Age-equivalent score, Grade-equivalent score: A score identified such that half the people (usually children) of the particular age or grade tested fall below it, and half fall above it. Not to be used in learning disabilities determination or diagnosis; use only standard scores for this purpose.

Answer: A reply to a question, a solution to a problem.

Aptitude and Achievement: Previously, aptitude referred to some sort of inborn or innate talent for a certain type of activityor pursuit, such as intelligence being an aptitude for school work. In contrast, achievement referred to what a person could do by virtue of experience, learning, or training. Thus, a reading achievement test measured how well a subject could read (or had learned to read). Nowadays, aptitude is known and more properly felt to reflect a developed combination of inborn potential and experience, with the connotation that future development will be higher in those with more of it, whereas achievement more specifically focuses on what has been learned or mastered at the point of testing.  In practice, the distinction is often more between whether one is hoping to predict the future of an individual, in which case one is said to be testing aptitude, or to gauge the current adequacy of one's learning, experience and mastery, in which case one is said to be testing achievement.  

Within the context of the Psychological Answers web site, we will usually mean the same thing when we say aptitude as when we say intelligence, and the types of tests of this are the Wechsler Intelligence Scale for Children (WISC, WISC - R(evised), WISC-III (3rd edition)), Wechsler Adult Intelligence Scale (WAIS, WAIS - R, WAIS - III), and Kaufman Assessment Battery for Children (K-ABC; mental processing section) - all individually-administered tests. Group-administered aptitude tests commonly encountered in the school setting include the Henmon Nelson, Lorge-Thorndike, Short Form Test of Academic Aptitude (SFTAA), Test of Cognitive Skills (TCS), and Cognitive Skills Index (CSI).  Achievement tests are such as, on an individual basis, the Woodcock Johnson, Wide Range Achievement Test (WRAT, WRAT-R, WRAT-3), K-ABC Achievement section, and Wechsler Individual Achievement Test (WIAT). In the school setting, you will encounter group administered achievement tests such as the California Achievement Test (CAT), Iowa Tests of Basic Skills (ITBS), California Tests of Basic Skills (CTBS), and Iowa Tests of Educational Development (ITED).

Attention Deficit Disorder: A chronic neuropsychological disorder beginning early in childhood with symptoms of inattentiveness/distractibility, overactivity, and impulsivity.   Also known as Attention Deficit Hyperactivity Disorder.

Bell Curve: see Normal Distribution.

Clinical: Concerned with actual observation and treatment of disorders rather than experimentation or theory - from Greek klinikos, pertaining to a (sick)bed. More particularly in this site, based on observation and given history rather than tests or other extra considerations.

Derived score: The result of transforming a Raw Score into other units. Standard Scores are a specialized type of derived score.

Disorder: Aclinically significant psychological pattern or syndrome that is associated with distress or disability and/or a significantly increased risk of death, pain, disablity, or loss of freedom, that is a manifestation of behavioral, psychological, or biological dysfunction.  A syndrome is a group of related - based on co-occurrence - or coincident signs and symptoms (lit., "running together")  - that suggests a common underlying pathogenesis,course, pattern, or treatment. The term disorder is more precisely, specifically, or concretely defined than syndrome, with a syndrome often being part of a disorder or several disorders.

Grade equivalent score: See at Age-equivalent score.

Information: Facts, data, conceptualizations, knowledge.

Intelligence: Wechsler felt it was the capacity to understand and cope with the world around one. Binet felt it was something that accounted for the rapid growth of mental capacity, had to do with good versus poor school performance, and thought it reflected the capacity for directed thinking or action, capacity to make adaptations to attain a desired end, and the power to self-monitor, self-criticize, and self-correct. Generally, as used in the Psychological Answers site, it refers to a general capacity for understanding, coping, and adapting to the world, including learning about the world, and for deliberately directing one's activity, including altering one's strategies and conceptualizations in the light of experience.  In the old days, the IQ referred to the Intelligence Quotient, which was Mental Age/Chronological Age, but this is no longer true.

Mean, Median, Mode:

Mean or arithmetic mean: The average of a set of values, which is their sum divided by the number of values.

