Research resources are most useful when they make reasoning visible. F1RMA Scholar therefore combines explanations, worked examples, proper tables and visual research aids so that a researcher can see not only what to do, but why a particular decision is defensible.
SAMPLE SIZE & STATISTICAL PLANNING
Choose the formula that matches the research design.
There is no single universal sample-size formula. The appropriate calculation depends on what the study is trying to estimate or compare, the type of outcome, the population structure, the expected effect and the planned analysis. F1RMA Scholar therefore separates calculators by research design rather than applying one survey equation to every study.
Research objective
Recommended calculator
Methodological basis
Main inputs
Estimate a population proportion
Population proportion / Cochran
Cochran-style proportion estimation
Confidence, precision, expected proportion, population size
Calculate precision from an existing sample
Margin of error
Normal approximation for a proportion
Confidence, sample size, proportion, population size
Use a simplified finite-population rule
Yamane
Simplified finite-population formula
Population size, precision
Finite population with explicit confidence and proportion
For a known finite population, adjust the initial result using:
n = n₀ / [1 + (n₀−1)/N]
n required sampleN population sizeZ critical valuep expected population proportione desired margin of error
When the expected proportion is unknown, 50% is commonly used because it produces the largest variance and therefore a conservative sample requirement under this formula. A non-response allowance should be applied to the recruitment target, not confused with the minimum completed sample.
F1RMA RESEARCH CALCULATOR
Calculate the sample size for your research design.
The result is a planning aid. It does not replace methodological judgement, study-specific power analysis, ethics requirements or specialist statistical advice for complex designs.
STEP 2
↓
Enter your study values
Complete the fields on the left, then press Calculate sample size to generate the required sample and explanation.
COMING NEXT
Linear Regression Power
Plan around expected effect size, number of predictors, alpha and statistical power.
COMING NEXT
Logistic Regression
Plan binary-outcome models using event rate, predictor count and model complexity.
COMING NEXT
Case-Control & Cohort
Study-specific epidemiological calculators based on expected risks, odds ratios and allocation ratios.
COMING NEXT
Survival Analysis
Plan around anticipated events, hazard ratios, alpha and power for time-to-event studies.
01 · LITERATURE REVIEW MATRIX
Compare studies instead of reading them in isolation.
A literature review matrix turns disconnected reading notes into a comparative evidence structure. Its value lies in what becomes visible across studies: repeated findings, contradictions, contextual differences, methodological concentration and unresolved questions. This supports synthesis because the researcher is no longer asking only, “What did this paper find?” but also, “How does this paper relate to the rest of the evidence?”
Study
Context
Design
Sample
Main finding
Limitation
Relevance
Study A
Urban SMEs
Cross-sectional survey
320
Perceived usefulness predicted adoption.
Urban sample only.
Establishes usefulness as a candidate predictor.
Study B
Rural enterprises
Interviews
28
Connectivity and agent access constrained use.
Small qualitative sample.
Identifies infrastructural mechanisms.
Study C
Urban + rural
Longitudinal
410
Initial adoption did not always lead to continued use.
One-country study.
Suggests adoption and sustained use should be separated.
Read vertically and the table gives three summaries. Read horizontally and a more interesting pattern emerges: the studies differ in context, design and whether they examine initial or continued use. That is where a defensible research gap begins to emerge. PRISMA 2020 similarly emphasises transparent identification and selection of evidence because synthesis is only as credible as the evidence base from which it is built (Page et al., 2021).
02 · OBJECTIVE-TO-DATA ALIGNMENT
Every research objective should have a visible route to evidence.
An alignment matrix tests whether the study can actually answer its own objectives. The principle is simple: each objective should connect logically to a construct or variable, a source of evidence, a measurement approach and an analysis.
Research objective
Construct / variable
Evidence required
Instrument / source
Analysis
Expected output
Determine students' level of satisfaction with online learning.
Satisfaction
Individual ratings
5-point Likert questionnaire
Frequencies, median/mean, dispersion
Satisfaction profile
Examine whether internet access is related to platform use.
Internet access + usage
Access indicators and use frequency
Questionnaire + system records
Correlation/regression as appropriate
Strength and direction of association
Explore reasons students disengage.
Student experience
Detailed explanations
Semi-structured interviews
Thematic analysis
Themes explaining disengagement
03 · SAMPLING BIAS VISUAL
A large sample can still misrepresent the population.
Consider an illustrative university survey where digitally active students are more likely to respond to an online voluntary questionnaire. The achieved sample can be large while still underrepresenting students with poor digital access.
Population versus achieved sampleIllustrative percentages
PopulationAchieved sample
30%
55%
45%
35%
25%
10%
The problem is not the number of responses; it is the selection mechanism. If low-access students are systematically less likely to enter the sample, the final dataset may overstate the accessibility or usefulness of the digital service being studied.
04 · SAMPLE SIZE
A calculator can estimate a number; it cannot design the study.
Sample-size calculations depend on assumptions such as confidence level, margin of error, expected proportion, design effect, statistical power and anticipated non-response. Researchers should therefore report not only the final number but the assumptions that produced it.
Assumption
Illustrative value
Why it matters
Population
5,000
Defines the finite population from which participants may be selected.
Confidence level
95%
Defines the confidence procedure used for interval estimation.
Margin of error
5%
Sets the desired precision under the specified assumptions.
