A provocative article was forwarded to me by a close family friend, concerning 10 New Jersey residents claiming that between them, 1,000 Gazan family members have been killed since October. “Are so many possible?” my Jewish friend asked, and I too was curious. So first to be clear my heart breaks considering people being butchered en masse based on religious affiliation, or caught up the ongoing collateral cross-fire. No one wants to see tragedy; it’s a blemish on all of our human developments. The statistics here are simply to understand and better answer questions for those interested.
And concerning said statistics, 1,000 is of course a large number of family; it comes to an average of 100 family per each New Jersey resident cited in the article, assuming those residents are all strangers. But even 100 family is large. Or is it not? How do we tell?
One thing to bear in mind is that families are very different across the globe. A typical Middle Eastern family with shorter life expectancies, and a burgeoning youth, looks different than say a typical American family with longer life expectancies, but fewer replacement population in successive generations.
Also what is the definition of “family”? It is different than the census definition of household of course, but from my point of view I would consider in-laws as well as cousins within the criteria. One could enlarge or constrict the definition [eg what do you do about multiple marriages, adoptions, etc.], and part of it may be culturally defined, but a comparable definition needs to drawn so one can assess ideas on family size.
In the US, we can consider the typical family size of 3 but this is a close dichotomy. Some households are without children at all. Others may see 2-3 children. In most circles I associate with the families are four, with two parents and two children. Each person generally has a sibling. Each person is generally married to the same size family, on average. And with the definition provided above we get intergenerational family sizes of about 24.
But in Gaza [as it is in other parts of the Middle East] global health officials have a higher family size estimate of 5, and perhaps a lesser dichotomy. Many more children, and average number of siblings. And with the definition provided above we get intergenerational family sizes of about 39.
What does that mean still, concerning the article’s average of "100 family dead" statistic? Not much so far, since we have to add some conditional probability to the data. How disperse can this data be? The news article is pointing to a select sample of NJ residents. And they in turn may neither be representative of the typical Gazan family, or the typical family clusters who have suffered higher mortality odds at the hands of the Israeli army.
There is a distribution around family sizes, just as there are around generational longevity. Remember when Elizabeth Warren claimed to be of Native American descent, but we later discovered it was possible through an extremely small chance of dominant genetic transfer in each of 6 generations? Same thing in this case, where we can determine the likelihood of the news article happening upon a larger cluster of New Jersey residents with unlucky Gazan roots. Something that would match what we might predict back from the nearly 20,000 Gazans killed in 2023 thusfar.
Something too that would match the spread of Gazans who have left the Middle East and have taken up roots in New Jersey. And it turns out that it would be very plausible to have found 10 NJ residents who collectively saw about 600 Gazan family killed. And 600 is on the high side of plausibility, all willing to talk from New Jersey. And of course we can round up to 1,000 to create media attention, but we are also almost doubling in order to round up.
We can’t simply believe we would generally get 1,000 by chance, given the overall civilian death statistics we currently know [or believe]. That would basically be a 4 sigma event, or 3 sigma at best if we assume the civilian death toll might also be off.
new week,
— Salil (@salilstatistics) November 18, 2023
same 300,000 lie pic.twitter.com/FYMNP9XlrK
But really, we are considering a less than 1% chance and for my sake this is simply the context in which I consider such a chance to unlikely be reasonable. All murders are regrettable, the true statistics aside. Though it’s not the first time I have seen exaggerated numbers [others have been in the war’s rally crowd estimates]. And generally one ultimate red flag of this are simply big round numbers, based on small anecdotes, which this 1,000 “statistic” clearly was.
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