Rounding Numbers in Study Data Quietly Drains Statistical Power

Round numbers have a way of creeping into scientific data. When patients are asked how old they were at a diagnosis, how many years they smoked, or how much they drink, answers cluster suspiciously around multiples of five and ten. Researchers call this heaping, or digit preference, and a new study in BMC Medical Research Methodology has now quantified exactly how much statistical power is lost as heaping becomes coarser. The message from a large simulation study and a real stroke case-control dataset is reassuring at one end and stark at the other: moderate rounding costs almost nothing, but dichotomizing a continuous variable, the most extreme form of heaping, can slash the effective sample size to roughly seventy percent of its original value.

The study, conducted by Matthias Becher, Willi Sauerbrei and Heiko Becher, builds on earlier work in which the team had examined a different consequence of heaping: bias in regression coefficients. Using data from the NAKO, a large German cohort study, they had previously looked at the age at which hypertension was diagnosed. Although the heaping looked visually striking, only 12.6 percent of observations were actually heaped, and simulations showed the resulting bias was small unless a very large proportion of participants gave heaped answers in broad categories. What that earlier analysis deliberately left open was the question of power, the ability of a study to detect a true effect at all, and that gap is what the new paper addresses.

The motivation is not merely academic. Discussions of data protection have led to restrictions on sharing research data, and heaping is sometimes introduced deliberately. In the German National Cohort, for example, a person’s exact age is disclosed only in justified exceptional cases; as a rule, researchers receive only the ten-year age group into which a participant falls. In effect, a post-hoc heaping is imposed on the data. Similar blurring, sometimes called bucketing, is used to prevent re-identification of individuals in shared datasets. Whether such masking leaves a statistical analysis essentially intact, or quietly cripples it, is precisely what the new simulations were designed to reveal.

The methodological core of the study is a simulation of a logistic regression model, the standard tool for binary outcomes in epidemiology. The simulated covariate X was normally distributed, with different means for the two outcome groups, chosen so that including X linearly in the model is correct. Values of X were then rounded to the nearest multiple of a rounding value delta, representing complete heaping, and logistic regressions were run on the rounded data. As the extreme case, the variable was dichotomized: each observation received the expected value of X given that it fell below or above zero, a choice made so that the expected regression coefficient matched that of the original data.

The results form a clear gradient. With increasingly coarse heaping, the mean p-value grows steadily more distorted, meaning the analysis becomes less and less able to detect effects that are genuinely present. Up to rounding to the nearest multiple of five, the loss of power is mild, and it remains almost negligible up to heaping to the nearest multiple of ten. The largest reduction, as expected, occurs when the variable is dichotomized. The simulations also clarified the bias side of the ledger: a noticeable bias in the regression estimate appeared only when heaping was rather coarse, at rounding values of ten or twenty, and there was no bias under dichotomization when the conditional expected values were assigned. Notably, the p-value after dichotomization does not depend on which values are assigned, so the familiar coding of zero and one leaves it unchanged.

To translate these findings into practical terms, the authors calculated the effective sample size after heaping as a percentage of the original sample size, estimating what sample would be needed to achieve the observed post-heaping power. For moderate levels of heaping the effective sample size stays close to the actual sample size, mirroring the power results. For coarser heaping it drops noticeably, reaching around seventy percent of the original under dichotomization. In other words, collapsing a continuous risk factor into two categories can be statistically equivalent to throwing away nearly a third of the study’s participants, without any of the savings that a genuinely smaller study would bring.

The real-data illustration comes from a case-control study on stroke conducted in Heidelberg, Germany, between 1998 and 2000, which originally examined dental infections and stroke risk with 303 ischemic stroke cases and 468 controls. For this analysis, teetotallers and never-smokers were excluded, leaving 181 cases and 221 controls, with years of smoking and total alcohol consumption as quantitative risk factors and age and sex as confounders. Because the original data showed little heaping, the authors induced it artificially: smoking was rounded to multiples of two, five and ten, and alcohol to multiples of fifty, one hundred, two hundred and five hundred, with dichotomization at the median as the final step, at cutpoints of 29 years for smoking and 115.012 litres for alcohol.

The pattern in the real data largely matched the simulations, with one instructive wrinkle. On the original data, the p-values were 0.049 for alcohol and 0.041 for smoking, both just inside conventional significance thresholds. As heaping intensified, the p-values climbed gradually, reaching 0.88 for alcohol and 0.12 for smoking when both variables were dichotomized. For alcohol, the change in the regression estimate under heavy heaping was remarkable, with the effect almost disappearing under dichotomization. Yet the relationship was not strictly monotonic: while the p-value generally rose with stronger heaping, there were exceptions, likely reflecting the particular data structure, which the authors note means that in real datasets the effect of heaping can be somewhat unpredictable.

The authors are careful about scope. Their simulations model a scenario in which all data are heaped, which is directly applicable to deliberate data blurring but not to typical epidemiological studies, where only a fraction of responses are heaped and the associated power loss would be smaller. The main analysis used a binary outcome and logistic regression, though supplementary simulations based on a linear model, resembling the relationship between age and systolic blood pressure, gave results fully in line with the logistic case, supporting the authors’ assumption that the findings generalize to regression models more broadly. They also situate heaping as a special kind of measurement error, noting that correction methods developed for measurement error by the STRATOS initiative may be transferable, even though, in their experience, such adjusted analyses are rarely performed in practice.

The practical conclusions cut in two directions. Mild heaping, whether arising from participants’ rounding habits or from deliberate data masking, is statistically tolerable, causing negligible power loss, and the authors judge the NAKO policy of releasing age only in ten-year groups to be acceptable on these grounds, while noting it makes re-identification considerably harder. For statistical disclosure control more generally, the results suggest that a bucketing function that is not too broad could allow data to be published anonymously while preserving almost full analytical power. The other direction is a warning: dichotomization of continuous variables remains widespread, from biomarkers dichotomized to assess prognostic effects to subgroup analyses in randomized trials, despite decades of criticism documenting inflated type I error and lost power. Extreme heaping, whether through dichotomization or rounding so coarse that very few distinct levels remain, should be avoided, because the price is paid mainly in lost power, with noticeable bias also appearing at coarse rounding values such as ten or twenty.

Subject of Research: Quantifying the loss of statistical power caused by increasing degrees of heaping in covariables

Article Title: Loss of power by degree of heaping in covariables

Article References: Becher, M., Sauerbrei, W., & Becher, H. (2026). Loss of power by degree of heaping in covariables. BMC Medical Research Methodology, 26(1), Article 223. https://doi.org/10.1186/s12874-026-03043-4

Image Credits: AI Generated

DOI: 10.1186/s12874-026-03043-4

Keywords: heaping, digit preference, statistical power, logistic regression, dichotomization, effective sample size, data protection, simulation study, case-control study, measurement error, statistical disclosure control, epidemiology