here is to carefully guard standardized tests so they can remain useful indicators of student performance. While I believe that informal tests that have not been standardized are also useful, and I include them in my test battery, there's no substitute for good norm-referenced tests. We use standardized tests to compare students to similar students in the national sample; informal tests can flesh out that information to inform instruction. Both are necessary sources of data.
You may have heard the term phonemic awareness but perhaps you’ve confused it with phonics. Or you know that it’s not phonics, but you’re not really sure exactly what it is!
Phonemic awareness is a big name for a very small part of the reading process, and yet it happens to be crucial to learning to read. Phonemic awareness is the understanding that words are made up of separate sounds—and the ability to manipulate those sounds in various ways.
Big deal, you might say. Can’t everyone do that? As it turns out, they can’t. Most children start school able to discriminate letter sounds, called phonemes, e.g., mat versus man. However, that discrimination isn’t necessarily at a conscious level. Research has shown that we hear a syllable as one acoustic unit, but we need to break it down into individual segments to analyze it. The catch is that we have to learn how to do this. It doesn’t happen naturally. And as with all learning, some children find this easier than others.
You might wonder why phonemic awareness is so important. Here’s why: It's essential for reading success. It enables children to benefit from phonics instruction, and being able to sound out words is the most important clue to identifying them. Context can help confirm that a word has been sounded out correctly, but it isn’t efficient as a first clue.
There are many different phonemic awareness tasks, such as rhyming, isolating a sound from a word, blending letter sounds into words, segmenting the sounds, or moving sounds around by adding, deleting, or substituting them. Some of these tasks are relatively easy and some not so much. For example, in a blending task, a child might be asked what word /s/ /a/ /t/ is (sat). A deletion task, also known as elision, requires a student to take away the /k/ sound in clap and say that lap is the word that’s left. A substitution task might require a student to take away the /s/ sound in side and replace it with a /t/ sound so that side becomes tide.
Incidentally, phonemic awareness isn’t phonics. Phonics instruction teaches children which letters are associated with which phonemes and why. You’ll often hear phonics referred to as decoding—and that readers who understand and can apply the relationship between letters and sounds can “break” the code. Pretty cool, don’t you think? Breaking the code is empowering to new readers.
Can you sound out these nonsense words? clag spanthet
Of course, you’re able to apply your knowledge of letter-sound correspondences and the rules that govern them because you’re a skilled reader and can do this automatically. We want children to be able to do this automatically too whenever they encounter words in print that they’ve never seen before. If they struggle with decoding, their cognitive resources are diverted from the demands of comprehension.
Getting back to phonemic awareness, it's fortunate that many children can acquire this skill from activities at home before they even enter kindergarten, and these can be presented in a fun way. For example, parents can encourage awareness of sounds within words by reading and reciting nursery or other rhymes aloud and inviting children to create their own. There are also many children’s books that emphasize rhyme, alliteration, or assonance. Similarly, children can play rhyming or alliteration games or repeat or create tongue twisters. Or they can clap or tap out each syllable in a word, make up sentences that contain words that start (or end) with a particular sound, or play with language in myriad ways. I’m always pleased when I hear young children spontaneously making up words that rhyme or start with the same letter, such as mitten kitten sitten shmitten. Or p-p-p-p-Peter.
Not all children will acquire phonemic awareness from these informal activities at home. Some will need direct instruction in the classroom. But while it’s preferable for this to occur in kindergarten or first grade, phonemic awareness can also be successfully taught to older students.
I’d love to hear about your experiences with this important topic!
Dr. Andrea Winokur Kotula is an educational consultant for families, advocates, attorneys, schools, and hospitals. She has conducted hundreds of comprehensive educational evaluations for children, adolescents, and adults.