Why English? | Reporting CONSORT Factorial Trials Through Factors, Levels, Main Comparisons, Interactions, Participant Flow and Interpretation

ORIENTATION

What this guide owns

Current fact check

The 2023 factorial extension recommends identifying the design, explaining why it was used, naming the treatment groups that form each main comparison, and reporting interaction estimates with precision. It applies to full, partial and fractional factorial structures.

Canonical boundary

This article owns reporting of completed factorial randomised trials. The Gold Standard factorial article owns the underlying design theory, while CONSORT 2025 owns generic trial reporting.

Worked example

Every chapter returns to a fictional 2×2 school trial testing a reading-discussion routine and a feedback checklist, producing four groups: neither, discussion only, checklist only and both. It is fictional, low-stakes and educational; it does not report a real school, clinical decision or guaranteed outcome.

Warm up with eduKate’s guides to explaining scientific evidence and asking better questions in class.

CHAPTER 1 OF 13

1. Identify the Study as a Factorial Randomised Trial

Back to contents

Why this move matters

Name the factorial design in the title and abstract and state the number of factors and levels.

Draw the factor table first

Name the factorial design in the title and abstract and state the number of factors and levels. List each factor, its levels, every treatment-group combination, who is eligible for each factor and the main comparison used for each conclusion.

Work one main comparison

Worked example: The abstract identifies a 2×2 full factorial randomised trial. Identify the treatment groups pooled on each side, the assumed relationship between factors, the estimand, estimate, precision and interaction check.

Keep margins and cells together

Report marginal main comparisons for the primary conclusions and treatment-group cells for flow, adherence, harms and outcomes when they reveal how combinations behaved.

Respect interaction uncertainty

Calling the study four-arm does not reveal the factor structure or planned pooled comparisons. A factorial design can study multiple interventions efficiently, but an interaction can change what a marginal effect means and may be estimated imprecisely.

Student, parent and career transfer

Make one evidence card for “Identify the Study as a Factorial Randomised Trial”: source location, plain-language meaning, limit and next question. A parent or teacher can ask for one everyday explanation and one specialist explanation; both must preserve the same conditions. This habit supports clinical trials, education research, experimental design, biostatistics, programme evaluation and evidence appraisal without promising a grade, admission, funding decision or job.

CHAPTER 2 OF 13

2. Define Factors, Levels and Treatment Groups

Back to contents

Why this move matters

List each factor with its levels and show every intervention combination that forms a treatment group.

Draw the factor table first

List each factor with its levels and show every intervention combination that forms a treatment group. List each factor, its levels, every treatment-group combination, who is eligible for each factor and the main comparison used for each conclusion.

Work one main comparison

Worked example: Discussion versus no discussion is one factor; checklist versus no checklist is the second. Identify the treatment groups pooled on each side, the assumed relationship between factors, the estimand, estimate, precision and interaction check.

Keep margins and cells together

Report marginal main comparisons for the primary conclusions and treatment-group cells for flow, adherence, harms and outcomes when they reveal how combinations behaved.

Respect interaction uncertainty

A factor is not the same as a four-cell treatment group. A factorial design can study multiple interventions efficiently, but an interaction can change what a marginal effect means and may be estimated imprecisely.

Student, parent and career transfer

Make one evidence card for “Define Factors, Levels and Treatment Groups”: source location, plain-language meaning, limit and next question. A parent or teacher can ask for one everyday explanation and one specialist explanation; both must preserve the same conditions. This habit supports clinical trials, education research, experimental design, biostatistics, programme evaluation and evidence appraisal without promising a grade, admission, funding decision or job.

CHAPTER 3 OF 13

3. State Whether the Design Is Full, Partial or Fractional

Back to contents

Why this move matters

Explain whether all combinations are used and whether every participant is eligible and randomised for every factor.

Draw the factor table first

Explain whether all combinations are used and whether every participant is eligible and randomised for every factor. List each factor, its levels, every treatment-group combination, who is eligible for each factor and the main comparison used for each conclusion.

Work one main comparison

Worked example: All students are eligible for both factors, so every combination can occur. Identify the treatment groups pooled on each side, the assumed relationship between factors, the estimand, estimate, precision and interaction check.

