Distribution

A distribution refers to the way in which researchers organize sets of scores for interpretation. The term also refers to the underlying probabilities associated with each possible score in a real or theoretical population. Generally, researchers plot sets of scores using a curve that allows for a visual representation. Displaying data in this way allows researchers to study trends among scores. There are three common approaches to graphing distributions: histograms, frequency polygons, and ogives. Researchers begin with a set of raw data and ask questions that allow them to characterize the data by a specific distribution. There are also a variety of statistical distributions, each with its unique set of properties.

Distributions are most often characterized by whether the data are discrete or continuous in nature. Dichotomous or discrete distributions are most commonly used with nominal and ordinal data. A commonly discussed discrete distribution is known as a binomial distribution. Most textbooks use the example of a coin toss when discussing the probability of an event occurring with two discrete outcomes. With continuous data, researchers most often examine the degree to which the scores approximate a normal distribution. Because distributions of continuous variables can be normal or nonnormal in nature, researchers commonly explain continuous distributions in one of four basic ways: average value, variability, skewness, and kurtosis. The normal distribution is often the reference point for examining a distribution of continuously scored variables. Many continuous variables have distributions that are bell shaped and are said to approximate a normal distribution. The theoretical curve, called the bell curve, can be used to study many variables that are not normally [Page 380]distributed but are approximately normal. According to the central limit theorem, as the sample size increases, the shape of the distribution of the sample means taken will approach a normal distribution.