To assess dementia, participants were asked, among other things, to recall 10 nouns immediately and after a delay, to serially subtract seven from 100, and to count backward from 20. The test was based on extensive research indicating it was a good measure of memory and thinking skills.

Participants also were asked about their education levels, income and health.

In a way, the dementia decline might seem unexpected. It occurred despite an increase in diabetes — the diabetes prevalence among older Americans surged to 21 percent in 2012 from 9 percent in 1990. It began to fall only very recently. And, the study found, diabetes increased the risk of dementia by 39 percent.

More older people today also have cardiovascular risk factors — high levels of blood pressure, blood sugar and cholesterol — which increase the risk of dementia. But more are taking medications for those conditions, so perhaps better control of those risk factors played a role in the decline.

The findings about obesity were especially puzzling. Compared with people of normal weight, overweight people and obese people had a 30 percent lower risk of dementia, the study found. Underweight people had a risk 2.5 times as great. Yet the obesity picture is muddled because other studies have found that obesity in middle age increases dementia risk in old age.

Then there is the education question. On average, older Americans in 2012 had one more year of schooling than older Americans in 2000. And years of education were associated with decreased dementia risk in this study, as in many others.

It is still not clear exactly why education would reduce the risk of dementia. There is the cognitive reserve hypothesis: that education changes developing brains in a good way, making them more resistant to dementia, and that people with more education have brains that are better able to compensate for dementia damage.

But education also is linked to more wealth. People with more education often live in environments that differ from those of people who have less schooling, and they tend to have better health over all. They also are less likely to smoke.