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While web surveys have become increasingly popular as a method of data collection, there is concern that estimates obtained from web surveys may not reflect the target population of interest. Web survey estimates can be calibrated to existing national surveys using a propensity score adjustment, although requirements for the size and collection timeline of the reference data set have not been investigated. We evaluate health outcomes estimates from the National Center for Health Statistics’ Research and Development web survey. In our study, the 2016 National Health Interview Survey as well as its quarterly subsets are considered as reference datasets for the web data. It is demonstrated that the calibrated health estimates overall vary little when using the quarterly or yearly data, suggesting that there is flexibility in selecting the reference dataset. This finding has many practical implications for constructing reference data, including the reduced cost and burden of a smaller sample size and a more flexible timeline.

Bias and mean squared error for linear combinations of the isotonic regression estimators are computed. The case of sampling three distinct populations and the case of sampling seven or fewer populations having common mean are studied in detail. Numerical results are given, and comparisons between isotonic and unbiased estimation procedures are made. Le biais et l'erreur quadratique moyenne des estimateurs isotoniques sont calcules. On etudie en detail le cas de trois populations distinctes, et celui de sept populations ou moins de meme moyenne. On enonce des resultats numeriques et on etablit une comparaison entre l'estimation isotonique et l'estimation sans biais.

The exact distribution of a nonparametric test statistic for ordered alternatives, the so-called $\bar{\chi}^2_{\operatorname{rank}}$ statistic, is discussed. Two tables are given.