Assessment, Statistics, and Research

The z- score defined  A z -score indicates how far a raw score lies from the arithmetic mean of a normally distributed set of scores. It expresses this distance in standard‑deviation units. Thus, a z -score of 1.0 means the score is one standard deviation above the mean, while a z -score of –1.0 means it is one standard deviation below the mean. z-scores are typically plotted along the x‑axis of a normal distribution —the familiar bell‑shaped curve. CALCULATE z -scores by using the calculator at the bottom of this page. Here's an image of the normal curve with z -scores below the curve. In APA style, z -scores are reported in lowercase italics . The uppercase Z refers to a different statistic. A z-score is calculated by subtracting the mean (M) from the raw score (X) and dividing the result by the standard deviation (SD): z = ( X - M ) / SD Example: If a test score is 60, the mean is 50, and the standard deviation is 10, then:      [ 60 - 50 = 10 ]     ...

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...