Statistical Language

Terms used to plan and interpret analyses

A quick reference for variables, distributions, research designs, formulas, and cautious conclusions.

This page is a reminder, not a replacement for the textbook. Return to the relevant textbook chapter when you need a fuller explanation or example.

Variables And Roles

Term Meaning
Categorical variable Places observations into categories.
Nominal variable Uses categories without a meaningful rank order.
Ordinal variable Uses categories with a meaningful order.
Quantitative variable Records numerical amounts or scores for which numerical differences are meaningful.
Outcome or dependent variable The response an analysis describes, predicts, or compares.
Predictor or independent variable The variable used to predict an outcome or define comparison groups.

The role of a variable depends on the research question. A variable can be an outcome in one analysis and a predictor in another.

Describing A Distribution

When describing one variable, consider:

  • frequency and percent for categories;
  • center, including the mean, median, or mode;
  • variability, including the range, standard deviation, or IQR;
  • shape, including symmetry or skew; and
  • missing, impossible, or unusual values.

Report what the output shows before offering a broader explanation for the pattern.

Comparing And Relating Variables

  • A difference describes how groups or conditions compare.
  • An association describes how two variables vary together.
  • A prediction uses one or more variables to estimate an outcome.
  • An interaction means the relationship between one predictor and the outcome differs across values of another predictor.

An observed association does not by itself establish that one variable caused the other.

Formula Syntax In R

Many R models use a formula:

outcome ~ predictor

Read this as “model the outcome using the predictor.” The variable on the left is the outcome. Variables on the right are predictors or grouping variables.

A two-predictor model may use:

outcome ~ predictor_1 * predictor_2

The * asks R to estimate both main effects and their interaction. The chapter that introduces this model will explain how to read the resulting output.

Writing A Conclusion

A complete short interpretation usually states:

  1. which variables or groups were analyzed;
  2. the important pattern in the output;
  3. the relevant statistics;
  4. whether the result supports the stated hypothesis; and
  5. any limitation needed to avoid an unsupported conclusion.

Use the wording and level of detail requested in each chapter. Statistical significance, practical importance, and causation are different claims and should not be treated as interchangeable.