Keep margins and cells together

Report marginal main comparisons for the primary conclusions and treatment-group cells for flow, adherence, harms and outcomes when they reveal how combinations behaved.

Respect interaction uncertainty

Different eligibility across factors changes denominators and interaction information. A factorial design can study multiple interventions efficiently, but an interaction can change what a marginal effect means and may be estimated imprecisely.

Student, parent and career transfer

Make one evidence card for “State Whether the Design Is Full, Partial or Fractional”: source location, plain-language meaning, limit and next question. A parent or teacher can ask for one everyday explanation and one specialist explanation; both must preserve the same conditions. This habit supports clinical trials, education research, experimental design, biostatistics, programme evaluation and evidence appraisal without promising a grade, admission, funding decision or job.

CHAPTER 4 OF 13

4. Explain the Rationale and Whether Interaction Is Expected

Back to contents

Why this move matters

State why interventions share a trial, whether efficiency or interaction is the primary purpose, and the biological, educational or operational rationale.

Draw the factor table first

State why interventions share a trial, whether efficiency or interaction is the primary purpose, and the biological, educational or operational rationale. List each factor, its levels, every treatment-group combination, who is eligible for each factor and the main comparison used for each conclusion.

Work one main comparison

Worked example: The interventions act through different classroom processes, but interaction remains possible. Identify the treatment groups pooled on each side, the assumed relationship between factors, the estimand, estimate, precision and interaction check.

Keep margins and cells together

Report marginal main comparisons for the primary conclusions and treatment-group cells for flow, adherence, harms and outcomes when they reveal how combinations behaved.

Respect interaction uncertainty

Assuming no interaction because it seems unlikely is not evidence that none exists. A factorial design can study multiple interventions efficiently, but an interaction can change what a marginal effect means and may be estimated imprecisely.

Student, parent and career transfer

Make one evidence card for “Explain the Rationale and Whether Interaction Is Expected”: source location, plain-language meaning, limit and next question. A parent or teacher can ask for one everyday explanation and one specialist explanation; both must preserve the same conditions. This habit supports clinical trials, education research, experimental design, biostatistics, programme evaluation and evidence appraisal without promising a grade, admission, funding decision or job.

CHAPTER 5 OF 13

5. Name Every Main Comparison and Estimand

Back to contents

Why this move matters

Identify which treatment groups are pooled or contrasted for each primary conclusion and whether interest concerns marginal effects or effects within another factor level.

Draw the factor table first

Identify which treatment groups are pooled or contrasted for each primary conclusion and whether interest concerns marginal effects or effects within another factor level. List each factor, its levels, every treatment-group combination, who is eligible for each factor and the main comparison used for each conclusion.

Work one main comparison

Worked example: Discussion groups with and without the checklist are pooled and compared with both no-discussion groups. Identify the treatment groups pooled on each side, the assumed relationship between factors, the estimand, estimate, precision and interaction check.

Keep margins and cells together

Report marginal main comparisons for the primary conclusions and treatment-group cells for flow, adherence, harms and outcomes when they reveal how combinations behaved.

Respect interaction uncertainty

A result is uninterpretable when readers cannot reconstruct who was compared with whom. A factorial design can study multiple interventions efficiently, but an interaction can change what a marginal effect means and may be estimated imprecisely.

Student, parent and career transfer

Make one evidence card for “Name Every Main Comparison and Estimand”: source location, plain-language meaning, limit and next question. A parent or teacher can ask for one everyday explanation and one specialist explanation; both must preserve the same conditions. This habit supports clinical trials, education research, experimental design, biostatistics, programme evaluation and evidence appraisal without promising a grade, admission, funding decision or job.

CHAPTER 6 OF 13

6. Report Eligibility and Recruitment for Each Factor

Back to contents

Why this move matters

Give criteria, consent, recruitment dates and exclusions for every factor, noting differences and changes over time.

Draw the factor table first

Give criteria, consent, recruitment dates and exclusions for every factor, noting differences and changes over time. List each factor, its levels, every treatment-group combination, who is eligible for each factor and the main comparison used for each conclusion.

Work one main comparison

Worked example: All schools enter both factors, and the report confirms that no factor-specific exclusion applies. Identify the treatment groups pooled on each side, the assumed relationship between factors, the estimand, estimate, precision and interaction check.

