Two studies have shown promising results in using non-probability-based surveys, and using statistical methods to make them representative. Goel et al. (2015) employed an online opt-in survey of social and political attitudes. The survey utilized 14 demographic questions and 49 attitudinal questions that were drawn from the 2012 General Social Survey (GSS) and recent Pew Research Center studies. To correct for the biases in the non-representative online data, the study generates population-level and subgroup-level estimates via model-based poststratification [Gelman and Little, 1997, Wang et al., 2015]. After statistical correction, the median absolute difference between non-probability and probability surveys is 7.4 percentage points. The authors find this to be comparable to the difference between various probability surveys themselves, and hence conclude that “non-representative surveys are a promising tool for fast, cheap, and (mostly) accurate measurement of public opinion.” Wang et al. (2015) conduct a series of daily voter intention polls in the Xbox gaming platform. After adjustments using regression and poststratification, the corrected estimates are comparable to estimates from a leading poll analyst that was based on aggregating traditional polls during the election cycle. From these results, the authors argue non-representative polling shows promise not only for election forecasting, but also for measuring public opinion on a broad range of social, economic and cultural issues.

Few studies look at economic variables. Smyk et al. (2020) study Wage Indicators (WI), an online survey in 17 countries and check if they provide wage distributions that match with benchmark data in each of these countries. They use covariate balancing propensity score to reweight the data. While these weights could match demography and human capital endowment of the representative samples, they are unable to match wage distributions from WI to the representative reference samples.

Propensity score adjustment seems to work better than post-stratification in settings where they have been compared directly. Isaksson and Forsman (2003) study political polls in Sweden and find that propensity score adjustment gives more accurate estimates than poststratification weighting. Yeager et al (2011) compared Internet surveys using non-probability samples of American adults with aggregate benchmark surveys. They tested the results for demographic and some non-demographic variables. Results indicate that post-stratification of non-probability samples did not consistently improve accuracy.

<mark>Szolnoki and Hoffmann (2013) compared a representative face-to-face survey with 2,000 respondents and a telephone survey with 1,000 respondents were compared with two online surveys, one based on quota sampling (2,000) and the other on snowball sampling (3,000) using identical questions. The objective was to assess consumer data for research in the wine business. The study did not conduct any reweighting for their online survey based on quota sampling. For the online survey with snowball sampling, they did not undertake reweighting because a weighting factor greater than five is seen as very problematic (Bandilla et al. 2003). Face-to-face data delivered the best results, followed by the telephone interviews and finally the online quota survey.</mark> <mark>Some studies do not directly study web surveys, but use data collected during regular survey interviews from households with and without Internet access. This helps avoid the possibility that collecting data via the Internet as opposed to face to face or over the phone may directly affect the answer to survey questions. Dever et al (2008) compare estimates collected during telephone interviews from households with and without Internet access using data from the 2003 Michigan Behavioral Risk Factor Surveillance System in the United States. Their analysis results</mark> 9