How Large Should the Secondary Component Be in an Embedded Mixed-Methods Design?

How Much Research Is Enough for a Component That Is Supposed to Be Secondary?

You are conducting an experimental study involving 300 students and want to embed qualitative interviews about how participants experience the intervention. Should you interview 10 students, 20, or perhaps 50? Would a smaller interview sample make the qualitative component less credible?

Now consider the reverse situation. Your primary investigation is a qualitative case study of institutional generative AI governance, but you want to administer a short questionnaire to characterize selected implementation practices. Does the questionnaire need hundreds of respondents? Could descriptive evidence from a smaller, clearly defined group be sufficient?

Researchers sometimes assume that a secondary component must be small because it receives less methodological priority. Others attempt to make the components comparable by matching sample sizes or allocating equal amounts of analysis.

Neither approach necessarily follows from the research question. The size of an embedded component should be determined by what it must establish, not by an arbitrary proportion of the primary study.

Size the Secondary Component According to Its Evidentiary Purpose

Determining the Appropriate Scope of an Embedded Component

What Does Secondary Mean in an Embedded Mixed-Methods Design?

Secondary describes the methodological role of a component within the overarching research design. It does not necessarily describe its sample size, analytical complexity, duration, or scientific value.

For example, an experimental trial may prioritize estimating the effect of an educational intervention while embedding qualitative inquiry about implementation. The qualitative component supports the primary evaluation by investigating experiences and contextual conditions that outcome measures cannot adequately capture.

Conversely, a qualitative institutional case study may embed a quantitative survey to describe how particular practices are distributed among a defined group.

Fetters, Curry, and Creswell (2013) describe embedding as a methods-level integration strategy in which one form of evidence is incorporated within a broader design.

The important distinction is the relationship between the components. A secondary component may involve substantial work while remaining subordinate to the central research purpose.

Why Is There No Universal Sample-Size Ratio?

Quantitative and qualitative components usually operate according to different sampling and inferential principles.

A quantitative trial may require a sample capable of supporting a prespecified effect estimate with acceptable precision or statistical power. Embedded qualitative interviews may instead require information-rich participants representing relevant implementation experiences.

Matching the numbers would not necessarily improve either component.

For example, interviewing 150 participants simply because a trial contains 300 students could impose substantial analytical demands without improving the qualitative answer proportionately.

Equally, interviewing only five participants because the component is secondary may provide insufficient evidence when the study must examine implementation across several institutions.

There is no established methodological rule that a secondary component must represent 5%, 10%, or any other fixed percentage of the primary sample.

What Should Determine the Size of the Secondary Component?

The starting point is the specific question the embedded component is intended to answer.

These considerations should be evaluated together. Feasibility may constrain a study, but convenience alone does not establish sample adequacy.

How Large Should an Embedded Qualitative Sample Be?

There is no universal number of interviews appropriate to every embedded qualitative component.

The necessary sample depends on the question, the qualitative methodology, the specificity of the participants, the variation being investigated, and the depth of analysis.

For example, an embedded investigation of how students experience one narrowly defined feedback activity may require a different sampling strategy from a study comparing implementation across multiple universities.

Malterud, Siersma, and Guassora (2016) propose information power as a way to consider qualitative sample adequacy. Their argument emphasizes the relationship between the study aim, sample specificity, theoretical background, quality of dialogue, and analytical strategy.

This approach does not provide a universal numerical threshold. Rather, it encourages researchers to consider how much relevant information the selected participants can contribute to the intended analysis.

Researchers should justify their sampling decisions in relation to the qualitative question rather than relying on a generic recommendation about interview counts.

Should Researchers Use Saturation to Determine Qualitative Sample Size?

Saturation is frequently invoked in qualitative sampling, but its meaning and appropriateness depend on the qualitative approach.

Hennink, Kaiser, and Marconi (2017) distinguish code saturation from meaning saturation, illustrating that identifying recurring issues and developing a nuanced understanding of those issues are not necessarily equivalent.

