Sizeweighted

Sizeweighted, or size-weighted, is a method of weighting data in statistical analysis in which each observation, estimate, or subgroup is weighted in proportion to its size, such as the number of observations in the subgroup or the population count it represents. This approach contrasts with equal weighting, where every unit receives the same weight regardless of size. The size-weighted mean, for example, computes a pooled estimate as the sum over groups of (n_i × x_i) divided by the sum of n_i, where n_i is the size and x_i the group estimate.

Calculation and interpretation typically involve applying weights proportional to size to combine estimates. For proportions, p_hat equals the sum of (n_i × p_i) divided by the total sample size. For rates or means, the same principle applies, yielding a summary that reflects the contribution of each group according to its size. Size weighting is common when groups differ in sample size or population relevance, ensuring that larger groups have proportionally greater influence on the overall estimate.

Applications span several fields. In meta-analysis and systematic reviews, size-weighted averages are used to aggregate subgroup results when sample sizes vary. In survey statistics, district- or region-level estimates can be combined to produce national figures. In ecology or economics, size-weighted summaries of measurements across sites or regions help produce representative indicators.

Advantages include a more representative aggregate when larger groups better reflect the population; limitations arise when group size correlates with bias, data quality, or measurement error. Care is needed to assess whether size weighting is appropriate for the specific context. Related concepts include weighted means and inverse-variance weighting.