Planned Contrast Analysis
Also known as: planned comparisons, planned contrasts, a priori contrasts, Kontrast Analizi — Planlanmış Karşılaştırmalar
Planned contrast analysis is a parametric hypothesis-testing method that evaluates specific, theoretically motivated comparisons among group means — comparisons that the researcher specifies before data collection, not in response to observed patterns. Formalized comprehensively by Rosenthal, Rosnow, and Rubin (2000), the approach assigns a set of contrast coefficients to the groups being compared, with the constraint that the coefficients sum to zero, and then tests whether the resulting weighted combination of means differs significantly from zero.
Key highlights
- Greater statistical power than omnibus ANOVA followed by post-hoc tests, because only the theoretically predicted comparisons are tested.
- Orthogonal contrasts are statistically independent and partition the total between-groups variance without overlap.
- Directly tests the researcher's theory rather than a global null hypothesis, making results more informative and interpretable.
- No multiplicity correction is required for a set of orthogonal planned contrasts, preserving the nominal alpha level.
Intuition
This section is available to Pro members. Upgrade to Pro
How it works
This section is available to Pro members. Upgrade to Pro
When to use it
Use planned contrast analysis when you are comparing three or more independent groups on a single continuous outcome and you have specific, theoretically derived hypotheses about which group combinations will differ — stated before you examine the data. The standard ANOVA assumptions must hold: continuous outcome, approximately normal distributions within groups (check with Shapiro-Wilk), homogeneity of variances across groups (check with Levene's test), and independence of observations. The minimum recommended total sample size is 20. If you lack a priori hypotheses, post-hoc tests such as Tukey's HSD are more appropriate. With three or more orthogonal contrasts, no multiplicity adjustment is needed for the planned set, but any contrasts added after inspecting the data should be treated as exploratory.
Strengths & limitations
- Greater statistical power than omnibus ANOVA followed by post-hoc tests, because only the theoretically predicted comparisons are tested.
- Orthogonal contrasts are statistically independent and partition the total between-groups variance without overlap.
- Directly tests the researcher's theory rather than a global null hypothesis, making results more informative and interpretable.
- No multiplicity correction is required for a set of orthogonal planned contrasts, preserving the nominal alpha level.
- The advantage disappears if the specified contrasts do not match the true pattern of group differences.
- The number of orthogonal contrasts is limited to k − 1, where k is the number of groups.
- Requires genuine a priori planning; post-hoc use of contrast coefficients chosen to match observed patterns is not valid.
- Like standard ANOVA, it is sensitive to violations of normality and variance homogeneity in small samples.
Common pitfalls
This section is available to Pro members. Upgrade to Pro
Applications
This section is available to Pro members. Upgrade to Pro
Frequently asked
What does it mean for contrasts to be orthogonal?
Two contrasts are orthogonal when the sum of the products of their corresponding coefficients equals zero. Orthogonal contrasts are statistically independent — their test statistics are uncorrelated — and together they partition the between-groups sum of squares without overlap. You can have at most k − 1 mutually orthogonal contrasts for k groups.
How is planned contrast analysis different from post-hoc tests?
Planned contrasts are specified before data collection based on theory. Post-hoc tests are applied after an omnibus ANOVA when you do not have specific prior predictions and want to explore which pairs of means differ. Planned contrasts are more powerful because they test fewer hypotheses, but they are only legitimate when the comparison was truly specified in advance.
Do I need to run an omnibus ANOVA first?
No. If your planned contrasts collectively address your research questions, you do not need a preceding omnibus F test. The omnibus test answers a different question — whether any means differ at all — whereas planned contrasts test specific, theoretically motivated patterns. Some researchers report both for completeness, but the omnibus result does not gate the contrast tests.
What effect size should I report?
The contrast correlation r is the recommended effect size: r = √(t² / (t² + df_within)). It is interpretable on the familiar 0-to-1 scale and directly quantifies the relationship between group membership (as weighted by the contrast) and the outcome. Report it together with the contrast estimate and its 95% confidence interval.
Sources
- 1.Rosenthal, R., Rosnow, R. L. & Rubin, D. B. (2000). Contrasts and Effect Sizes in Behavioral Research: A Correlational Approach. Cambridge University Press.ISBN 978-0521659802
You have read it. What now?
Cite this page
ScholarGate. (2026, June 1). Contrast Analysis. ScholarGate. https://scholargate.app/statistics/contrast-analysis