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How to Design and Evaluate Research in Education Book Cover
How to Design and Evaluate Research in Education, 5/e
Jack R. Fraenkel, San Francisco State University
Norman E. Wallen, San Francisco State University

Descriptive Statistics


Bar graph   A graphic way of illustrating differences among groups.
Categorical data   Data (variables) that differ only in kind, not in amount or degree.
Correlation coefficient   A decimal number between .00 and +1.00 and –1.00 that indicates the degree to which two quantitative variables are related.
Crossbreak table   A table that shows all combinations of two or more categorical variables and portrays the relationship (if any) between the variables.
ETA   An index that indicates the degree of a curvilinear relationship.
Five-number summary   Consists of the lowest score, the first quartile, the median, the third quartile, and the highest score. This summary provides a quick overview about the central tendency, variability, and shape of the distribution with just five numbers.
Frequency distribution   A tabular method of showing all the scores obtained by a group of individuals.
Frequency polygon   A graphic method of showing all of the scores obtained by a group of individuals.
Mean   The sum of the scores in a distribution divided by the number of scores in the distribution; the most commonly used measure of central tendency.
Measures of central tendency   Indices representing the average or typical score attained by a group of subjects; the most commonly used in educational research are the mean and the median.
Median   That point in a distribution having 50 percent of the scores above it and 50 percent of the scores below it.
Mode   The score that occurs most frequently in a distribution of scores.
Negatively skewed   A distribution in which there are more extreme scores at the lower end than at the upper, or higher, end.
Normal distribution   A theoretical "bell-shaped" distribution having a wide application to both descriptive and inferential statistics. It is known or thought to portray many human characteristics in "typical" populations.
Outlier   Scores or other observations that deviate or fall considerably outside most of the other scores or observation in a distribution or pattern.
Parameter   A numerical index describing a characteristic of a population.
Pie chart   A graphic method of displaying the breakdown of data into categories.
Positively skewed   A distribution in which there are more extreme scores at the upper, or higher, end than at the lower end.
Probability   The relative frequency with which a particular event occurs among all events of interest.
Qualitative data   Data that are not numerical.
Quantitative data   Data that differ in amount or degree, along a continuum from less to more.
Range   The difference between the highest and lowest scores in a distribution; measure of variability.
Scatterplot   The plot of points determined by the cross-tabulation of scores on coordinate axes; used to represent and illustrate the relationship between two quantitative variables.
Standard deviation   The most stable measure of variability; it takes into account each and every score in a distribution.
Standard score   A derived score that expresses how far a given raw score is from the mean, in terms of standard deviation units.
Statistic  A numerical index describing a characteristic of a sample.
T score  A score derived from a z score by multiplying the z score by 10 and adding 50.
Variance   The square of the standard deviation; a measure of variability.
z score  The most basic standard score that expresses how far a score is from a mean in terms of standard deviation units.