For an embedded implementation study, recognizing common barriers may require different evidence from understanding how those barriers operate across contrasting settings.

Researchers should not assume that the appearance of repeated codes automatically establishes sufficient interpretive depth.

Nor is saturation a universal requirement across all qualitative traditions. Some approaches use different criteria for evaluating sampling and analytical adequacy.

The researcher should explain the selected adequacy principle and demonstrate how it fits the qualitative methodology.

How Does Variation Across Sites Affect Sample Size?

When the embedded component investigates several classrooms, departments, or institutions, the sampling strategy must account for relevant contextual variation.

Suppose an experimental evaluation includes students from eight courses taught by different instructors.

Interviewing students from only one course may provide useful information about that course but may not adequately address implementation differences across the trial.

Researchers might therefore select participants across relevant course contexts, instructional arrangements, or implementation profiles.

However, including participants from every site is not automatically necessary. The decision depends on whether site-level differences are central to the supporting question.

The sample should represent the variation required for the intended analysis, rather than merely maximize geographic or institutional coverage.

Should Both Experimental Conditions Be Represented?

Not always. If the embedded qualitative question concerns experiences of a specific intervention, sampling participants who received that intervention may be sufficient.

If the question concerns differences in experiences between intervention and comparison conditions, both groups may be relevant.

However, qualitative comparisons should not automatically be interpreted as causal estimates.

Purposive selection, especially when based on post-treatment experiences or outcomes, may create groups that are not comparable in the same way as the original randomized groups.

The qualitative sample should be designed to investigate the supporting question while respecting the inferential limitations of the sampling procedure.

How Large Should an Embedded Quantitative Sample Be?

The appropriate quantitative sample depends on the statistical objective.

If the purpose is to describe a bounded group, researchers may use a census of eligible members or a sample sufficient for the intended descriptive analysis.

If the purpose is to estimate a population proportion with specified precision, the sample design and required uncertainty must be considered.

If the component involves group comparisons or statistical modeling, sample requirements depend on the anticipated effect sizes, variability, model complexity, and relevant assumptions.

Researchers should not assume that descriptive statistics are automatically reliable because they are simple to calculate.

A percentage based on a small convenience sample may accurately describe respondents while providing little basis for estimating the corresponding population proportion.

The supporting role of the quantitative component does not remove the need for appropriate statistical justification.

Can a Small Quantitative Component Be Scientifically Useful?

Yes, when its purpose and conclusions are appropriately limited.

For example, a qualitative case study of AI assessment governance may include descriptive administrative data from all departments within one institution.

The number of departments may be small, but the data could still provide relevant contextual information about the bounded case.

However, such evidence would not necessarily support statistical generalization to other universities or sophisticated modeling of institutional predictors.

The scientific contribution depends on whether the indicators are meaningful and adequately support the claims being made.

A modest descriptive component can be valuable without being treated as a miniature population survey.

Does the Secondary Component Need Its Own Sample-Size Justification?

Yes. The primary component's sampling rationale cannot automatically justify the secondary component.

For example, a randomized trial may have a sample-size calculation based on detecting a particular treatment effect. That calculation does not determine how many qualitative interviews are needed to investigate implementation experiences.

Likewise, a qualitative case study's purposive sampling rationale does not justify the precision of a supporting quantitative estimate.

Each component should be evaluated according to its own methodological purpose.

Researchers should explain how the secondary sample supports the question it addresses and how that evidence will contribute to integration.

How Does Participant Overlap Affect the Secondary Sample?

Embedded components may use identical, nested, partially overlapping, or different samples.

When individual-level integration is necessary, selecting secondary participants from the primary sample may be useful.

For example, interviews with trial participants may be linked to their intervention exposure or outcome profiles where appropriate consent and secure linkage procedures exist.

However, different participants may be more suitable when the supporting question concerns implementation staff, institutional administrators, or other stakeholders.

Sampling relationships should support the level of integration intended rather than a universal requirement for participant overlap.

Can a Secondary Component Be Too Small?

Yes. A component may be too small or insufficiently developed to support the question it claims to answer.

