We characterize the two-site marginals of exchangeable states of a system of quantum spins in terms of a simple positivity condition. This result is used in two applications. We first show that the distance between two-site marginals of permutation invariant states on N spins and exchangeable states is of order 1/N. The second application relates the mean ground state energy of a mean-field model of composite spins interacting through a product pair interaction with the mean ground state energies of the components.

The proportion of elderly people in general population samples is increasing. Therefore, it is becoming more important to pay special attention to older respondents when assessing the quality of data. The main hypothesis of the current article is that interviewer effects are higher in the older age-group. We use data collected in 13 countries during Round 7 of the European Social Survey. The results support the supposition that older respondents tend to need more clarification, are more prone to misunderstand the questions, and are likely to have longer interviews. In line with the expectations, we also observe that among older respondents, particularly those aged 71 and above, interviewer effects are more common than among younger respondents.

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Mixed mode data collection designs are increasingly being adopted with the hope that they may reduce selection errors in single mode survey designs. Yet possible reductions in selection errors achieved by mixing modes may be offset by a potential increase in total survey error due to extra measurement error being introduced by the additional mode(s). Few studies have investigated this empirically, however. In the present study, we compute the Mean Squared Error (MSE) for a range of estimates using data from a mode comparison experiment. We compare two mixed mode designs (a sequential web plus mail survey, and a combined concurrent and sequential CATI plus mail survey) with a single mode mail survey. The availability of auxiliary data on the sampling frame allows us to estimate several components of MSE (sampling variance, non-coverage, nonresponse and measurement bias) for a number of sociodemographic and target variables. Overall, MSEs are lowest for the single mode survey, and highest for the CATI plus mail design, though this pattern is not consistent across all estimates. Mixing modes generally reduces total bias, but the relative contribution to total survey error from different sources varies by design and by variable type.