Median: The mid-most value of a set of values, observations, or scores, where half are higher and half lower.

Mode: The most frequent value in a set of measurements of a variable.

For standard scores that follow a normal distribution, they are all the same.

Neuropsychology: The study of neuropsychological (brain-related) aspects of thinking, feeling, experience, and behavior. Neuropsychological tests are psychological tests that have been studied as to their relationship to the functioning or nature of the brain.

Normal distribution: (A roundabout explanation!) The set of obtained measurements of a characteristic - such as intelligence - of a group of people can be distributed along a horizontal line (x-axis) in order of increasing size of the obtained values (e.g., for intelligence, whole numbers such as 85, 87, 98, 115, etc.). If we graph this distribution or set of measurements using a line that follows the rule that, for every time a value (for instance, 85) occurs or is observed, the height of the line is increased by a given, fixed amount (that is, moved up the y-axis one point), then the vertical dimension at any point on the x-axis - at any intelligence level, for our example - will then represent how many people in the group had that level of intelligence, or, in other words, the frequency of that level of intelligence.  The resulting graph is said to depict a frequency distribution.  A normal frequency distribution is a bell shaped curve (most cases falling towards the middle, with fewer cases the farther from the middle one goes) with certain formal statistical properties: a) It is made up of all real numbers, b) it has only one mode or peak, c) it is symmetrical, d) the mean = mode = median, e) the curve changes from concave to convex at +1 and - 1 standard deviation from the mean, and, most important, f) the number, proportion or percentage of cases falling under the curve is always the same at points (or between points) that are defined in terms of the mean and standard deviation.  All these characteristics or properties, however, are secondary.  The only way one knows for sure if the distribution is normal is if the height of the graph line (called y), as one moves along the x-axis, is specified by a certain function (or rule) called the normal density function or normal probability density function. That is, y = f(x) (Read this as "y is a function of, or calculated value based on, x"), where f(x) is the normal density function. Also called the Gaussian, or normal probability curve.

This is the function, and the normal bell curve it specifies. SD = standard deviation; M = mean; e = base of natural system of logarithms - about 2.718; pi = approx. 3.1416.

Normal? This just means that similar distributions are found amazingly often, enough so that it seems "normal" to find it when one is examining the distribution of traits or quantities. For example, many physical measurements such as height and chest circumference, and psychological ones such as intelligence, follow this rule fairly closely, and so does, for instance, the pattern of random errors in repeated measures of the same variable.

Percentile rank: The percentile rank of a given value or score indicates the percent of the population that scores below it.

Raw Score: A score on a psychological/neuropsychological test in such basic units of observation as number correct, number of errors, time for completion, kg, etc.  (Compare to Derived Score or Standard Score.) A raw score is one measure of a variable.

Sign: an objective, definitive or obvious manifestation or evidence of an illness or disordered function of the body. Often distinguished from symptom, which often connotes subjective report or the patient's experience.

A Standard Score is a "derived" score as opposed to a Raw Score. Standard scores are very special, however, among derived scores.  Standard scores are so called because they are derived from the standard deviation (a special kind of average deviation) and the mean (average) of the variable in question. The basic standard score is the Z-score, in which the mean is 0 and the standard deviation is 1. However, the most common standard scores in psychology use a constant multiple (usually fractional) of the standard deviation as their units, to avoid fractional units, and a mean high enough that negative values are unlikely to be obtained. In addition to being associated with the mean and standard deviation of a set of scores, standard scores have other helpful properties if they fall on the well-known "normal" or "bell" curve, as do scores that reflect many human characteristics (and other characteristics as well), such as intelligence or height: They tell us a good deal about where the individual who obtained it stands relative to the general population, and, in addition, they can be added, subtracted, or averaged, making them useful for comparison purposes.

The most common psychological example of a standard score is the IQ (properly termed "deviation IQ"), or "IQ equivalent" standard score. Here, raw scores from the IQ test are converted into standard scores (called IQs) whose mean is 100, and whose standard deviation is 15. For such standard scores, the constant is 1/15, and each IQ is expressed as a certain number of 15ths of the standard deviation plus 100: The IQ 104 is the mean plus 4 fifteenths of a standard deviation; the IQ 89 is the mean added to (-11) fifteenths of a standard deviation, or (100)+((-11/15)x15) = 89.

