NEW DELHI >> More and more Indian families with one girl are aborting subsequent pregnancies when prenatal tests show another female is on the way, according to a new study published Tuesday.

The decline in the number of girls is more pronounced in richer and better educated households, according to research in the medical journal Lancet.

Those numbers show that a 1996 law that bans testing for the gender of a fetus has been largely ineffective, the study said.

In India, there is a huge cultural preference for boys in large part because of the enormous expense in marrying off girls and paying elaborate dowries. Officials have acknowledged that current laws have proved inadequate at combatting the widening sex ratio gap.

The study said that between 4 million and 12 million girls are thought have been aborted from 1980 to 2010.

Raw data from India’s census released in March showed 914 girls under age 6 for every 1,000 boys. A decade ago, many were horrified when the ratio was 927 to 1,000.

Researchers studied census data and government surveys of more than 250,000 births to conclude that gap is even wider in families that already have a girl.

The ratio was 906 girls under 6 to every 1,000 boys in 1990 and had declined further by 2005, when it was 836 to every 1,000.

That decrease was even more marked in families where the mothers were wealthier and had 10 or more years of education compared with a poor and uneducated mothers — presumably because the wealthy are more easily able to obtain illegal abortions.

But in families whose first child was a boy, there was no decrease in the girl to boy ratio for the second child, the study said.

“Reliable monitoring and reporting of sex ratios by birth order in each of India’s districts could be a reasonable part of any efforts to curb the remarkable growth of selective abortions of girls,” the authors suggested.

The study was led by Prof. Prabhat Jha of the Centre for Global Health Research, Dalla Lana School of the University of Toronto and other researchers, including the former Registrar General of India, Jayant K. Banthia.

According to the current CIA “World Factbook,” the United States has a birth ratio of 955 girls per 1,000 boys. In China, where families with a strong preference for boys sometimes resort to aborting their baby girls, there was a birth ratio of 885 girls per 1,000 boys.

The factbook puts India’s birth ratio at 893 girls to 1,000 boys.

India tracks gender ratios for children under the age of 6 but not at birth.