Assessment, Statistics, and Research

  The bell curve is also known as the normal curve or normal distribution . The bell curve has mathematical  properties that allow researchers to draw conclusions about where scores (or data) are located relative to other scores (or data). Click hyperlinks for more details. The three measures of central tendency (mode, median, mean ) are at the same middle point in a normal curve. The numbers representing the middle of the bell curve divide the distribution in half. On the x -axis in the normal distribution, the mean is at zero and there are standard deviation units above and below the mean.  The height of the curve indicates the percentage of scores in that are a. You can see that a large percentage of the scores are between 1 and -1 standard deviations. About 68% of scores fall between +1 and -1 standard deviations from the mean.  Look at the illustration below to see that there are about 34% of the scores in falling one standard deviation above the mean and another 34% in one st

  The term correlation can refer to a statistic and a type of research.  Understanding correlations is an important building block of many complex ideas in statistics and research methods. My focus in this post is on the common correlation statistic, also called the Pearson r . The Pearson r is a statistical value that tells the strength and direction of the relationship between two normally distributed variables measured on an interval or ratio scale . Researchers examine the two sets of values and calculate a summary statistic called a correlation coefficient . The longer name for a common correlation statistic is the Pearson Product Moment Correlation Coefficient but sometimes it is referred to as the Pearson r . The symbol for correlation is a lower case and italicized r .  In behavioural research, we normally round values to two decimal points. A moderately strong positive correlation example is r = .78.       Sometimes, the relationship between the two variables is negativ

  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