For example, interviews with two conveniently available students may provide illustrative accounts but may be insufficient for a claim about implementation variation across numerous courses.

Similarly, a small survey may not provide sufficiently precise estimates for subgroup comparisons.

The problem is not the numerical size alone. It is the mismatch between the evidence available and the inferential demands of the research question.

Researchers should reduce the scope of the supporting question when the available evidence cannot sustain a broader claim.

Can a Secondary Component Be Too Large?

Potentially. A component may become unnecessarily extensive relative to its supporting purpose.

For example, an experimental trial may include interviews intended only to investigate feedback acceptability. Expanding the qualitative inquiry into a multisite investigation of teachers' professional identities could create a new research purpose that is no longer primarily supportive of the experiment.

However, a large sample does not automatically make a component independent.

The relevant question is whether its scope, analytical objectives, and contribution remain connected to the primary design.

Researchers should distinguish a comprehensive supporting component from an investigation that has developed its own overarching purpose.

How Should Researchers Balance Rigor and Feasibility?

Feasibility is an important design consideration, particularly when the embedded component requires additional recruitment, transcription, data management, or statistical analysis.

However, methodological requirements should not be reduced arbitrarily to fit the available time.

A researcher may narrow the supporting question, focus on fewer relevant contexts, or select a more manageable analytical approach.

Such changes can be defensible when the resulting evidence remains sufficient for the revised purpose.

By contrast, reducing the sample while retaining claims that require broader coverage or greater precision may weaken the study.

The appropriate response to limited resources is often a more focused question rather than an inadequately supported version of the original question.

How Does Component Size Affect Integration?

The secondary component must provide enough evidence to contribute meaningfully to the integrated interpretation.

For example, a trial may estimate an average intervention effect, while qualitative interviews investigate implementation experiences across relevant contexts.

If the interviews represent only one narrow implementation setting, the researcher should avoid using those accounts to explain the entire trial.

Similarly, a supporting quantitative survey may describe selected respondents without establishing how widely their experiences occur across the primary qualitative case.

Guetterman, Fetters, and Creswell (2015) discuss joint displays as tools for integrating quantitative and qualitative results.

A joint display can make visible which findings correspond and where evidence is missing.

Integration quality depends on the appropriateness of the relationship, not on equal sample sizes.

How Should the Size of the Embedded Component Be Reported?

The methodology should identify the supporting question, sampling approach, sample size, and rationale for adequacy.

For qualitative components, researchers should explain the relevant participant variation, analytical approach, and criteria used to assess information sufficiency.

For quantitative components, they should report the sampling design and relevant considerations concerning precision, power, or descriptive scope.

Recruitment losses, nonresponse, and limitations affecting integration should be disclosed.

The report should also distinguish what the secondary component established from what the primary component established.

Researchers should not justify sample size merely by stating that the component was embedded.

Determining Interview Scope Within an Educational Intervention Trial

The proposed interview count is not derived from a fixed proportion of the trial sample. It is a provisional estimate informed by the supporting question and intended sampling variation.

If interviews reveal that implementation differs substantially between courses, the researchers may need additional contextual evidence or a narrower interpretation.

If the qualitative analysis adequately addresses the focused question, expanding the sample solely to match a percentage of trial participants would offer no necessary methodological advantage.

The defensible decision is the one that produces sufficient evidence for the supporting interpretation while preserving the trial's primary purpose.

Common Mistakes When Sizing Embedded Mixed-Methods Components

How to Determine a Defensible Secondary Component Size

Begin by specifying the supporting question and what evidence is necessary to answer it.

Then apply sampling and analytical criteria appropriate to the secondary component rather than borrowing the primary component's sample-size justification.

Document the sampling rationale and explain how the resulting evidence supports the planned integration.

The correct size is not necessarily the smallest feasible sample. It is the scope that adequately serves the supporting question without introducing unnecessary complexity.

Check Whether Your Secondary Component Is Adequately Sized

Frequently Asked Questions About Embedded Component Size

Size the Supporting Component for Its Question, Not Its Position

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