Assessment, Statistics, and Research

Variance is a measure of the dispersion of values in a distribution of values.  In psychology and behavioral science statistics, the variance is typically a reference to the extent to which numerical values vary around the arithmetic mean of a data set. Theoretically, the values vary around a population mean but in most cases, researchers work with samples. In statistics, write sigma squared for the population variance σ 2 Write final form sigma squared for the sample variance  ς2 In reports, write VAR for variance. How it works If we have a set of different numerical values such as scores on a test we can calculate a mean, which is the average of all the scores divided by the number of scores. The difference of one score from the mean is a deviation score. X is a score and the Greek letter mu μ is the symbol for the population mean. In a sample, which is what we normally have in psychology, we subtract a score X from the sample mean M . Thus, X - M = the deviation score....

  Skewed Distributions* Skewed distributions have one tail that is longer than the other tail compared to the "normal" distribution, which is perfectly symmetrical. Skew affects the location of the central values of the mean and median. Positive Skew Below is an image of positive skew, which is also called right skew. Skew is named for the "tail." If you had statistics, you may have heard a professor say, "the tail tells the tale." The tail is the extended part of the distribution close to the horizontal axis. The large "hump" area to the left represents the location of most data. In behavioural science, the high part often refers to the location of most of the scores. Thus, in positively skewed distributions, most of the participants earned low scores and few obtained high scores as you can see by the low level of the curve, or the tail, to the right. Negative Skew As you might expect, negatively skewed distributions have the long tail on the le...

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...

Can you answer these questions that every counselor ought to know? Choose the BEST available answer. I'll post the answers below. 1. If the correlation between a test of intelligence and a test of achievement is usually between .88 and .92, how well can you use the intelligence test results to predict achievement test results? A. Very well B. Moderately well C. Not well at all D. None of the above 2. A personality test score was high on a scale of Extraversion. The validity of the Extraversion scale was reported as .52 to .57 compared to similar tests. How much confidence should the person have that their score is "valid?" A. A high degree B. A moderate degree C. A low degree D. None of the above 3. School counselors administered a questionnaire to 1,000 students. They calculated results for answers about four school improvements rated on a scale of 1 to 5. Most of the scores were in the range of 18 to 20. The counselors reported a mean rating o...

Who would think that a simple statistic like a mean or a median would make a difference? In large samples involving thousands of people, and when data are normally distributed (close to the shape of a bell curve), the mean and median will be nearly the same. In fact, in a theoretical distribution called the normal curve , the mean , median , and   mode are in the middle. But, many samples are not normal distributions . Instead, the often contain extreme scores called outliers or a lot of scores bunched up at high or low levels ( skewed ). Sadly, even people that understand statistics, continue to report the mean as if they are not thinking about their samples. Suppose you work for a company where the top person earns $300,000 but most folks earn $30,000 to $60,000. Well that $300,000 is gonna skew results and the mean will look much higher than the median. I ran some fictitious data on a sample of 10 people. Nine earn between $30 and $60K and one earns $300K. The Mean ...