Assessment, Statistics, and Research

  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...

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 ...