- Vocabulary at 22 months predicts educational attainment;
- Reading to kids can help vocabulary;
- Therefore, read to kids to help them in the long run.
High IQ folks tend to have lots of books in the house and tend to read to their kids 'cause they enjoy it. They have high IQ kids because of assortative mating and intelligence's heritability. Even if they never read a word to their kids, those parents' kids would probably wind up with pretty decent outcomes just from innate IQ and hearing their parents talking: higher IQ folks have a vocabulary range maybe twice or three times the average. And I know I've seen studies suggesting that, if you control for number of books in the house, the amount of reading a parent does with his kid doesn't have much effect on the kid's outcomes.
So then vocabulary at 22 months may predict educational attainment because they've gotten a taste for reading from their parents, because they've inherited good genes from their parents, or a combination of both. Simply looking at differences in mean educational attainment by differences in mean vocabulary at 22 months doesn't tell you much at all about the effect of reading on educational attainment.
Similarly, sorting kids by income and vocabulary scores tells you little about the effect of income on kids' ability if IQ predicts income and if IQ is heritable. The report linked above contains this graph:
Income may well be doing some of the work here, but ignoring IQ seems a bit odd. Especially since the Millennium Cohort Study included measures of parental educational achievement, as seen in the study of the effects of prenatal maternal drinking that was also based on MCS data. Sounds like there's fodder there for a future honours research project.