Research Methods & Statistics

Research methodology is the set of decisions that determine what a study can legitimately claim. Those decisions are made in a specific order, and each one constrains the next: the research question shapes the design, the design determines what analysis is appropriate, and the quality of measurement bounds what any analysis can recover. A study with an elegant statistical model built on an unvalidated instrument is not a strong study; it is a precise answer to an unreliable question.

This section is organised around that sequence rather than around statistical techniques in isolation. It is written for researchers designing and defending their own studies, and for the research administrators, reviewers and methodologists who assess them.

How this section is organised

Eight sub-sections follow the arc of a study from design through analysis and reporting:

• Study design — randomised controlled trials, cohort and case-control studies, cross-sectional and longitudinal designs, and quasi-experimental approaches, with the validity threats specific to each.
• Sampling and statistical power — power analysis and sample size calculation before data collection, and the sampling strategies that determine what a sample can generalise to.
• Quantitative analysis — regression, ANOVA, t-tests, confidence intervals, effect sizes, and the assumptions each technique depends on.
• Qualitative methods — thematic analysis, grounded theory, phenomenology and ethnography, with the rigour criteria qualitative work is judged against.
• Research paradigms and mixed methods — the ontological and epistemological assumptions underneath any chosen method, and how quantitative and qualitative strands are combined.
• Measurement, reliability and validity — whether an instrument measures what it claims to, including internal consistency, test–retest reliability and instrument development.
• Survey research — questionnaire construction, scale design, response rates and sampling frames.
• Methods fundamentals — the orienting vocabulary that the sub-sections above build on.

Where evidence synthesis lives

Systematic reviews, meta-analysis, scoping reviews and PRISMA reporting are covered under Scholarly Publishing, in its evidence-synthesis section, rather than duplicated here. Evidence synthesis is a form of secondary research with its own reporting standards and publication conventions, and it sits more naturally alongside publication practice than alongside primary study design.

Related: Relative Frequency and Frequency Distributions — How to calculate and report relative frequency, frequency distributions, cumulative frequency, and relative cumulative frequency — including the empirical-probability link via the law of large numbers, class-interval trade-offs for continuous data, and row/column/total percentages in contingency tables.

Method choice is a reporting obligation, not just a design one

Most reporting guidelines are organised by study design: CONSORT for randomised trials, STROBE for observational studies, PRISMA for systematic reviews, ARRIVE for animal research. Choosing a design therefore also chooses the checklist a manuscript will be assessed against, and increasingly the checklist a funder or journal requires at submission. Pages in this section note the applicable reporting standard alongside the method itself, because in practice the two are inseparable.

Related reading: Delphi method — The Delphi method builds expert consensus through anonymous, iterated rounds of rating and feedback. This guide covers round structure, panel selection, how consensus is measured, stopping rules, and modified/real-time variants, with a worked example.

Related reading: Poisson distribution — How to recognize count data that fits a Poisson distribution, the formula and its single parameter (lambda), the four assumptions that must hold, worked examples, and when to switch to negative binomial or Poisson regression instead.

Related reading: content validity index — Content validity is whether an instrument’s items adequately sample the full construct domain, as judged by expert panels. Covers the expert-panel process, the content validity ratio (CVR), the content validity index (CVI), and the distinction from face validity, each worked through a hand-calculated illustrative example.

Related reading: z-score — How to calculate a z-score, what standardization does (and doesn’t) do to a distribution, and how to correctly read a standard normal (z) table, including a full table. For more on this, see CASRAI’s guide to survey tools for academic research. CASRAI also has a dedicated explainer on empirical research.