This may explain why those “no difference” outcomes were so prevalent in the early same-sex parenting studies:

First, the participants were aware that the purpose was to investigate same-sex parenting and may have biased their responses in order to produce the desired result.

Second, participants were recruited through networks of friends or through advocacy organizations, resulting in a sample of same-sex parents of higher socioeconomic status than is typical of parents in a same-sex relationship generally.

Third, on average, samples of fewer than 40 children of parents in a same-sex relationship virtually guaranteed findings of no statistically significant differences between groups.

In other words, researchers would sometimes recruit subjects via posts on an LGBT-friendly site, state that they were doing a study on gay parenting, and then hand select 20-40 participants. (Not exactly the unbiased scientific method that you learned about in high school.)

In any field of study, such factors have a major impact. But when you take into account the cultural/political landscape leading up to redefining marriage, it’s clear that something other than scientific inquiry played a role in the outcomes. One analysis revealed that:

studies which recruited samples of children in same-sex unions showed that 79.3 percent (range: 75–83) of comparisons were favorable to children with same-sex parents. In comparison, there were no favorable comparisons (0%, range 0–0) in studies that used random sampling. The evidence suggested strong bias resulting in false positive outcomes for parent-reported measures in recruited samples of same-sex parents.

According to the 2010 census data, there were 594,000 same-sex couple households in the United States- about 1% of all households. Of those couples, 115,000 reported having children. That’s only 0.02% of households in the US where same-sex couples are raising children. Finding a population that small at random is not only cumbersome but also takes considerable time which was in short supply in the run-up to redefine marriage.