When psychologists collect data, these data, at their most basic, can be classified as either categorical or measured variables. Categorical variables are discrete variables in that people belong to certain categories and not others. Measured variables are generally those that go beyond mere categorization, relying upon numerical, and often continuous, values.
More complex classification of variables further breaks down these two types of variables. Nominal variables are named categories, and even if they might be assigned a number, the number operates as a label only. Ordinal variables are those that place respondents in a specific order, such as first, second, or third place. Interval measures are numerical values for which each unit on a scale is equidistant from the previous unit. Ratio variables are interval measures that also have a true, meaningful zero value.
When using statistics, researchers generally rely on a set of data on which they can conduct further analyses and that will be generalizable to a population. The most basic descriptive analyses that can be conducted on a data set are measures of central tendency. These include the mean, the mathematical average of the data; the median, the value, when responses are arranged from smallest to largest, that sits in the middle of the data set; and the mode, the most frequently occurring value in the data.
In addition to central tendency, researchers are also interested in the spread of a data set, also known as dispersion. A basic measure of dispersion is the range, the smallest number in the data set subtracted from the largest. Researchers also may calculate mean deviation, or the extent to which, on average, scores differ from the mean. Related to the mean deviation are the variance and standard deviation, transformations of the mean deviation that accounting for sample versus population values, which is necessary for most inferential statistical analyses. When talking about a sample, researchers use the uncorrected standard deviation, which divides the mean deviation by N. However, if a researcher is interested in making generalizations to a population, he or she would use the unbiased estimate of the standard deviation, which uses N – 1 as the denominator instead.
Any inferential statistical analysis will consider sample statistics, which are the results of analyses conducted on the data collected from a sample. In addition, sample statistics can also be used to estimate values for a population, also known as population parameters. We use sample statistics because it is unnecessary (and usually impossible) to conduct analyses on an entire sample. However, it is possible to draw inferences about a population based upon the statistics of one’s sample.
Additional Online Resources
Online video tutorial on levels of measurement: http://www.sophia.org/tutorials/identifying-level-of-measurement
“Arthur Benjamin: Teach Statistics before Calculus!” TED Talk: http://www.ted.com/talks/arthur_benjamin_s_formula_for_changing_math_education
Exploring the mean and the median: http://onlinestatbook.com/stat_sim/descriptive/index.html
Tutorial about measures of dispersion: http://www.sophia.org/tutorials/measures-of-dispersion--2
Test your knowledge of the keywords and definitions in the chapter.
Interactive Quiz for Chapter 14
Instructions: For each question, click on the radio button beside your answer. When you have completed the entire quiz, click the “Submit my answers” button at the bottom of the page to receive your results.