Comparing weighted and unweighted analyses applied to data with a mix of pooled and individual observations

Smaller organisms may have too little tissue to allow assaying as individuals. To get a sufficient sample for assaying, a collection of smaller individual organisms is pooled together to produce a simple observation for modeling and analysis. When a dataset contains a mix of pooled and individual organisms, the variances of the observations are not equal. An unweighted regression method is no longer appropriate because it assumes equal precision among the observations. A weighted regression method is more appropriate and yields more precise estimates because it incorporates a weight to the pooled observations. To demonstrate the benefits of using a weighted analysis when some observations are pooled, the bias and confidence interval (CI) properties were compared using an ordinary least squares and a weighted least squares t-based confidence interval. The slope and intercept estimates were unbiased for both weighted and unweighted analyses. While CIs for the slope and intercept achieved nominal coverage, the CI lengths were smaller using a weighted analysis instead of an unweighted analysis, implying that a weighted analysis will yield greater precision.