To translate sample size and statistical power accurately, a translator has to preserve the study design hidden behind the numbers. “A sample of 400” is not simply a count that can be copied into another language and forgotten. The number may have been chosen to achieve a target margin of error, detect a specified effect size, limit Type I error, reduce Type II error, allow subgroup analysis, compensate for attrition or satisfy a regulatory or operational requirement. A translation that changes those relationships can make a carefully designed study appear weaker, stronger or different from the one that was actually planned.
This guide explains how to translate sample size, statistical power, alpha, beta, Type I error, Type II error, detectable difference and power analysis in research reports, academic papers, technical documentation, educational material and study protocols. The central search intent is practical: how do you translate statistical design language without turning “not enough evidence” into “no effect,” “80% power” into “80% confidence,” or “5% significance level” into “5% probability that the result is wrong”? The answer is to preserve what each quantity controls and the conditions under which it has meaning.
A reliable translation first separates design inputs from study results. Sample size, target power, significance level and assumed effect size usually belong to the design stage. Observed estimates, confidence intervals and p-values belong to the analysis stage. They interact, but they are not interchangeable. The translator should record the design question, planned comparison, assumptions and decision rule before rebuilding the prose. This keeps the target text faithful even when sentence order changes or a language prefers a different way of expressing probability and uncertainty.
A fifty-second orientation
Statistical power is the probability that a specified analysis rejects a null hypothesis when a particular alternative is true. It is commonly written as 1 − β, where β is the probability of a Type II error under that specified alternative. A Type I error occurs when a true null hypothesis is rejected under the test framework, with its probability controlled by α. NIST guidance on hypothesis testing and sample-size determination emphasises that required sample size depends on choices such as α, β, variability and the size of the difference the study is designed to detect.
Those quantities describe a decision system, not a guarantee about one completed study. A design with 80% power does not mean that 80% of the data are correct, that the conclusion is 80% true, or that the study has an 80% chance of being replicated. Likewise, α = 0.05 does not mean there is a 5% probability that the null hypothesis is true after observing the data. Translation becomes accurate when these roles remain distinct.
1. Start with the research question, not the sample-size number
A sample size only makes sense relative to what the study is trying to estimate or compare. A survey estimating a proportion, an experiment comparing two means, a diagnostic study estimating sensitivity, and a survival study comparing time-to-event outcomes can all have “n = 300,” yet the design logic behind those 300 observations may be completely different. Translators should therefore avoid presenting sample size as a universal measure of quality.
Before translating a study-design paragraph, write the question in plain language. Is the study trying to estimate a population value within a given precision? Detect a minimum difference between groups? Demonstrate that a process stays within a tolerance? Compare a rate? Test a non-inferiority margin? The wording in the target language should preserve that purpose because the purpose determines what “enough participants” means.
A strong working note might read: “Two-group comparison; detect a specified difference; two-sided test; α stated; target power stated; expected variability stated.” That note is more useful than copying the final n. If a later sentence says “the study required 120 participants,” the translator now knows what required means. It is a design result under assumptions, not a universal scientific threshold.
2. “Sample size” can refer to planned, enrolled, analysed or effective observations
Research documents often contain several sample-size numbers. The planned sample size may be 500. The enrolled sample may be 472. The number with complete data may be 455. The primary analysis may use 448 observations after applying pre-specified exclusions. A weighted survey may then report an effective sample size that differs again. These values cannot be collapsed into one generic “sample size” without changing the audit trail.
Translate the qualifiers with the number: target sample size, recruited sample, final analytic sample, per-protocol population, intention-to-treat population, evaluable sample, complete-case sample or effective sample size. If the source uses a project-specific label, preserve its definition rather than replacing it with a familiar statistical term that has a narrower meaning.
This distinction matters because readers may compare the achieved sample with the planned design. If a target translation silently turns “448 participants were analysed” into “the sample size was 448,” it may imply that the original design itself called for 448. The digits match, but the study history has been rewritten.
3. Planned sample size is conditional on assumptions
A sample-size calculation is usually a conditional statement. It says, in effect: given this model, this outcome, this variability, this effect worth detecting, this significance level, this target power and this allocation, a particular number of observations is required. Change one assumption and the number may change.
