Statistical Analysis and Interpretation

Your statistical analysis provides hard data about the results of your research or project. How you interpret and apply your findings is critical for making data-driven decisions.

What is statistics? There are several meanings. It is a field of study, but statistics also describes tools for analyzing information. The normal curve is the foundation on which statistics are built. Choosing the correct tools for your study or assessment is essential, and so is your application of them.

Descriptive statistics are used to present something of a profile of what you have found. Averages (mean, median, and mode) describe the middle of a group of scores. Measures of dispersion (range, variance, and standard deviation) describe the spread of data.

Survey research typically uses descriptive statistics to present findings. Standardized educational tests, such as ACTs, use T-scores to indicate where a one falls compared to others on the normal curve. There's always a margin of error as to the accuracy of scores, so don't take them as absolutes.

Inferential statistics use samples to make inferences about larger populations. The t-test, for example, is often used to compare the means of two groups to determine whether or not they are significantly different. ANOVA (analysis of variance) and other such statistics are applied to more groups and when more variables are involved in the analysis.

Sample size, randomness, and normality are major considerations for using these powerful inferential statistics. A common mistake is to apply them to data when assumptions have not be met. There are other options, called nonparametric statistics, that have fewer assumptions and are based on the median rather than the mean. The Kruskal-Wallis test, for example, may be substituted for ANOVA when assumptions are unmet.

For other pages about statistics, see

Levels of Measurement

Measures of Central Tendency



Measures of Variability

Common Statistical Symbols

Need assistance selecting, analyzing, interpreting, and applying statistics in the real world? From dissertations to strategic planning and evaluation to workplace problem solving, Research Assessment Adviser can help.

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