BB2025 Chap.5 Comparing Groups with t Tests and ANOVA
Comparing Groups with t Tests and ANOVA
Select the comparison from structure
For continuous outcomes, the route depends on how many conditions are compared and whether observations are independent or linked. Independent t procedures compare unrelated groups. Paired procedures analyse within-pair differences.
One-way ANOVA evaluates whether several population means can share one value, while repeated-measures ANOVA preserves multiple observations from the same unit. Rank-based procedures offer different estimands when mean-based assumptions are unsuitable.
Describe before testing
Print sample sizes, centres, spreads and the direction in which higher values should be read.
Inspect extreme observations, balance and dependence. Parametric robustness is a reasoned judgement about the estimator and sample, not permission to ignore a coding error or an outcome whose scale makes the mean misleading.
Use the omnibus result correctly
A significant F statistic says that not all means are equal. It does not identify the groups that differ or establish a ranking.
Planned contrasts or adjusted pairwise comparisons provide the local estimates and intervals. Repeated measures add assumptions about within-person covariance and require attention to time order, carryover and missing visits.
What this chapter covers
- 01
Independent and paired observations
- 02
Difference scores and sign conventions
- 03
Independent and paired t procedures
- 04
Welch and pooled variance routes
- 05
One-way omnibus ANOVA
- 06
Repeated-measures ANOVA
- 07
Planned contrasts and multiplicity
- 08
Rank-based comparison methods
Worked example · free
Calculate a paired mean change
- 2Identify linked observations and define the sign.
- 3Sum and average the difference scores.
- 3Interpret the observed change and design limitation.
Key terms
- Independent Samples
- Observations contributed by unrelated units whose errors can be treated as separate under the design.
- Paired Samples
- Linked observations from the same or deliberately matched units analysed through their within-pair relationship.
- Welch Test
- A two-group mean comparison that does not require equal population variances.
- Omnibus Test
- A global comparison assessing whether a set of population means or distributions can share one value.
- Planned Contrast
- A pre-specified linear comparison among group means that represents a scientific question.
- Sphericity
- A repeated-measures condition concerning equality of variances among pairwise difference scores.
Comparing Groups with t Tests and ANOVA FAQ
How do I decide between an independent and paired test?
Ask whether each value in one condition has a meaningful link to one value in the other. Repeated measures from the same participant and deliberately matched pairs are linked; separate treatment groups are independent. Pairing changes the unit of analysis to the within-pair difference, so it must come from the design rather than convenience.
Why not run several t tests instead of ANOVA?
Each unadjusted pairwise test creates another opportunity for a false rejection across the family. ANOVA supplies one global test of equal means, after which planned contrasts or adjusted pairwise comparisons address the specific differences. The omnibus result alone still does not identify which pairs differ, so both stages have distinct roles.
When should I use a non-parametric alternative?
Consider the outcome scale, extreme observations, sample size, distribution of the relevant values and the estimand. Rank-based tests are useful when a mean-based model is poorly supported, but they do not simply reproduce the same question without assumptions. State whether the conclusion concerns ranks, distributions or a location shift under additional shape conditions.
Exam move
For every group-comparison scenario, write three items before naming a test: outcome scale, number of conditions and independence or linkage. Compute one paired difference set by hand so the sign convention is secure. For ANOVA output, use a fixed sequence: group summaries, omnibus F with degrees of freedom, effect size, planned or adjusted contrasts and the design limitation.
Review rank-based procedures by writing the estimand they support rather than treating them as automatic fallbacks. Make a small decision table that pairs each design with its parametric route, rank-based route and target quantity. When practising post-hoc output, hide the significance column and interpret estimates and intervals first. This stops a threshold from replacing group direction, effect size and clinical relevance.
Add the multiplicity method only after naming the planned family of comparisons. Redraw one repeated-measures question as a difference column and one independent question as two group columns. The layout itself should reveal why their standard errors differ. For a three-group result, write the omnibus question and each contrast question on separate lines.
State which answer is supported by the F test and which requires a comparison. This prevents a global difference from being assigned to an untested pair.
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