Do not translate such a result as if the sample number existed independently of the assumptions. Words such as assuming, based on, under, with, allowing for and designed to detect are mathematically important. Removing them can make a calculation sound like a fixed rule issued by an authority rather than the consequence of a design choice.
A useful review question is: “Could another valid study of the same topic require a different sample size?” If yes, the target wording should not imply universality. This is common. Different outcomes, effect thresholds, expected event rates, missingness assumptions or analysis methods can all produce different sample-size requirements.
4. Type I error is not simply “being wrong”
In a hypothesis-testing framework, a Type I error refers to rejecting a null hypothesis when that null hypothesis is true under the model and decision rule. It is often summarised as a false positive, but that phrase can become misleading when translated into domains where “positive” has a separate clinical or operational meaning.
Translate the statistical role, not only the everyday metaphor. If the source says “the Type I error rate was controlled at 5%,” the target should preserve the testing context and the probability level. Do not rewrite it as “the study allowed 5% wrong answers.” That sentence sounds intuitive but gives the reader the wrong denominator and the wrong event.
Likewise, do not present α as the observed proportion of errors in a completed experiment. It is usually a feature of the decision procedure specified in advance. A target phrase such as “significance level α = 0.05” is often clearer than an informal paraphrase when the audience can handle the notation.
5. Type II error is conditional on a specified alternative
A Type II error occurs when the procedure does not reject the null hypothesis even though the relevant alternative is true. But β is not one universal number for every possible alternative. It depends on the particular effect or departure the power calculation considers, along with sample size, variability, decision threshold and model.
This means that “the Type II error rate is 20%” is incomplete unless the design context makes clear which alternative and analysis it refers to. A translation should preserve phrases such as “for a difference of at least five units” or “at the assumed event rate.” Removing the specification can make β sound like a permanent property of the study.
Do not translate failure to reject the null as proof that the null is true. A low-powered study can fail to detect an effect that matters. Even a well-powered study is designed around particular effects and assumptions. “No statistically significant difference was detected” is not automatically equivalent to “the groups are the same.”
6. Statistical power is detection probability under a design model
Suppose a fictional design has 80% power to detect a particular difference at a specified α. Under the design assumptions and if that alternative is true, the planned procedure has an 80% probability of producing a result that crosses the rejection threshold. This is a long sentence, but each clause protects meaning.
A shorter target can still be accurate: “The study was designed for 80% power to detect the specified difference.” What should be avoided is “The study was 80% accurate” or “There was an 80% chance the hypothesis was correct.” Those sentences answer different probability questions.
Power can also be described for a range of possible effect sizes rather than one threshold. If a graph shows a power curve, translate the axes and legend carefully. The curve is not necessarily showing the probability that an effect exists. It shows the operating behaviour of the test under assumed true effects.
7. “80% power” is not “80% confidence”
Power and confidence belong to different ideas. Power concerns the probability that a testing procedure will detect a specified alternative under repeated use. A confidence level belongs to an interval-estimation procedure. They may both be expressed as percentages, which makes mistranslation easy when a target language uses similar words for confidence, certainty, reliability or assurance.
If a source says “90% power and a 95% confidence interval,” preserve both numbers with their labels. Do not harmonise them because they appear inconsistent. There is no requirement for those percentages to be equal. They often reflect different design and reporting choices.
A glossary should therefore define power and confidence interval separately. A bilingual equivalent alone may not be enough. Include a concept note such as “probability of detecting the specified alternative under the planned test” for power and “interval procedure with stated repeated-sampling coverage” for a frequentist confidence interval.
8. Effect size is the signal the design is trying to detect
Power depends strongly on the effect size used in the calculation. A large difference is generally easier to detect than a small one under comparable noise and design conditions. Therefore a study powered to detect a large difference may have much less power for a smaller difference.
The phrase “effect size” can refer to a raw difference, a standardised difference, a ratio, a correlation, a risk difference or another parameter. Translate the actual measure rather than treating effect size as one universal scale. If the source says “standardised mean difference of 0.4,” do not shorten it to “40% effect.”
