Statistics: Descriptive

Descriptive statistics are numerical measures of a condition and often considered a snapshot of a point in time. As such, they are useful for understanding but not designed to predict. This entry discusses the use of statistics for reporting basic results.

In many cases, it is only necessary to produce an estimate of the number, proportion, or distribution of one variable at a time (univariate statistics). In other cases, it is more helpful to subdivide the data and look at the interaction between one variable and another (multivariate statistics), as when, for example, considering if a particular speech pattern is more likely in one region or another.

Normally, a small group (sample) is studied to infer or generalize the results to a much larger group (population). The generalizability of the statistics is dependent on the relationship between the sample and population. The ideal scientifically drawn sample is one where there is a known equal chance for each member of the population to be in the sample. Random selection is the most common method to create a representative sample. Convenience or purposive samples do not produce representative results because many in the population have no chance of being in the sample. The lack of generalizability results from the assumption that those in the sample are fundamentally different from the population so the results are equally inconsistent.

Data levels are broadly divided into two main categories: nonparametric and parametric. Nonparametric data use categories where there is no strong relationship between the data and an actual number, such as geographic area, gender, or diagnosis code. Parametric data include those measures where a number can accurately describe the condition, such as decibel, weight, or grade point average.

Parametric Data

With parametric data, the major descriptive techniques include measures of central tendency and measures of dispersion. These two concepts are compared to the standard bell curve. Imagine if one were measuring the height of large group. Some people are tall and some are short, but most fall somewhere in the middle. Plotting height by the number of people at each height provides a curved line that starts low with the few very short people, [Page 1836]progressively rises for the larger groups at average height, and drops for fewer people who are very tall.

Figure 1 Bell curve or normal distribution: The typical distribution where measures are plotted by the number of cases at each measurement level

Measures of Central Tendency

Measures of central tendency represent the variable at the height of that curve or the most common measure. Mean or average is the sum or all measures divided by the number of measures and the most common measure of central tendency. Mean is the appropriate descriptive measure where there is a normal distribution of scores (most representing the bell-shaped curve).

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