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A contrast is a linear combination ${\sum }_i{c}_i{\mu }_i$ of group means with ${\sum }_i{c}_i=0$. It compares responses without depending on a common additive level. Treatment contrasts and factorial contrasts specify comparisons in a design of experiments.

Design of experiments chooses experimental units, treatments, replication, blocks in experimental design and randomization so that scientifically useful treatment contrasts can be estimated with meaningful standard errors. Allocation determines which measurements supply independent treatment information.

Use one-way analysis of variance to compare a quantitative response variable across levels of one categorical factor; for example, compare task accuracy across three independently assigned teaching methods. The ordinary independent-groups procedure tests the null hypothesis that all group population means are equal. Its F-test compares variation associated with the group factor against within-group error variation; a significant result indicates that not all population means are equal, without identifying which groups differ.^[ref]

The classical one-way normal linear model assumes independent observations and within-group errors approximately following a normal distribution with a common variance. Repeated observations on the same people require a different dependence structure; pronounced unequal variances may call for Welch's one-way analysis of variance. Planned contrasts or appropriately controlled follow-up comparisons identify scientifically relevant differences. Report the means, differences and confidence intervals, not just significance. Causal interpretation depends on the design of experiments, particularly randomization, rather than on the F-test alone.

Preregistration creates a time-stamped record of research questions and planned methods before the relevant results are examined. Specify the design, recruitment and stopping rules, outcome definitions, exclusions, principal tests, model choices and any conditional decision rules. For existing data, disclose prior access and what was already known. A sufficiently precise record helps readers distinguish prior predictions from choices prompted by the results.^[ref]

It does not prohibit useful changes or new discoveries: report departures, their timing and reasons, and distinguish exploratory analysis from confirmatory analysis. A vague or selectively followed registration does not solve selective reporting, and preregistration cannot repair a poor measure or inadequate design of experiments. A registered report adds pre-result peer review and conditional publication acceptance, which are not implied by registration alone.

Methods for defining questions, obtaining observations and evaluating claims in psychology. Design of experiments can identify effects of assigned conditions; an observational study measures existing variation. Qualitative research methods examine meanings and processes in context. The method must fit the question and the intended inference.