Proportion Data OLS Prevention

OLS regression applied to proportions or percentages produces predictions that can fall outside [0, 1], residuals that are heteroscedastic by construction, and standard errors that are biased. These are not edge cases —they are guaranteed consequences of applying a linear model to a bounded outcome. The appropriate alternative is logistic, beta, or Dirichlet regression, depending on the data structure.

STEP 1 —The Pitfall

Proportion data appears frequently in biology: cell viability percentages, survival fractions, disease prevalence, composition data (relative abundances in microbiome studies, flow cytometry fractions). Researchers routinely analyze these with t-tests or OLS regression, sometimes with an arcsine-square-root transformation that was recommended in older textbooks but is no longer considered best practice.

The specific harms: OLS can predict negative viability or >100% survival. Residuals are heteroscedastic —they cluster near 0 and 1 —violating OLS assumptions. The standard errors are biased, making all confidence intervals wrong. The effect sizes are on the wrong scale for scientific interpretation.

[Image placeholder: Scatter plot of a proportion outcome (y-axis: 0—) vs. a continuous predictor (x-axis). OLS regression line shown with the fitted line extending below 0 and above 1 outside the data range. Beta regression line shown staying within [0,1] with correct boundary behavior.]

OLS on proportion data (left): regression line exits the valid [0, 1] range. Beta regression (right): stays bounded and correctly models the distribution.

STEP 2 —Journal Requirement

Journals with quantitative methods reviewers consistently flag OLS on proportion outcomes as a methodological error. The standard requirement is logistic regression (for 0/1 binary outcomes), beta regression (for continuous proportions in (0, 1)), or Dirichlet regression (for compositions summing to 1). The arcsine-square-root transformation is specifically discouraged in PLOS Computational Biology and Methods in Ecology and Evolution guidelines.

STEP 3 —Licklider Solution

Input

Outcome variable type declared via Outcome Type Lock (proportion / binary / compositional / continuous)
Or: auto-detection from data range (values in [0, 1] or [0, 100] with high proportion of boundary-adjacent values)
Selected analysis method (t-test / ANOVA / OLS regression)

Output

Proportion data detection: outcome declared or detected as proportion/percentage triggers the guard
OLS block: linear regression / t-test on proportion outcome raises a Method Mismatch error
Alternatives surfaced: logistic regression (binary), beta regression (continuous proportion), Dirichlet (composition); rank-based fallbacks (Mann–Whitney / Kruskal–Wallis) as methodology references — not a verified in-app rank pipeline (see Non-Parametric Alternatives)
Arcsine-square-root transformation offered with a note that it is not the current best practice

Guard

The guard blocks OLS-based analysis when the outcome is declared or detected as a proportion. The user must either: (1) switch to an appropriate method, (2) declare that the outcome is continuous despite appearances (with explanation), or (3) proceed with an explicit override that is recorded in the analysis log and disclosure text.

[Image placeholder: Licklider guard dialog showing: "Proportion outcome detected —outcome variable ranges from 0 to 1. OLS regression assumptions are violated for bounded data. Recommended: Beta regression (continuous proportion) or Logistic regression (binary outcome). Override requires explicit declaration."]

Proportion OLS guard dialog: detected bounded outcome, blocked OLS, recommended alternatives.

STEP 4 —Draft Output (Draft / Needs review)

Cell viability (proportion, range 0.12—.98) was analyzed using
beta regression (betareg R package, logit link, maximum likelihood
estimation) to account for the bounded nature of the outcome variable.
OLS regression is not appropriate for proportion outcomes due to
guaranteed heteroscedasticity and the possibility of out-of-range predictions.