When the mean is 100, 100 will be at the 50^th percentile - half the people will score lower and half higher. From the known statistical properties of the normal or bell curve, we know that, within one standard deviation of the mean (±15), about 68% of the scores will fall. That is, 68% of the scores will be between 100 plus 15 and 100 minus 15, or between 85 and 115; half of the 68%, or 34%, of the scores will be above 100, and half below it. So at +1 standard deviation, or 115, we are at the 84^th percentile (100 = 50th%ile, ½ of 68%=34%, 50%  + 34% = 84%), and at -1 standard deviation, or 85, we are at the 16^th percentile (50 - 34 = 16). Thus, an IQ of 100 is at the 50^th percentile, an IQ of 115 is at the 84^th, and an IQ of 85 is at the 16^th.  Over 97% (about 97.7%) of the scores will fall within 2 standard deviations, so an IQ of 130 (2 standard deviations above the mean) is at the 98th percentile (rounded off), and an IQ of 70 is at the 2nd percentile.

Standard scores are superior in many ways to other derived scores such as percentile ranks or age- or grade-equivalents. In particular, percentiles and age or grade equivalents cannot be used for comparison purposes, because they cannot be added, subtracted, or averaged.  In diagnosing learning disabilities, where a key (necessary) component is that the subject has a "severe discrepancy" between intelligence and mastery of a specific academic skill, only standard score comparisons can be used without creating serious problems.

Other common psychological standard scores are T-scores (mean 50, standard deviation 10), scaled scores (mean 10, standard deviation 3), and Z-scores. Most intelligence tests, like the Wechsler Scales (Wechsler Adult Intelligence Scale/WAIS, WAIS-R, WAIS-III; Wechsler Intelligence Scale for Children/WISC, WISC-R, WISC-III) and Kaufman-Assessment Battery for Children (K-ABC) use deviation IQ standard scores, and so do most individual achievement tests, such as the Woodcock Johnson, Wide Range Achievement Test (WRAT, WRAT-R, WRAT-3), and Wechsler Individual Achivement Test (WIAT).  If you have only percentile rank scores, as is often the case with the group administered achievement tests given in school (ITED, ITBS, CTBS, CAT) you must convert these back to standard scores before doing any arithmetic operations.

Once you have standard scores, you can compare easily between tests, even if they are not the same kind of standard score: 100 IQ = 50 T = 50th percentile; 115 IQ = T 60 = 84th percentile; 85 IQ = T 40 = 16th percentile; IQ 127 = 68 T = 96th percentile.

Standard deviation: You might think of this as the average deviation, to understand or remember its importance (though technically it is a special weighted average - the square root of the average of the squared deviations).  Measures of human characteristics (like intelligence) will vary in most populations - thus they can be called "variables."  One can compute the average or mean of a set of measures of a particular characteristic (i.e., scores or raw scores) by adding them up and dividing the sum by the number of measurements. The set of measures will then vary about their mean or average value.  The deviations (difference from average) of the scores of individuals will be positive (if above the mean) and negative (if below the mean).  If we square the deviations to avoid negative numbers, and add these up and find their average, then take the square root of that average, we will have the standard deviation.  It would seem to be easier and more straightforward just to average the absolute values of the deviations and get an average deviation, but the standard deviation has a number of very handy statistical properties that the average deviation does not, especially if the scores in question have a normal distribution and are expressed as standard scores.

Symptom: A phenomenon or experience that accompanies a disease. Generally distinguished from sign, which indicates something observable rather than reported or subjective.  However, not always necessarily so in some usages, usually further specified as "objective symptom."

Syndrome: A group of related - based on co-occurrence - or coincident signs and symptoms (lit., "running together")  - that suggests a common underlying pathogenesis,course, pattern, or treatment; generally, the term disorder (q.v.)   is more precisely, specifically, or concretely defined than syndrome, with a syndrome being part of a disorder or several disorders.

Z-score. The basic standard score.