Expected proportion
50%
Often used as a conservative assumption when prevalence is unknown.
Non-response allowance
+15%
Increases the recruitment target where not everyone is expected to respond.
Why sample size eventually levels offConceptual illustration, not a calculator output
05 · QUESTIONNAIRE PLANNING MATRIX
Map objectives to constructs before writing questions.
Questionnaire design should begin with measurement logic rather than a list of interesting questions. The researcher first identifies the objective, defines the construct, selects an indicator and only then writes the item.
Construct
Indicator
Proposed item
Response format
Planned use
Internet access
Reliability
My internet connection is reliable enough for online learning.
1–5 Likert
Composite access measure
Internet access
Affordability
The cost of internet limits my participation in online learning.
1–5 Likert
Barrier analysis
Ease of use
Navigation
I find the learning platform easy to navigate.
1–5 Likert
Usability score
The CDC's questionnaire evaluation work stresses that respondents may interpret wording differently from what researchers intend. Cognitive interviewing can therefore be used to examine how respondents understand a question, retrieve information and decide on an answer (CDC, n.d.).
06 · RESEARCH TIMELINE
A useful timeline shows dependencies, not just dates.
Research stages do not all run independently. Ethics approval may need to be completed before a pilot, the pilot before full data collection, and data cleaning before analysis. A timeline should therefore show the sequence and overlap of activities.
Show how interpretation develops from the raw data.
A theme should capture patterned meaning rather than merely rename a topic. A structured worksheet makes the analytic trail visible.
Raw participant statement
Initial code
Category
Theme
Interpretation
“Sometimes I wait two weeks before my supervisor responds.”
Delayed responses
Communication delays
Fragmented supervisory support
Support is inconsistent across time.
“One meeting tells me to change it, the next tells me to change it back.”
Conflicting feedback
Inconsistent guidance
Fragmented supervisory support
Students experience unstable academic direction.
“I don't know when I am allowed to contact my supervisor.”
Unclear expectations
Access uncertainty
Fragmented supervisory support
Supervisory boundaries are poorly communicated.
08 · STATISTICAL SIGNIFICANCE
A smaller p-value does not mean a stronger relationship.
Consider two illustrative studies. Both are statistically significant, but the size of the observed relationships is very different.
Study
Sample size
Correlation
p-value
Interpretation
Study A
120
r = .42
.003
Moderate relationship; statistically significant.
Study B
4,000
r = .08
<.001
Very small relationship; statistically significant.
Effect-size comparisonIllustrative correlations
The correct interpretation considers effect size, confidence intervals, design, measurement quality and substantive importance. Statistical significance is only one part of the evidential argument.
SPSS, R, Stata or Excel will calculate statistics from incorrectly coded data without knowing that the values are conceptually wrong. Software accuracy is therefore not the same as research accuracy.
10 · SUPERVISOR FEEDBACK TRACKER
Track corrections as research decisions, not scattered comments.
Supervisor comment
Location
Action required
Status
Evidence of change
Problem is too broad.
Chapter 1, p. 7
Narrow population and context.
Done
Problem paragraph rewritten.
Explain theory choice.
Chapter 2, p. 31
Add comparative justification.
In progress
Two competing theories reviewed.
Sampling frame unclear.
Chapter 3, p. 48
Define accessible population and frame.
Pending
—
The final column matters because “Done” is not evidence. The researcher should be able to identify what changed and where the correction was addressed.
11 · DISSERTATION PROGRESS AUDIT
Measure research readiness, not just word count.
A dissertation can contain thousands of words and still be methodologically incomplete. Progress should therefore reflect the readiness of each research component rather than document length alone.
Illustrative research readiness profileExample only
12 · RESEARCH DECISION LOG
Create an audit trail for important methodological changes.
Research often changes during implementation. A decision log records why an item was removed, why a sample changed, why a variable was recoded or why an analytical procedure was revised. This improves transparency and later makes the methodology and limitations sections easier to write. The National Academies of Sciences, Engineering, and Medicine (2019) emphasise the importance of transparent methodological and analytical decisions for credible and reproducible research.
Decision
Reason
Evidence / source
Date
Exclude participants under 18.
Ethics and study scope.
Approved protocol.
08 Sep 2026
Add interview question on transport cost.
Issue emerged during pilot.
Pilot notes.
16 Sep 2026
Use Spearman correlation.
Distribution and scale characteristics did not support the originally planned Pearson analysis.
Diagnostic results.
01 Oct 2026
RESOURCE COLLECTIONS
Use the right resource for the stage of your research.
Plan the StudyResearch Question CheckerProblem Statement BuilderObjective Alignment MatrixResearch Timeline PlannerResearch Decision Log
Review the EvidenceLiterature Review MatrixSearch LogSource Appraisal ChecklistResearch Gap WorksheetReference Verification Checklist
Page, M. J., McKenzie, J. E., Bossuyt, P. M., et al. (2021). The PRISMA 2020 statement: An updated guideline for reporting systematic reviews. BMJ, 372, n71. https://doi.org/10.1136/bmj.n71
Centers for Disease Control and Prevention. (n.d.). Collaborating Center for Questionnaire Design and Evaluation Research. CDC CCQDER
National Academies of Sciences, Engineering, and Medicine. (2019). Reproducibility and replicability in science. National Academies Press. https://doi.org/10.17226/25303
