A solution to minimum sample size for regressions.

Area of Science:

• Biostatistics
• Reproducible Research
• Statistical Modeling

Background:

• Regressions and meta-regressions are vital for estimating patterns and effect sizes across disciplines.
• Low sample sizes (N) in biological and medical studies raise concerns about research reproducibility.
• Determining the minimum N for reliable regression model selection is crucial.

Purpose of the Study:

• To identify the minimum sample size (N) required to accurately discern data patterns using regression models.
• To compare the effectiveness of information theoretic model selection versus R-squared for determining minimum N.
• To provide evidence-based recommendations for sample size in regression and meta-regression studies.

Main Methods:

• Generated synthetic datasets (null, simple linear, quadratic) with varying variances and effect sizes.
• Employed information theoretic model selection, specifically Akaike Information Criterion weights (AICc wi), to evaluate minimum N.
• Assessed the utility of coefficient of determination (R2) and adjusted R2 for model selection and minimum N determination.

Main Results:

• Data patterns were clearly identified at N ≥ 8, even with very low variance, though false positives/negatives occurred below this.
• Accurate statistical inference required N ≥ 25 in conditions with high data variance.
• Akaike Information Criterion weights (AICc wi) effectively distinguished between models (e.g., linear vs. null), while R2 and adjusted R2 proved inadequate.

Conclusions:

• A minimum N of 8 is informative for low-variance data, but N ≥ 25 is necessary for high-variance data in regression.
• Information theory indices (e.g., AIC) are superior to R2 or adjusted R2 for comparing alternative regression models.
• Insufficient sample size and reliance on R2 for model selection contribute to poor reproducibility; recommend N ≥ 25 for regression/meta-regression.