Also preserve whether the chosen effect is expected, clinically important, practically important, minimally detectable or simply used as a planning scenario. Those labels describe why the number was chosen. Replacing one with another can overstate what the researchers knew before the study.
9. Minimum detectable effect is a design threshold, not a guaranteed observed effect
The minimum detectable effect is often the effect magnitude associated with a specified power under a given design. It does not mean every real effect smaller than that value is absent, and it does not mean the observed estimate will equal or exceed the threshold.
Translate “designed to detect a 5-point difference” differently from “observed a 5-point difference.” The first belongs to planning; the second describes results. A single missing verb can collapse the distinction. This is especially dangerous in abstracts where design and results appear in adjacent sentences.
A useful check is to label every number in the manuscript as assumed, planned, observed or derived. When a target sentence moves the number earlier for stylistic reasons, retain that status explicitly. The number should not change epistemic category because the grammar changed.
10. Variability and noise change how much data are needed
For many designs, greater variability makes a fixed effect harder to distinguish from noise. That can increase the sample size needed for a given power. The source may describe variability using standard deviation, variance, event rates or other model-specific parameters.
Do not translate “assumed standard deviation” as “observed standard deviation” when the number came from prior data or planning assumptions. A planned value is input to the sample-size calculation. The completed study may later report a different observed variability.
This distinction becomes important when a protocol amendment changes the sample size after a blinded reassessment or updated nuisance parameter. Translate the reason and method carefully. The larger n may reflect revised variability assumptions rather than a change in the effect researchers hope to detect.
11. One-sided and two-sided tests are not typographic variants
A one-sided test and a two-sided test use different rejection regions and can produce different sample-size requirements under otherwise similar assumptions. The source’s choice should not be removed because the target audience finds “two-sided” technical.
If the study is designed to detect departures in either direction, preserve “two-sided.” If the hypothesis test is intentionally directional, preserve the stated one-sided design and its justification where present. Do not infer sidedness from the observed direction of the result after the study.
A common translation error is to turn “two-sided α = 0.05” into “5% on each side.” Depending on the statistical procedure, that wording may misrepresent how the source defines the overall level. Keep the original formal description unless the explanatory adaptation is mathematically verified.
12. Allocation ratio changes the meaning of “per group”
A two-group study does not always allocate equal numbers to each group. A 2:1 allocation might plan twice as many observations in one arm as in the other. If the source says “180 participants total with 120 assigned to A and 60 to B,” a translation must not turn that into “90 per group.”
Translate total sample size, per-group sample size and allocation ratio as separate quantities. The word total is especially important. “A sample size of 100 per group” means 200 observations across two groups, while “a total sample size of 100” does not.
If group sizes differ because of expected attrition, unequal costs, ethical considerations or design efficiency, preserve the explanation only when the source provides it. Do not invent a rationale from the numbers. The translator’s job is to keep the allocation structure visible, not explain why the designers chose it unless the text already does so.
13. Attrition inflation is not extra statistical power by itself
Many studies increase the recruitment target to allow for dropouts, missing data or non-evaluable observations. Suppose a calculation requires 200 analysable participants and the protocol plans to recruit 250 to allow for attrition. The power calculation may still be based on 200 analysable participants.
A translation should preserve this chain: required analysable sample, expected loss, recruitment target. Do not write “250 participants were required for power” if 250 includes a contingency margin. That wording implies the power calculation itself demanded 250 complete observations.
Likewise, “allowing for 20% attrition” can be calculated in more than one way depending on whether the percentage is applied to the target or expressed as the expected retained fraction. Translate the source’s stated method or final numbers rather than recreating the calculation from memory.
14. Clustered data can reduce effective information
When observations are grouped into schools, clinics, households, classes or other clusters, members of the same cluster may be correlated. A sample of 1,000 clustered observations can therefore contain less independent information than 1,000 independent observations under a simple model.
The source may describe a design effect, intracluster correlation coefficient or inflation factor. Preserve those terms and the level at which randomisation or sampling occurs. “Twenty schools with fifty students each” is not equivalent to “one thousand independently sampled students” for every analysis.
