Quantification of behavioral data with effect sizes and statistical significance tests

Costello et al. (2022) compared how well different ways of reading single-case graphs agree with each other.

They looked at visual inspection, two effect-size numbers (RD and g), and two statistical tests (Tau z and PWD).

The team ran these metrics on sets of graphs that already existed and checked how often they told the same story.

The numbers matched each other: Tau z, PWD, RD, and g all pointed the same way.

Visual inspection alone was shaky; different viewers did not always agree.

Adding the small math steps made the decision clearer and more repeatable.

Carlin et al. (2022) ran a simulation the same year and reached the same rule: use Tau to spot an effect, then RD or g to size it.

The two papers together form a direct replication, one with real data and one with fake data, giving the same advice.

Dowdy et al. (2021) review shows the field is already pooling these exact metrics in meta-analyses, so the practice is ready for journals.

Falligant et al. (2020) tested a different aid (fail-safe k) and also warned: numbers help, but check them before trusting your eyes.

You no longer need to choose between eyes and numbers. Run Tau z for a quick yes/no, add RD to show how big, and write both in your paper. Reviewers expect it, and your graphs will convince faster.