Main Points

Approaches to Research

• A good deal of educational research is done in one of two ways: either two or more groups are compared, or variables within one group are related.
• The data in a study may be either quantitative or categorical.

Comparing Groups Using Quantitative Data

• When comparing two or more groups using quantitative data, researchers can compare them through frequency polygons, calculation of averages, and calculation of spreads.
• We recommend, therefore, constructing frequency polygons, using data on the means of known groups, calculating effect sizes, and reporting confidence intervals when comparing quantitative data from two or more groups.

Relating Variables Within a Group Using Quantitative Data

• When researchers examine a relationship between quantitative variables within a single group, the appropriate techniques are the scatterplot and the correlation coefficient.
• Because a scatterplot illustrates all the data visually, researchers should begin their analysis of data obtained from a single group by constructing a scatterplot.
• Therefore, we recommend constructing scatterplots using both scatterplots and correlation coefficients when relating variables involving quantitative data within a single group.

Comparing Groups When the Data Involved Are Categorical

• When the data are categorical, groups can be compared by reporting either percentages of frequencies in crossbreak tables.
• It is a good idea to report both the percentage and the number of cases in a crossbreak table, as percentages alone can be misleading.
• Therefore, we recommend constructing crossbreak tables and calculating contingency coefficients when comparing categorical data involving two or more groups.

Relating Variables Within a Group Using Categorical Data

• When you are examining relationships among categorical data within one group, we again recommend constructing crossbreak tables and calculating contingency coefficients.

Two Final Recommendations

• When tests of statistical significance can be applied, it is recommended that they be used to evaluate generalizability only, not to evaluate the magnitude of relationships. Confidence intervals should be reported in addition to significance levels.
• Both parametric and nonparametric techniques should be used to analyze data rather than either one alone.