INTERPRETATION AND ANALYSIS

Interpretation and Analysis

Interpretation and Analysis

Descriptive Statistics

In the context of the data provided, it might be said that measurement provides a means for quantifying important phenomena of interest. In many measurement contexts, researchers are interested solely in efficiently describing the data. Descriptive statistics are the indexes through which such data summarization may be accomplished. Unlike contexts in which the researcher is interested in drawing generalizations from data, descriptive statistics are not used to draw inferences to a larger population (Joliffe, 1986).

For example, consider a situation in which a teacher has recently administered an examination. Fundamentally, the teacher has constructed the test in the hope that those with more knowledge of the course material will perform better (receive higher scores) than those with less knowledge of the course material. After scoring the examinations, the teacher records each student's grade in the instructor's grade book, which is organized alphabetically. Although these data can be easily used to identify the performance of any individual student, the alphabetic organization does not provide for easy interpretation of scores as a whole.

One way to use descriptive statistics to make sense of these data would be to construct a frequency table in which scores are rank ordered from largest to smallest along with the number of individuals receiving each score. This information can also be presented graphically in the form of a frequency distribution in which test score is plotted along the x-axis and frequency is plotted along the y-axis. An examination of such representations of these data can quickly reveal the general shape (e.g., normal, bimodal, skewed) of the distribution of observed scores (Joliffe, 1986).

Descriptive data are not confined to use with univariate data. In many cases, for example, there is interest in the extent to which variability associated with one measure is associated with variability ...