UPenn professor of statistics Abraham Wyner published a piece on why he entirely dismisses the death tolls reported from Gaza as fake numbers. His article has been shared widely, also appealing to his authority as a statistician. However, in the following I want to explain why I consider his arguments to be largely 1) unsubstantial and 2) probably not of good faith.
His arguments are largely based upon two observations: 1) The death toll increases very regularly during the period from October 26 to November 10 for which Hamas Government Media Office reported some more detailed data. However, Wyner does not give an argument why the variation of 15% should be too small. If the pattern of attacks was completely regular and only chance would account for the variation of daily fatalities, then the Poisson distribution would predict a variation of 6%. Why shouldn’t there be only a small variation of daily fatalities during a two weeks period of constant IDF advance without huge changes in tactics? People without knowledge of statistics trust Wyner’s authority as a statistician when he says that 15% variation would be unnatural. However, he provides no material or mathematical argument whatsoever why a higher variation would be expected. Before and after those two weeks, by the way, the variation was significantly higher. For these periods Gaza Health Ministry / Government Media Office published less comprehensive data sets, yet one wonders whether there is also some level of deliberateness involved in picking only these two weeks to object to the limited variation.
2) The numbers of killed adult males are not much higher than the numbers of killed adult females, which is generally atypical in wars and would imply that only very few Hamas/PIJ combattants or male civilians engaged in hostilities have been killed, significantly less then what is to be expected from other known IDF and Hamas estimates. Wyner takes this argument from a report published by the Washington Institute. However, the hypothesis entertained in this very report is very much at odds with Wyner’s hypothesis that Hamas would report far too many fatalities. The Washington Institute report assumes that the Gaza Health Ministry and Hamas Government Media Office in fact simply underreported the number of killed adult males. This makes a lot of sense. Armies around the world, particularly in authoritarion and semi-authoritarian regimes, want to avoid that their enemies and also their own public and supporters and fighters and often even some of their commanders get to know the true numbers of fighters killed. Particularly when the Gaza Health Ministry was reporting lists of the deceased with ID numbers to the Palestinian Health Ministry in Ramallah or even to the public, it is clear that Hamas wants to avoid Israel to get information about killed fighters and their identities. Wyner is of course free to contradict. But instead he just cites the Washington Institute report and silently reinterprets its findings without any argument and without even mentioning the hypothesis originally entertained by the Washington Institute. This is clearly intellectually disingenous.
There is a third argument 3), namely an anomalous negative correlation between male and female fatalities. Well, there is a day in the numbers where the male death toll actually decreased. So obviously some corrections or methodological modifications (which might be politically motivated, like excluding Hamas fighters from the death toll) have been made on this day (as it commonly happens in all kinds of health statistics offices around the world), two other days with nearly no added male fatalities and two other days with nearly no added female fatalities may be explained by corrections, late reporting or methodological modifications, too. Now Wyner, who obviously knows that chance cannot account for a negative number of daily deaths, includes the negative number into his data set for which he wants to test whether the negative correlation with female fatalities can be explained by chance. The so-called p-value test now tells that if male and female casualty numbers would vary independently, randomly then there is only a very tiny chance of p<0.0001 that this negative correlation will be observed. However, here we have a classic example for the proneness of the p-value test to misinterpretations of its result. Wyner tests a particular hypothesis of randomly distributed male and female fatalities to then reject it. However, we already knew from the beginning that this hypothesis is crap, since obviously negative fatality numbers are to be explained by some more specific mechanism. Then Wyner abstracts from that and tells us: hooray, the whole date set cannot be explained by chance, it must be manipulated, his alternative hypothesis (according to which Hamas fabricated the numbers entirely according to a pre-determined scheme in a top-down approach, yet they added a decrease of male fatalities for one day) must be true …
Here is my plausible explanation for the negative correlation between killed men and women: It might be that the reports of killed men had to go through an extra step of clearance, which would sometimes take an extra day. In fact this is quite compatible with the data with many days with many dead women reported followed by a next day with many dead men reported. Such a clearance process, with limited administrative capacities for counting deaths, would also contribute to the low daily variation of overall fatalities. Maybe there are arguments against this, but certainly not this p-value test.