Keep margins and cells together

Report marginal main comparisons for the primary conclusions and treatment-group cells for flow, adherence, harms and outcomes when they reveal how combinations behaved.

Respect interaction uncertainty

Participants not randomised for a factor must not silently enter that factor’s analysis. A factorial design can study multiple interventions efficiently, but an interaction can change what a marginal effect means and may be estimated imprecisely.

Student, parent and career transfer

Make one evidence card for “Report Eligibility and Recruitment for Each Factor”: source location, plain-language meaning, limit and next question. A parent or teacher can ask for one everyday explanation and one specialist explanation; both must preserve the same conditions. This habit supports clinical trials, education research, experimental design, biostatistics, programme evaluation and evidence appraisal without promising a grade, admission, funding decision or job.

CHAPTER 7 OF 13

7. Describe Randomisation Across Factors and Treatment Groups

Back to contents

Why this move matters

Report sequence generation, restrictions, allocation probabilities, concealment, implementation and any separate randomisation stages.

Draw the factor table first

Report sequence generation, restrictions, allocation probabilities, concealment, implementation and any separate randomisation stages. List each factor, its levels, every treatment-group combination, who is eligible for each factor and the main comparison used for each conclusion.

Work one main comparison

Worked example: A central system assigns one of the four combinations with balanced probabilities. Identify the treatment groups pooled on each side, the assumed relationship between factors, the estimand, estimate, precision and interaction check.

Keep margins and cells together

Report marginal main comparisons for the primary conclusions and treatment-group cells for flow, adherence, harms and outcomes when they reveal how combinations behaved.

Respect interaction uncertainty

Independent randomisations can produce different allocation structures from one four-group sequence. A factorial design can study multiple interventions efficiently, but an interaction can change what a marginal effect means and may be estimated imprecisely.

Student, parent and career transfer

Make one evidence card for “Describe Randomisation Across Factors and Treatment Groups”: source location, plain-language meaning, limit and next question. A parent or teacher can ask for one everyday explanation and one specialist explanation; both must preserve the same conditions. This habit supports clinical trials, education research, experimental design, biostatistics, programme evaluation and evidence appraisal without promising a grade, admission, funding decision or job.

CHAPTER 8 OF 13

8. Justify Sample Size for the Trial Objectives

Back to contents

Why this move matters

Show calculations for each main comparison or interaction, assumptions about other factors, multiplicity, attrition and the rule used when required sizes differ.

Draw the factor table first

Show calculations for each main comparison or interaction, assumptions about other factors, multiplicity, attrition and the rule used when required sizes differ. List each factor, its levels, every treatment-group combination, who is eligible for each factor and the main comparison used for each conclusion.

Work one main comparison

Worked example: The larger of the two main-comparison requirements determines the total sample. Identify the treatment groups pooled on each side, the assumed relationship between factors, the estimand, estimate, precision and interaction check.

Keep margins and cells together

Report marginal main comparisons for the primary conclusions and treatment-group cells for flow, adherence, harms and outcomes when they reveal how combinations behaved.

Respect interaction uncertainty

A trial powered for marginal effects may have little power to detect interaction. A factorial design can study multiple interventions efficiently, but an interaction can change what a marginal effect means and may be estimated imprecisely.

Student, parent and career transfer

Make one evidence card for “Justify Sample Size for the Trial Objectives”: source location, plain-language meaning, limit and next question. A parent or teacher can ask for one everyday explanation and one specialist explanation; both must preserve the same conditions. This habit supports clinical trials, education research, experimental design, biostatistics, programme evaluation and evidence appraisal without promising a grade, admission, funding decision or job.

CHAPTER 9 OF 13

9. Prespecify Factorial or Multiarm Analysis

Back to contents

Why this move matters

Describe whether analysis is at the margins or inside the table, adjustment for other factors, interaction handling, covariates, missing data and whether choices were data dependent.

Draw the factor table first

Describe whether analysis is at the margins or inside the table, adjustment for other factors, interaction handling, covariates, missing data and whether choices were data dependent. List each factor, its levels, every treatment-group combination, who is eligible for each factor and the main comparison used for each conclusion.