Do not translate “clusters” as merely “groups” if the target word suggests an informal classification rather than a statistical sampling unit. A glossary note can explain that clusters are units within which observations may be correlated. This protects the sample-size logic behind the design.
15. Repeated measures create another information structure
A study with one hundred participants measured at five time points does not automatically have a sample size of five hundred independent participants. The observations are repeated within the same people. The analysis and power calculation may exploit that structure, but the count of measurements and the count of independent participants remain different.
Translate participants, visits, observations and measurements separately. “500 observations from 100 participants” is often more informative than a generic “sample of 500.” If the source uses n for people and a larger count for records, preserve the distinction in tables and captions.
The same principle applies to paired designs. The relevant variability may concern within-pair differences rather than separate group variances. Do not rewrite a paired study as an independent-group comparison because the final table happens to show two columns of values.
16. Missing data can change the analysed sample without changing recruitment history
A source may say 300 participants were recruited but only 275 contributed to a particular model because some variables were missing. Another analysis may use 289. Translating every result as if it came from “the 300 participants” can hide the changing denominator.
Preserve the analytic n beside the result where the source does so. If the manuscript explains complete-case analysis, imputation or another missing-data method, translate the method rather than assuming that missing values were simply discarded.
Do not infer loss of statistical power solely from the visible drop in n. The effect depends on the design, missingness pattern and analysis. A translation can say that the analytic sample was smaller; it should not add a causal explanation or quantitative power claim that the source did not make.
17. Post hoc power is not the same as planned power
Planned power is calculated before observing the study outcome using design assumptions. Some reports also present a post hoc or observed power calculation after the study. These are not the same operation, and the latter can be controversial or uninformative depending on how it is used.
If the source explicitly reports observed power, preserve the label rather than shortening it to power. Do not rewrite a retrospective calculation as if it had determined the original sample size. Chronology matters.
A stronger target sentence can often retain the distinction with one adjective: “planned power was 90%,” “post hoc power was reported as…”. The translator does not need to adjudicate the methodological debate unless the article itself discusses it. The job is to keep the design stage and result stage separate.
18. “Underpowered” is a technical criticism, not a synonym for “small”
A small study can be adequately powered for a large effect under a simple outcome, while a much larger study may still have limited power for a rare event, tiny effect or demanding subgroup comparison. Therefore “small sample” and “underpowered” are not interchangeable descriptions.
If an author says a study was underpowered for a secondary endpoint, preserve that scope. Do not generalise it to “the study was underpowered” if the primary endpoint had adequate design power. Conversely, do not soften a stated limitation into “the sample was modest” when the source is making a specific claim about detection probability.
Translate the object after for: underpowered for what effect, outcome, subgroup or interaction? The preposition carries the limitation. A reader needs to know which inference the design may not support.
19. Equivalence and non-inferiority designs have different decision goals
Some studies are not designed to detect any difference from zero. Non-inferiority studies ask whether a new option is not unacceptably worse than a comparator by more than a specified margin. Equivalence studies ask whether differences fall within a pre-specified range.
Translate the margin and the direction carefully. “Non-inferiority margin of five units” is not a minimum detectable difference in the ordinary superiority sense. If the sign convention matters, preserve which direction represents worse performance.
Do not rewrite “failed to demonstrate non-inferiority” as “proved inferior.” The failed decision can arise from uncertainty as well as a truly unacceptable difference. The logic of the hypothesis framework must survive the translation.
20. Multiple comparisons can change the error-control strategy
A study testing many endpoints or hypotheses may adjust significance thresholds or use another multiplicity-control strategy. Sample size can be affected because a stricter decision threshold can reduce power for a fixed n.
Translate family-wise error rate, false discovery rate, adjusted alpha and multiplicity according to the source. Do not assume that every p-value threshold is 0.05. If a table marks several levels of significance, preserve the legend that defines them.
Also preserve whether an adjustment was pre-specified or exploratory. A target text should not imply confirmatory error control when the source calls the analysis exploratory. This is another example of statistical vocabulary carrying design status as well as arithmetic meaning.