A last argument is certainly ridiculous, namely that civilian-to-combattant-fatality ratio would be much higher according to Hamas numbers than during previous wars. Yes, exactly, this is most likely the case, because the IDF changed their operational tactics (also under pressure from the government). With the same line of argument we could say, Hamas numbers must be quite accurate, because they used to be quite accurate in previous wars (if we exclude the question of who is a combattant). However, we know that IDF tactics changed. The question is in how far Hamas fidelity of reporting changed during this war in which the stakes are much higher for both parties than in previous wars in Gaza.
By the way in a 2011 paper—instantly rebuked by several climate scientists—Abraham Wyner also claimed to have proven that renowned climate scientist Michael Mann manipulated his statistics to prove global warming following the industrial revolution. I have not looked into Wyner’s paper myself, but given the degree of dishonesty observed now maybe I do not want to. Recently Wyner has earned around $100.000 for giving “expert testimony” in defense of two right-wing climate denialists which face a lawsuit for defamation of Michael Mann.
Of course it is very clear that there are many flaws in the data by Gaza Ministry of Health and Hamas Government Media Office. Responsibilities shifted. Administrative capacities collapsed. Civilians killed by “friendly” fire like in al-Ahli hospital (by a faild PIJ rocket) are included in the death toll (very regular practice, I have rarely seen death tolls for wars making such a distinction all the time, Israeli authorities also do not make this distinction for October 7, although I have to emphasise that the conspiracy theories that most Israeli civilians were not killed by Hamas but by friendly fire are completely made up, based on manipulation and denial of what Hamas’ explicit terrorist directives). Fighters are very probably excluded from death lists. There is no distinction between combattants and non-combattants in the list (however, while estimates have been published by Israeli authorities, most of the Israeli reporting on the victims of the October 7 attack and massacre also do not make this distinction).
However, there are two major lines of argument why the death tolls published by the Gaza Ministry of Health and Hamas Government Media Office are to be considered good estimates for the numbers of civilians/non-combattants killed (after substracting a small und unknown number of combattants included in the toll and after adding an unknown number of people still buried under ruins):
1) According to an investigation by Yuval Abraham published in Mekomit IDF intelligence spied on Gaza Ministry of Health and concluded that their data gathering for the death tolls is at least sufficiently methodologically sound that it can be used for estimates of civilian fatalities caused by Israeli attacks. And in fact IDF officials used this data because their own intelligence was too busy with identifying new targets to care about post-strike evaluations of fatalities.
2) Two statistical analyses published in The Lancet confirms accuracy of Gaza Ministry of Health data by checking its strong correlation with data collected at various health facilities in a decentralised manner, data on UN staff and by satellite imagery, but also by checking the internal consistency of the decentrally collected data which would still add up to containing the majority of the ministry of health death toll. Wyner objects that UN staff would not be a representative sample because of UNRWA’s links to Hamas, however, even according to Israeli estimates the portion of Hamas/PIJ fighters within UNRWA staff is lower than within the general adult population—Hamas militants within UNRWA are still a huge problem questioning UNRWA’s impartiality as a humanitarian organisation, but the fact that some Qassam militants have day jobs in UNRWA does not provide any objection to the JHU study.
Why does all this matter? We simply should not live in denial of the scores of Palestinian civilians dying in Gaza. Considering the best estimates we have it is very likely that for every killed Hamas/PIJ combattant 2.5 Palestinian civilians and around 0.02 IDF soldiers get killed in Gaza. The ratio of civilians killed is far worse than in any of the liberation operations against cities held by Daesh like Mosul, Raqqa, Falluja, Marawi. Both IDF/Israeli government and Hamas/PIJ strategy and tactics have to be held accountable for this horrendous scale of death and suffering.