Work one main comparison

Worked example: The plan uses marginal comparisons and reports the interaction without switching methods after seeing its p-value. Identify the treatment groups pooled on each side, the assumed relationship between factors, the estimand, estimate, precision and interaction check.

Keep margins and cells together

Report marginal main comparisons for the primary conclusions and treatment-group cells for flow, adherence, harms and outcomes when they reveal how combinations behaved.

Respect interaction uncertainty

Choosing the analysis after observing interaction can bias estimates and error rates. A factorial design can study multiple interventions efficiently, but an interaction can change what a marginal effect means and may be estimated imprecisely.

Student, parent and career transfer

Make one evidence card for “Prespecify Factorial or Multiarm Analysis”: source location, plain-language meaning, limit and next question. A parent or teacher can ask for one everyday explanation and one specialist explanation; both must preserve the same conditions. This habit supports clinical trials, education research, experimental design, biostatistics, programme evaluation and evidence appraisal without promising a grade, admission, funding decision or job.

CHAPTER 10 OF 13

10. Estimate and Report Interaction With Precision

Back to contents

Why this move matters

For each primary outcome, present the interaction estimate and confidence interval even when interaction is not the main objective.

Draw the factor table first

For each primary outcome, present the interaction estimate and confidence interval even when interaction is not the main objective. List each factor, its levels, every treatment-group combination, who is eligible for each factor and the main comparison used for each conclusion.

Work one main comparison

Worked example: The report shows whether the checklist changes the effect of discussion and how uncertain that change is. Identify the treatment groups pooled on each side, the assumed relationship between factors, the estimand, estimate, precision and interaction check.

Keep margins and cells together

Report marginal main comparisons for the primary conclusions and treatment-group cells for flow, adherence, harms and outcomes when they reveal how combinations behaved.

Respect interaction uncertainty

A nonsignificant interaction does not prove no interaction. A factorial design can study multiple interventions efficiently, but an interaction can change what a marginal effect means and may be estimated imprecisely.

Student, parent and career transfer

Make one evidence card for “Estimate and Report Interaction With Precision”: source location, plain-language meaning, limit and next question. A parent or teacher can ask for one everyday explanation and one specialist explanation; both must preserve the same conditions. This habit supports clinical trials, education research, experimental design, biostatistics, programme evaluation and evidence appraisal without promising a grade, admission, funding decision or job.

CHAPTER 11 OF 13

11. Present Flow, Adherence, Harms and Outcomes by Useful Denominators

Back to contents

Why this move matters

Show information for each main comparison and, where informative, each treatment-group combination so combination-specific patterns remain visible.

Draw the factor table first

Show information for each main comparison and, where informative, each treatment-group combination so combination-specific patterns remain visible. List each factor, its levels, every treatment-group combination, who is eligible for each factor and the main comparison used for each conclusion.

Work one main comparison

Worked example: Flow is shown for both factors and the four cells, revealing lower adherence when both interventions are assigned. Identify the treatment groups pooled on each side, the assumed relationship between factors, the estimand, estimate, precision and interaction check.

Keep margins and cells together

Report marginal main comparisons for the primary conclusions and treatment-group cells for flow, adherence, harms and outcomes when they reveal how combinations behaved.

Respect interaction uncertainty

Marginal totals can hide a problem confined to one combination. A factorial design can study multiple interventions efficiently, but an interaction can change what a marginal effect means and may be estimated imprecisely.

Student, parent and career transfer

Make one evidence card for “Present Flow, Adherence, Harms and Outcomes by Useful Denominators”: source location, plain-language meaning, limit and next question. A parent or teacher can ask for one everyday explanation and one specialist explanation; both must preserve the same conditions. This habit supports clinical trials, education research, experimental design, biostatistics, programme evaluation and evidence appraisal without promising a grade, admission, funding decision or job.

CHAPTER 12 OF 13

12. Report Recruitment and Follow-up Dates for Each Factor

Back to contents

Why this move matters

State when each factor opened, changed or closed and explain differences, additions or removals.

Draw the factor table first

State when each factor opened, changed or closed and explain differences, additions or removals. List each factor, its levels, every treatment-group combination, who is eligible for each factor and the main comparison used for each conclusion.

