Assessment, Statistics, and Research

  A z -score tells you the distance of the score from the arithmetic mean of a set of scores that are normally distributed. The z -score represents standard deviation units thus, a z -score of 1 means it is one standard deviation above the mean of the set of scores. A z -score of minus one (-1) means the score is one standard deviation below the mean of the set of scores. The z -scores are often plotted along the x -axis of  a normal distribution, which is sometimes called the bell curve. Use lower case italics when reporting z -scores in APA style. The upper case Z is a different score. You can calculate a  z -score by subtracting a raw score from the mean and dividing by the standard deviation of the set of scores. Example: A raw score on a test = 60. If the mean = 50 and the standard deviation = 10 then (60-50) = 10 and 10 divided by 10 = 1.0. The z score is 1.0, it is one standard deviation above the mean. Most z - scores fall between -3.0 and +3.0 but it is possibl...

When counselors and psychologists report test scores, they often report one of the scores found in the table below. When several tests are used, it is helpful to know how the scores compare from one test to another. A good place to begin is to locate the average score-- that's the row where z = 0. Then look at the broad middle range between z = -1 and z = 1. About 68% of people score between z = -1 and z = 1. Intelligence Tests use Standard Scores abbreviated as SS. These scores take the place of the old IQ score. An average IQ is 100 -- about 68% of people score between 85 and 115. Here's a table from Appendix B of Applied Statistics: Concepts for Counselors Each row contains the equivalent score on a different scoring system. For example, a z -score of 1 equals a T score of 60, and a standard score of 115. The score is at the 84 th percentile. z T Standard Percentile Ra...

Intelligence tests (IQ tests) are in the news lately as people banter about terms from many decades ago. IQ tests are widely used because they measure the ability of people to solve various problems, predict academic achievement, and help with job placement in some settings. The tests also help neuropsychologists assess functioning in people with impairments due to head injuries and brain diseases. During part of my childhood, I passed a facility where American IQ testing began. I saw people on swings and on the grounds of the Vineland Training school in Vineland NJ. It turns out that a little over 100 years ago, American psychologist, Henry Goddard, brought a test by French scientist, Alfred Binet , to the New Jersey Training School for Feeble-Minded Girls and Boys in Vineland, NJ. The test was modified and widely used in the U.S. What tests are used today? Today, a number of tests are available in the US and elsewhere. Popular American tests are the Wechsler Intelligenc...

What are age scores? Age scores, also called age-equivalent scores , are supposed to help people understand how a person’s test score compares to other people of the same age. They are often provided to teachers and parents to show how children scored on achievement tests compared to their age peers. A common age-equivalent abbreviation is AE .  Age scores are reported with a hyphen. The first number refers to age in years and the second number refers to the age in months. A score of 8-4 is supposed to mean a test performance typical of children age 8-years and 4-months. The scores appear convenient and make a kind of common sense. An age score of 7-6 is supposed to mean that a child earned a test score similar to children age 7-years and 6-months. But there are problems with the scores. What tests report age scores? Age scores are commonly reported with results of achievement tests. They are sometimes reported with results of intelligence tests. Old i...