BackAn index that triggers a metric tonne of annoyance
Criticizing the GHI for a sample size of 3,000 is, at best, misinformed and misguided
PremiumSo you say you’re interested in the Global Hunger Index (GHI)? You know, the one that was recently released and has caused heartache in India. Heartache, not just because India is ranked 107th out of 121 countries, but also because it is ranked below the neighbours we like to think of as basket-cases —Bangladesh, Sri Lanka, Pakistan and Nepal.
How is that possible? Well, I’m interested in this GHI, too. Because it, and other such indices that sometimes make the news, reflect an Indian reality that anyone with their eyes open in this country can see. Reality that’s no less so than world-class highways or the second-wealthiest man on the planet. Given that, why the testy reaction to the GHI?
For example, there’s an 15 October Government of India press release titled “Global Hunger Report 2022 - The index is an erroneous measure of hunger and suffers from serious methodological issues" (https://bit.ly/3yVWaiB). Consider what’s in there. One part of the Index, it points out, “is based on an opinion poll conducted on a very small sample size of 3,000 ... a miniscule [sic] sample for a country of India’s size." Indeed, how can a sample of 3,000 accurately reflect a nation of 1.4 billion people?
This sounds like a pretty serious objection. Except that statisticians who carry out surveys know that it makes little sense. Why so? Sampling a population is a well-understood statistical exercise. It involves a sample size, but also a margin of error and confidence level in your results that you are comfortable with. These three numbers are, as you might imagine, related by a formula. For example, you might be comfortable with a margin of error of 4% and a confidence level of 95%—these are typical numbers for opinion polls held before elections. Suppose you conduct a poll like this and find that 60% of your sample prefers candidate B over candidate T. What it means is that if you conducted the same poll with the same sample size 20 times, in 19 of those polls (95% confidence level) you’ll find that between 56% and 64% (60% +/- 4% margin of error) of the sample prefers B over T.
If that’s confusing, the point is that you can be pretty confident of those results—because of the 95% and 4% figures. But note: I have not mentioned the sample size. For those error and confidence figures, the formula says you need a sample of about 600 people. No more. But note: I have not mentioned the size of the full population either. The truth is, that doesn’t really matter. When you have a large-enough population, increasing your sample size beyond a certain size makes—perhaps counter-intuitively—only a marginal difference to your results.
For example, suppose you are dissatisfied with the 4% margin of error and want to reduce it to 3%—better than most election-time opinion polls. That would need you to expand your sample from 600 to just 1,000 people. And what about the GHI’s sample size of 3,000? With that number, and sticking with a confidence level of 95%, the formula gives us a margin of error of 1.8%—far more accurate than most opinion polls claim.
But note again that India’s population of 1.4 billion doesn’t figure in these calculations. That number has pretty much no bearing on the accuracy of the opinion poll.
The conclusion of all this? Criticizing the GHI for a sample size of 3,000 is, at best, misinformed and misguided. The government’s statisticians should have known better.
Another objection to the GHI in the press release goes like this: starting in March 2020 - the outbreak of the pandemic - India has run “the largest food security programme in the world." This scheme gives 5kg of grain free every month to 800 million people, and “has been extended till December 2022." The idea is that “the poor, needy and the vulnerable households/beneficiaries do not suffer on account of non-availability of adequate foodgrains during the times of economic crisis."
To underline how massive this exercise is, the press release offers up a small flood of other numbers. For example, we are told the programme has distributed 112.1 million MT (metric tonnes) of foodgrain, equivalent to a ₹3.91 trillion subsidy. (Aside: Those two particular numbers suggest that a kilo of the foodgrain costs the government ₹35).
The flood of numbers continues. Through the pandemic, “supplementary nutrition" of 5.31 million tonnes of foodgrain “was provided to approximately 77.1 million children ... and 17.8 million pregnant women and lactating mothers." Break those figures down to find that about 56kg of grain was distributed to each of these people (kids, pregnant and lactating women), over the 2.5 years since the pandemic began. That’s about 2kg per person per month. Make of that what you will.
The question, however, is this: do large numbers like these show that the Global Hunger Index is flawed? That is, if India runs the world’s largest food security programme, giving nearly 60% of all Indians free food because they cannot afford it—does it necessarily follow, as the press release states, “there is absolutely no reason why the country’s undernourishment levels should increase"? That we cannot rank so low on the GHI?
No, because the two have little to do with each other. The GHI is based on specific malnourishment measures. Food handouts over 2.5 years don’t necessarily change that—or at least, we have no data that shows such change. Besides, the size of the programme, by itself, has no bearing on those measures. It is that large precisely because we have nearly the world’s largest population, and certainly the world’s largest population in need of food security.
In fact, I leave you by underlining that last thought. Yes, we have the world’s largest food security programme. But what does it say about India circa 2022 that 800 million Indians—nearly 60% of us—so poor that they need five free kg of foodgrain?
Once a computer scientist, Dilip D’Souza now lives in Mumbai and writes for his dinners. His Twitter handle is @DeathEndsFun.
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