Err, no. All that “statistically significant” means is that if an inferential statistic is based on a random sample, the measure is unlikely to have been different from some a priori well-we’re-not-going-to-publish-this level (usually 0), based on a usually a priori probability — e.g., that the measure is non-zero and is statistically significant at a .05 level means that with the model assumptions the chances that the measure is really zero (or on the other side) is less than 5%.

There are three major problems with common social-science and behavioral-studies uses of statistical significance. One is what you describe, the confusion of statistical significance with meaning, and on that point, you should not back down (though you do back down in the quoted sentence, if not in the rest). Even if all of the model assumptions are correct, you can easily get to statistical significance simply by having a large enough sample. This is very common with census public-use microdata samples. Don’t back down: effect size, effect size, effect size!

A second major problem is when the study is not a random sample of a broader population, either because you have a complete-population calculation or when you have a convenience sample (e.g., psychologists using undergraduate students in psych classes). In that case, using statistical significance implies some hypothetical superpopulation of which the study population is some random sample. This is an interesting absurdity — if you’re looking at a study using the entire population of home foreclosures in 2008, for what hypothetical superpopulation would this be a random sample — all of the hypothetical years of home foreclosures when we had George W. Bush as president and a once-in-a-lifetime financial crisis?

The third major problem is subtler and has to do with some of the logical inconsistencies in standard inferential statistics and a priori cut-lines for what statistical significance is. Whoever said that we want to be 95% certain that the measure is different from 0? Whoever set 0 as the a priori “we don’t care anymore” measure? There are some alternatives that some philosophers suggest (Bayesian perspectives on statistics), but that’s well outside my area of expertise.

Social scientists, public health researchers, and social service organizations spend a lot of time looking for ways to help poor people, and it’s easy to get caught up in the search for a magic bullet. Is it learning self-control through play? Early childhood literacy? Grocery stores in the inner city? Vegetables in school lunch? Gang tattoo removal programs? Workforce education? Using former violent offenders to intervene and talk down bad situations? Stricter gun licensing? These are all real solutions that people bring up, and a lot of them would be useful, but none of them address the core problem: poverty sucks. And I think that’s because there’s no strong constituency for addressing poverty per se in American politics/society, so policy-makers and social service organizations can’t get too focused on poverty, per se, if they want to be successful (in getting money and power).