Assessment, Statistics, and Research

 Kurtosis is a statistical concept. The value indicates whether a distribution is similar to the normal curve or different from the normal curve. Compared to the normal curve, kurtotic distributions of data appear either peaked in the middle or flat. In a normal distribution, the value of kurtosis = 0. The peaked distribution has a positive value. It's called leptokurtic (think leap). The flatter distribution has a negative value. It's called platykurtic (think of the animal, Platypus). There are different formulas for calculating kurtosis. In Excel, the function for kurtosis can be found under Formulas, More Functions. In the drop down list, choose KURT. Please check out my website     www.suttong.com    and see my books on    AMAZON         or   GOOGLE STORE Also, consider connecting with me on     FACEBOOK     Geoff W. Sutton         TWITTER  ...

Understanding the Bell Curve and Standard Deviation The bell curve—also known as the normal curve or normal distribution—has mathematical properties that allow researchers to understand where scores (or data points) fall in relation to one another. In a normal distribution, most scores cluster around the center, with fewer scores appearing as you move toward the extremes. Central Tendency in a Normal Curve In a normal distribution, the three measures of central tendency—mode, median, and mean—all fall at the same central point. This midpoint divides the distribution into two equal halves. Standard Deviation Units On the x‑axis of a normal curve, the mean is placed at zero. Standard deviation units extend outward in both directions from the mean. These units help us understand how far a score is from the average. The height of the curve at any point represents the percentage of scores in that area. A large portion of scores fall close to the mean. In fact, about 68% of all scores lie be...

  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...

Averages Can Be Deceiving What You Need to Know About Averages Most people assume that a simple statistic like a mean or a median tells the whole story. It doesn’t. Averages can clarify—but they can also mislead—depending on which one you use and how your data are distributed. Understanding the mean, median, and mode helps you interpret test scores, salaries, evaluations, and research findings with greater accuracy. CALCULATOR : I have included a basic calculator at the bottom of this page. The Mean, Median, and Mode Mean The mean is the arithmetic average of a set of numbers. You calculate it by adding all the values and dividing by the number of values. Example: For the data 1, 2, 3, 4, 5, the sum is 15 and the mean is 3. The mean uses every value in the dataset, which makes it useful but also sensitive to extreme scores. Median The median is the middle value when numbers are arranged from lowest to highest. Half the values fall above it and half fall below it. Example: In the set 1,...