Work one main comparison

Worked example: Both factors recruit together for the full school year, with no mid-trial factor change. Identify the treatment groups pooled on each side, the assumed relationship between factors, the estimand, estimate, precision and interaction check.

Keep margins and cells together

Report marginal main comparisons for the primary conclusions and treatment-group cells for flow, adherence, harms and outcomes when they reveal how combinations behaved.

Respect interaction uncertainty

A dropped factor can create calendar-time and eligibility differences. A factorial design can study multiple interventions efficiently, but an interaction can change what a marginal effect means and may be estimated imprecisely.

Student, parent and career transfer

Make one evidence card for “Report Recruitment and Follow-up Dates for Each Factor”: source location, plain-language meaning, limit and next question. A parent or teacher can ask for one everyday explanation and one specialist explanation; both must preserve the same conditions. This habit supports clinical trials, education research, experimental design, biostatistics, programme evaluation and evidence appraisal without promising a grade, admission, funding decision or job.

CHAPTER 13 OF 13

13. Interpret Main Effects, Interactions and Efficiency Carefully

Back to contents

Why this move matters

Connect each conclusion to its comparison and estimand, discuss interaction uncertainty, harms, multiplicity and whether combination effects limit transfer.

Draw the factor table first

Connect each conclusion to its comparison and estimand, discuss interaction uncertainty, harms, multiplicity and whether combination effects limit transfer. List each factor, its levels, every treatment-group combination, who is eligible for each factor and the main comparison used for each conclusion.

Work one main comparison

Worked example: The conclusion reports two marginal effects and avoids claiming that the combined cell equals their simple sum. Identify the treatment groups pooled on each side, the assumed relationship between factors, the estimand, estimate, precision and interaction check.

Keep margins and cells together

Report marginal main comparisons for the primary conclusions and treatment-group cells for flow, adherence, harms and outcomes when they reveal how combinations behaved.

Respect interaction uncertainty

Two effective factors do not guarantee that their combination is additive, safe or acceptable. A factorial design can study multiple interventions efficiently, but an interaction can change what a marginal effect means and may be estimated imprecisely.

Student, parent and career transfer

Make one evidence card for “Interpret Main Effects, Interactions and Efficiency Carefully”: source location, plain-language meaning, limit and next question. A parent or teacher can ask for one everyday explanation and one specialist explanation; both must preserve the same conditions. This habit supports clinical trials, education research, experimental design, biostatistics, programme evaluation and evidence appraisal without promising a grade, admission, funding decision or job.

PRACTICE LAB

Build a factor-comparison decision trail

Student route

1. Choose one original report inside this guide’s scope.
2. Copy its objective and underline actor, action, context, evidence and intended decision.
3. Draw the specific reasoning chain used in this article.
4. Mark each step reported, inferred, contested or unknown.
5. Rewrite the conclusion so it preserves the narrowest important limitation.

Parent or teacher route

Ask the learner to explain CONSORT Factorial Trials’s central reporting method twice: once to a classmate and once to a method specialist. Praise a precise correction and a well-stated unknown; both show disciplined attention to evidence.

Early-career route

Create a one-page CONSORT Factorial Trials audit with source link, date checked, scope, method logic, decisive wording, contrary evidence, limit and next action. A colleague should be able to continue without guessing.

Continue with eduKate’s guides to reading course and career information and giving useful feedback in group projects.

USEFUL NEXT READING

Connect this narrow owner to its neighbour

Read the factorial design-theory guide for a related but different reader job. Return here when the question is specifically how to report several interventions in one trial without confusing factors, treatment groups or interactions. This boundary keeps one canonical owner per intent.

For English practice across research, school and career communication, visit the English at work and in public life guide.

FREQUENTLY ASKED QUESTIONS

Questions students and parents often ask

What is a factor?

An intervention and its comparator levels considered as one randomised dimension of the design.

How many groups are in a 2×2 factorial trial?

Four treatment-group combinations when the design is full.

What is a main comparison?

The prespecified contrast used to draw a primary conclusion about a factor or interaction.

Why report interaction?

One intervention may change the effect of another, altering the meaning of marginal estimates.

Is a four-arm trial always factorial?

No. A factorial trial has a defined factor structure and related main comparisons.

Which core guideline applies now?

Use CONSORT 2025 with the factorial extension until an aligned update is published.