One can distinguish between three distinct populations. The first is the target population or the set of persons for which inferences are to be made. The second is the potential covered population, which in this case includes persons having access to the Internet and who use it. The third is the realized sample, which includes persons who are exposed to the offer to participate in the survey and accept the offer. The potential covered population may not cover the target population well because of those without Internet access or because of those who have access but do not use the Internet and are hence unreachable. The realized sample may not cover the target population or the potentially covered population. Due to self-selection, the reachable respondents among the potentially covered population may be a biased sample. Thus, the realized sample of volunteers will be expected to overrepresent or underrepresent some demographic groups of the target population, making inferences based on this sample biased.<sup>9</sup>

# **<mark>2.2.Methods for Correcting Bias</mark>**

<mark>Post-stratification, raking, propensity score adjustment (PSA), and matching are popular methods to address biases in online surveys. The efficacy of these different adjustment procedures in improving the representativeness of the web surveys is still debated (Bethlehem and Stoop 2007, Vehovar et al. 1999). Nonetheless, to apply these methods, we need a probability-based reference survey (or a subsample of the survey) that represents the distribution in the true population.</mark> <mark>Poststratification indicates a process of stratification after the sample has been selected and is often appropriate when the sample is not properly balanced by the representation. After the data is obtained, typically, weights are determined for each stratum by dividing the proportion of population in that stratum (from the reference-survey) by the proportion of the sample in that stratum.</mark> <mark>The most prevalent method for weighting is iterative proportional fitting, more commonly referred to as raking. With raking, a researcher chooses a set of variables where the population distribution is known, and the procedure iteratively adjusts the weight for each case in the internet sample until the sample distribution aligns with the population for those variables. Raking is popular because it is relatively simple to implement, and it only requires knowing the marginal proportions for each variable used in weighting.</mark> Propensity score adjustment aims to correct differences caused by the varying inclinations of individuals to participate in web surveys (Duffy et al. 2005). That is, it adjusts for selection-bias due to observed covariates. More technically, a propensity score ( _psi_ ) is the conditional probability that a person will be in one condition rather than in another (e.g., ‘being in the web or the reference survey’) given a set of observed covariates used to predict the person’s condition. The web surveys are then weighted by the inverse of the propensity score, that is 1/ _psi_ (see Lee 2006, Schonlau et al. 2004, 2007). Since the propensity score refers to both the web and reference survey respondents, the propensity score weight for the reference survey is the inverse of propensity of being in the reference survey (1/(1- _psi_ )).

> 9 This general criticism is not only applicable to web surveys. In phone surveys, too, for example, coverage may be incomplete due to non-response. However, it is possible to randomly sample respondents from the potential covered population because telephone users list is usually known. This contrasts with a Web survey where there is currently no way to identify all Internet users (Valliant and Dever, 2011).

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