If a Web survey allows respondents to self select into the survey, it is necessary to adjust for selection bias. In our paper we handle the statistical problem working on empirical data coming from a Web survey on graduates of an University; the task of the survey is their enrolment in the labour market.

We investigated whether it is possible to adjust for selection bias using propensity scores. The target population is represented by a statistical register maintained by the university administration: for each graduate there is an administrative record where each event in the student career - from the university enrolment to the degree or to the abandon - is registered. This register is used to estimate the propensities, in other words to find out the variables that capture the difference between the Web respondents and the general population. In the contribution a propensity based estimator of the mean and an estimator of its variance are proposed. For few study variables we have tried also to impute the response for not web respondents using the donor pool individuated by the propensity matching. In the contribution we examine the sensitivity of the results to alternative specifications of the method and of the model for the imputation, we refer to  the choice of variables for the propensity score model and the choice of matching method (number of digits in the matching, radius or nearest neighbour matching).