2x2 and 3x2 Factorial ANOVAs

What are confidence intervals?

Confidence intervals give a range around a sample mean that is likely to contain the true population mean.

How do you calculate a confidence interval?

CI = sample mean ± (Z × StE); StE = SD / √n

How can confidence intervals be interpreted?

A 95% CI means 95% of CIs from repeated samples would contain the population mean; non-overlapping CIs suggest a likely meaningful difference.

How should variables be nested in ANOVA?

Nest the high‑priority variable within the lower‑priority variable conceptually when forming or testing hypotheses.

What should you do if your data violate sphericity?

Apply Greenhouse–Geisser or Huynh–Feldt corrections to adjust degrees of freedom.

How should variables be plotted to best see an interaction?

Use a line graph with the lower‑priority variable on the x‑axis and the other variable shown as separate lines.

What relationship between lines suggests an interaction?

Non‑parallel lines, indicating the effect of one variable depends on the level of the other.

Which analyses follow up a significant interaction in a 3×2 ANOVA?

Run planned contrasts for the repeated‑measures factor and simple main effects to test the effect of one variable at each level of the other.

What should you do if the interaction isn’t significant?

Do not run follow‑up interaction tests; interpret only the main effects.