Assessing the representativeness of non-probability surveys: The case of public library users' survey in Florence

With the growing spread of big data, as a potential source of low-cost and timely data, there is a greater interest in whether and how it is possible to use data from non-probability samples to make inference. The main problem when the data generating mechanism is unknown and/or is presumably very different from random sampling is that estimators of population characteristics must be assumed to be biased, unless convincing evidence to the contrary is provided. Therefore, it becomes necessary to identify indicators/measures of the potential risk of non-random selection bias and to adopt predictive inference methods able to remove this bias. Users registered in the public library system of the city of Florence are a non-random subset of the resident population. Among these, the respondents to a web survey for the evaluation of the libraries’ services are the result of a further process of self-selection. The representativeness of the respondents’ data is investigated in order to evaluate the possibility to make inference on the whole Florentine population.