21. Worked translation case: a two-group power calculation
Consider this fictional source: “The primary comparison required 128 evaluable participants, 64 per group, to provide 80% power at a two-sided α of 0.05 to detect an eight-point difference, assuming a standard deviation of 16 points. The recruitment target was increased to 150 to allow for incomplete follow-up.”
The translation record should contain at least six labelled items: evaluable sample 128; allocation 64 and 64; target power 80%; two-sided α 0.05; detectable difference eight points; assumed standard deviation 16; recruitment target 150 because of incomplete follow-up. None should be collapsed into “150 subjects were required for 80% power.”
A flawed target might say: “A sample of 150 provided 80% confidence that an eight-percent difference would be found.” This changes power into confidence, points into percent, and the recruitment target into the analysable sample. It also turns “designed to detect” into a promise that the difference would be found.
A repaired translation keeps the design status of every number. It may reorder the clauses for readability, but “assuming,” “to detect,” “power,” “two-sided α,” and “allow for incomplete follow-up” must still control the correct quantities. This is the kind of long sentence where a structured working note is more reliable than translating left to right.
22. Worked translation case: failure to reject is not evidence of equality
Use another fictional source: “The exploratory subgroup contained 32 participants and was not powered to detect moderate differences. No statistically significant group difference was observed. The confidence interval remained compatible with both a small benefit and a small harm.”
A mistranslation might say: “The 32-participant subgroup proved that the groups were equivalent.” That removes the explicit power limitation, converts non-significance into equivalence and ignores the interval. The target is more decisive than the source.
The repaired version should preserve exploratory, not powered, not statistically significant, and the range of effects compatible with the interval. These phrases work together. If one is dropped, readers can overinterpret the negative result.
This example also shows why statistical translation benefits from links across concepts. The power article, confidence-interval article and p-value article describe different parts of the same inference system. A translation should connect them rather than forcing one metric to carry the whole conclusion.
23. Worked translation case: clustered recruitment
Imagine a fictional education study: “Thirty schools will be recruited, with approximately 20 students per school. The calculation assumes an intracluster correlation of 0.04 and allows for ten percent student-level attrition. The design targets 90% power for the primary comparison.”
The nominal count is about 600 students before attrition, but the design also depends on the number of schools and the assumed within-school correlation. A translation that reports only “n = 600” loses the cluster structure that motivated the calculation.
Preserve approximately because the number per school may vary. Preserve school as the cluster level. Preserve the assumed intracluster correlation as an input, not an observed result. Preserve the attrition allowance as a recruitment assumption rather than an actual loss already observed.
If the source later reports 28 recruited schools, do not silently modify the earlier protocol paragraph. The planned and achieved designs are different historical facts. A translated document should make the timeline visible rather than retroactively making the plan match reality.
24. Practice clinic with explained answers
Practice one: power versus confidence. The source says “80% power with 95% confidence intervals.” Preserve both. Do not standardise them to one percentage. The first describes detection behaviour under a specified alternative; the second describes an interval procedure.
Practice two: planned versus enrolled. The protocol planned 240 participants and 226 enrolled. Translate both numbers with their statuses. “Sample size was 226” may be appropriate in a results sentence, but it should not replace the planning statement.
Practice three: evaluable versus recruited. A design requires 100 complete observations and recruits 120 to allow for loss. The power requirement applies to the analysable target unless the source states otherwise. Do not write that 120 complete observations were required for power.
Practice four: Type I error. α = 0.05 does not mean five percent of study conclusions are known to be wrong. Translate it as the pre-specified significance level or Type I error probability within the stated test framework.
Practice five: Type II error. β = 0.20 corresponds to 80% power for the specified alternative. Do not translate β as the probability that the null hypothesis is true when the result is non-significant.
Practice six: minimum detectable effect. A study designed to detect a difference of ten units can still observe an estimate of six units. The design threshold is not a rule forbidding smaller estimates. Preserve designed to detect rather than will detect.
