Bill Gates should hire a statistical advisor
Another view of the Indian states

A skewed view of ten Indian states

Economist_indiasexratio The Economist published this chart to illustrate the problem of the "missing girls" in Indian society.

The girls-to-boys ratio (ages 0-6) should be about 952 but in India, it is 914. That's an average number for 35 territories, and the most skewed ratio was 830 in Punjab.

Curiously, the Economist chose to focus on only 11 states instead of showing all 35. The first 10 of these had sex ratio below the natural number of 952 while the last one was over the average. Nowhere on the chart or in the article is it explained whether the unmentioned 24 states all had above-average sex ratios: unlikely, unless certain states have much higher youth population than others.

In fact, the reference line of 952 is misplaced. Readers will find that there are two metrics depending on which survey one is looking at, either sex ratio at birth or sex ratio for children aged 0-6. The natural ratio of 952 is for the 0-6 measure but the data by territory are all for the at-birth measure. Instead, the dotted red line needs to be at 904, which is the national average sex ratio at birth for India for the 2006-8 period.


The lethal error in this chart is not starting the horizontal axis at zero. 
Redo_indiangirls1 By cutting off the same amount from each bar, this chart messes up the ratio of lengths, and presents a misleading picture of the relative sex ratio between territories.  We may think Punjab's sex ratio is half that of Gujarat (in the original chart) but as the chart on the right shows, that is far from the truth!


The other unfortunate practice, typical of the Economist, is to stick a second set of data on the right of the chart as an afterthought. In fact, that data representing the change in the sex ratio over time is more interesting than what the exact sex ratio was in each territory in 2006-8.

A much better way to present the data, without favoring one series or another, is the Bumps chart, as shown below. We can clearly see that the improvement in sex ratio is concentrated on those states that started out the decade in a worse shape.




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My main concern is that there are no confidence intervals. They are actually fairly small so everything is very significant but you don't know that from graph.

The correct reference line is the natural birth rate for the population, not the average for India. The message that they want to send is that most states are different from the natural rate not different from each other. One question is does this vary across ethnic groups ? In which case it is unknown.


Shouldn't the Bumps chart start at 0 as well, if that's your critique on the bar chart?


Yeah I'm curious to learn your justification for not starting the bumps chart at 0.


> the dotted red line needs to be at 904, which is the national average sex ratio at birth for India for the 2006-8 period.

The dotted red line is supposed to show the global average, not the Indian average. The whole point of the article is that the Indian average is not the same as the global ("natural") average.

Alberto Cairo

The bump chart doesn't need to start at 0 (although it is certainly better if it does...). Regardless of the baseline, the relative proportions between the slope of the lines don't change in the bumps chart (same can be said about time-series charts). In the case of a bar chart, the proportions between the length of the bars DO change if you don't set 0 as your baseline. I think that's the point the article is trying to make.


Alberto: thanks for your explanation.

Bob and Ken: to make this clear, the Economist line is the ENTIRE WORLD's sex ratio for CHILDREN 0-6 YR OLD while the individual bars give the INDIAN STATE's sex ratio AT BIRTH. Regardless of whether one chooses to compare the Indian States to the whole of India or the entire world, one must use sex ratio at birth rather than for children 0-6. Those two measures are not the same.

Moreover, there is something going on between the reference line and how the designer selected 11 out of 35 states. I can't imagine that there are only 10 states that have ratios below world normal when the overall Indian average is well below world normal... that's why I made the assumption that the designer probably picked the 11 states based on the overall Indian average, not the world average. But here I'm only guessing at her intention.


@Kaiser regarding Bob and Ken's point: I realize Wikipedia may not be the best source for this information, but they quote an average at birth ratio of between 103 to 107 boys for 100 girls, which translates to 930 to 970 girl births per 1000 boys, essentially the same as the Economist. So it appears that, worldwide, the 0-6 year old ratio and the ratio at birth are not very different. This makes sense as the shorter life expectancy of males probably doesn't come into effect until much older than 6 years of age.

And as Bob and Ken say, the whole point of this article is to point out that sex-selective abortion is causing the ratio to be distorted, so suggesting a comparison to the average within India seems to miss the point.


Mary: I confused you as I reversed the at-birth and the 0-6 year in my orginal comment, which I have now fixed.

Let me clarify once again: the issue is comparing apples and oranges. The state-level data is the sex ratio at birth while the world aggregate number is the sex ratio for children between 0-6 years old.

You have to read the accompanying article to see that the 952 natural rate is not an at-birth number as the chart implies but it is the 0-6 number.

Paragraph 1: "Nature provides that slightly more boys are born than girls: the normal sex ratio for children aged 0-6 is about 952 girls per 1,000 boys. Since 1981, the ratio has steadily fallen below that point: there were 945 girls per 1,000 boys in the 1991 census, 927 in 2001 and now 914."

Paragraph 2: "it is significant the sex ratio at birth is improving, not worsening. In 2003-05 the figure was 880 girls born per 1,000 boys. In 2004-06, that had risen to 892 and in 2006-08, to 904."

The clincher: "go to the sample surveys that India carries out more often. These show a different pattern. The figures are not strictly comparable, because sample surveys show the sex ratio at birth, whereas the census gives it among infants up to the age of six."


They should have used a comparative at birth measure but they are right to use an international one as that is the comparision.

Bar charts not starting at 0 are not a great idea but as we're showing a difference from a stable average it's not the worst crime, surely?

Chris Pudney

I think this report might contain the original data (and better charts than the Economist's).

Egg Syntax

I'm with Ken et al. The 904 figure that you suggest using ("the national average sex ratio at birth for India for the 2006-8 period") is different from the global at-birth ratio; that's part of the point. I agree that they should use an at-birth ratio, but it's the global at-birth ratio that's the relevant benchmark (somewhere between 930 and 970 if Mary's source is correct).


Thank you for this article and interesting data of the situation in India. These numbers are really high for such poor country.

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