Practice seven: allocation. A total n of 150 with 2:1 allocation gives 100 and 50 when exact divisibility and the stated ratio apply. Do not translate it as 75 per group. The ratio is part of the sample-size meaning.
Practice eight: repeated measures. Fifty participants measured four times produce 200 measurements, not 200 independent participants. Translate the unit of observation explicitly where the source distinguishes them.
Practice nine: underpowered subgroup. If the source says the secondary subgroup was underpowered, preserve the limitation for that subgroup. Do not generalise it automatically to the primary analysis.
Practice ten: non-inferiority. “Failed to show non-inferiority” does not automatically mean “proved inferior.” Preserve the decision framework and uncertainty rather than replacing it with a more dramatic conclusion.
Practice eleven: one-sided versus two-sided. A two-sided α of 0.05 should not be translated as 5% on each side unless the source explicitly defines that allocation. Preserve the formal wording when unsure.
Practice twelve: variability. If a sample-size calculation assumes a standard deviation of 12 but the completed study observes 15, translate both as assumption and result. Do not overwrite the planning number retroactively.
25. Frequently asked translation questions
Does a larger sample always mean a better study? No. Sample size affects precision and power, but design quality also depends on sampling, measurement, bias control, analysis and whether the data answer the intended question. Translate claims about adequacy according to the source rather than equating bigger with better.
Is 80% power a universal minimum? No universal rule applies to every study. Many fields commonly use targets such as 80% or 90%, but the appropriate target depends on context, consequences, conventions and design. Preserve the study’s stated rationale.
Can I translate “accept the null” as “the null is true”? Not safely. Modern statistical reporting often prefers “fail to reject” because non-rejection does not establish truth. Follow the source’s framework and preserve any technical distinction it makes.
Should I recompute every sample-size calculation? Independent checks are useful when the inputs are clear, but the translator should not silently replace the source calculation with a new one. Statistical software, design details and correction factors may not be visible in the prose. Query discrepancies rather than guessing.
What should I do if the study says “powered at 0.8”? Preserve the numerical meaning and consider rendering it as 80% power if that matches the project’s style and the source clearly treats 0.8 as a probability. Do not change the probability scale in one place while leaving related tables on another scale without explanation.
What is the strongest final review question? Ask whether the target lets a technically informed reader reconstruct the same planned comparison, error rates, detectable effect, assumptions and sample counts as the source. If yes, the design meaning has probably survived.
26. A practical release checklist for sample-size translation
- Identify the primary research question and analysis before translating n.
- Distinguish planned, enrolled, evaluable and analysed samples.
- Preserve total sample size versus per-group sample size.
- Keep allocation ratio attached to the correct groups.
- Preserve α, β, target power and whether the test is one-sided or two-sided.
- Keep the assumed effect size and variability labelled as assumptions.
- Distinguish minimum detectable effect from observed effect.
- Preserve attrition or nonresponse inflation separately from the analysable requirement.
- Keep clustering, repeated measures and paired structures visible.
- Do not convert non-significance into proof of no effect.
- Do not convert failure of non-inferiority into proof of inferiority.
- Keep exploratory and confirmatory analyses distinct.
This checklist is intentionally relationship-focused. Numbers can be copied perfectly while the design becomes wrong. Translation quality depends on preserving what each number controls and which assumptions connect it to the research question.
27. Continue through the established eduKate translation architecture
This specialist article belongs beneath the broader Master Art of Translation architecture rather than replacing it. For neighbouring statistical concepts, continue with Confidence Intervals, Standard Errors and Margin of Error, P-Values, Statistical Significance and Effect Sizes, and Standard Deviation, Variance, Z-Scores and Coefficient of Variation.
The Vocabulary Learning Hub supports the lexical distinctions behind technical terms such as power, confidence, effect, error, detection and equivalence, while How English Works supports the grammar of condition, comparison, modality and evidence status. Together, those owners help readers understand why a statistically accurate translation depends on more than copying notation.
The final principle is simple: sample-size language is a design map. Preserve the question, the assumptions, the error trade-offs, the detectable effect and the count of observations at each stage. Then write the target prose naturally. The words may change, but the study the reader imagines should remain the same study.