Are the Gaza Health Ministry casualty numbers for the 2023 conflict fake?

Question

Tablet Magazine claims that the casualty numbers reported by the Gaza Health Ministry from the 26th of October to the 10th of November have suspicious statistical properties that indicate fraud.

The Claims

Specifically, they claim that the deaths per day are suspiciously consistent day to day (claim 1):

This regularity is almost surely not real. One would expect quite a bit of variation day to day. In fact, the daily reported casualty count over this period averages 270 plus or minus about 15%. This is strikingly little variation. There should be days with twice the average or more and others with half or less. Perhaps what is happening is the Gaza ministry is releasing fake daily numbers that vary too little because they do not have a clear understanding of the behavior of naturally occurring numbers.

and that we should expect a large positive correlation between deaths of women and children, and deaths of men and women, but we see a very small positive correlation between deaths of women and children, and a large negative correlation between deaths of women and men (claim 2):

Consequently, on the days with many women casualties there should be large numbers of children casualties, and on the days when just a few women are reported to have been killed, just a few children should be reported. This relationship can be measured and quantified by the R-square (R2 ) statistic that measures how correlated the daily casualty count for women is with the daily casualty count for children. If the numbers were real, we would expect R2 to be substantively larger than 0, tending closer to 1.0. But R2 is .017 which is statistically and substantively not different from 0.

The daily number of women casualties should be highly correlated with the number of non-women and non-children (i.e., men) reported. Again, this is expected because of the nature of battle. The ebbs and flows of the bombings and attacks by Israel should cause the daily count to move together. But that is not what the data show. Not only is there not a positive correlation, there is a strong negative correlation, which makes no sense at all and establishes the third piece of evidence that the numbers are not real.

They claim there are some unusual individual days (claim 3):

Consider some further anomalies in the data: First, the death count reported on Oct. 29 contradicts the numbers reported on the 28th, insofar as they imply that 26 men came back to life. This can happen because of misattribution or just reporting error. There are a few other days where the numbers of men are reported to be near 0. If these were just reporting errors, then on those days where the death count for men appears to be in error, the women’s count should be typical, at least on average. But it turns out that on the three days when the men’s count is near zero, suggesting an error, the women’s count is high. In fact, the three highest daily women casualty count occurs on those three days.

Finally, they claim that the percentage of men killed implies noncombatant men are killed at an implausibly low rate (claim 4):

There are other obvious red flags. The Gaza Health Ministry has consistently claimed that about 70% of the casualties are women or children. This total is far higher than the numbers reported in earlier conflicts with Israel. Another red flag, raised by Salo Aizenberg and written about extensively, is that if 70% of the casualties are women and children and 25% of the population is adult male, then either Israel is not successfully eliminating Hamas fighters or adult male casualty counts are extremely low. This by itself strongly suggests that the numbers are at a minimum grossly inaccurate and quite probably outright faked. Finally, on Feb. 15, Hamas admitted to losing 6,000 of its fighters, which represents more than 20% of the total number of casualties reported.

Questions

1. Are the claims about the underlying data true? (i.e., have they correctly reported the numbers).
2. Are these features unusual for casualty data reported in a warzone?
3. Are there non-fraud explanations?
4. Are there other means to test the validity of the casualty data? (The article discusses the comparison to UNRWA casualties that has been made, but argues that UNRWA staff are more likely to be killed than civilians because they're Hamas fighters.)

Answer 1

The evidence does not suggest that the casualty numbers are faked. Whether that is because of a lack of evidence or because the casualty numbers are not fake is an open question. That said, Abraham Wyner's narrative is based on shoddy use of the data and has been questioned or "debunked" by multiple authors:

• Are Hamas Death Figures Fake?
• A note on “How the Gaza Ministry of Health Fakes Casualty Numbers”
• oct7factcheck.com

As skeptics.SE does not appreciate link dump answers, here is some of my own analysis.

Claim 1 Cumulative charts are often misleading. In the figure I sampled 15 random normally distributed numbers with mean 200 and standard deviation of 100 to represent casualty statistics:

It looks random because it is random. However, here is the numbers plotted with Wyner's method:

I've only added 7200 to all numbers and plottd cumulative numbers rather than daily ones and added a regression line. This shows that the apparent consistency is illusory. Had I been able to get Seaborn to plot with bars instead of dots, I'm sure the effect would have been even more convincing.

The mean and standard devition of the data is 270 and 42.25 respectively, meaning that the relative standard deviation is 270/42.25 = 15.6%. Wyner claims that is too low:

This is strikingly little variation. There should be days with twice the average or more and others with half or less.

His assertion is questionable because the daily tallies are sums of random variables. On the dates Wyner analyzed, Israel likely bombed dozens of targets every day. While the number of people killed in a single bombing obviously varies greatly, the total number of people killed in a dozen bombings varies much less. It's analoguous to how the (relative) variation of 10 dice rolls is much larger than the variation of ten sums of ten dice rolls.

Moreover, this is the full dataset:

Red bars indicate the dates Wyner selected, 2023-10-27 to 2023-11-10 (inclusive range). And contrary to his claim, the date 2023-10-26 is not included.

Claim 2 and 3 R2 is a bit above my head, but according to the debunkers linked to, Wyner would have gotten a much larger R2 value had he analyzed the full dataset. Here is a plot of casualties divided by gender and age:

A point glossed over in Wyner's analysis is that the MOH only reports cumulative casualty statistics for females and children. Hence, I've had to infer the male deaths by subtracting the children and women from the total. Blue bars for children, red for women and green for "men" (total - children - women). The tallies for men go negative on some days, also noted by Simpson, Stone, and Rose:

Perhaps the most bizarre examples of disinformation occurred in early December, when the GMO was the leading provider of Gazan casualty statistics. Between 1 December and 8 December the recorded number of dead men declined from 4,850 to 3,499, with multiple individual declines occurring over the period (2 December, 5 December, 8 December). It was the statistical equivalent of the resurrection of over a thousand men!

Indeed, if we zoom in we see that the number of men killed on December 2, December 4, and December 9 are -87, -24, and -806 respectively:

These numbers do not imply widespread resurrection, as the critics claim, but rather that there is a lag for the gender and age series. Presumably, casualties can be updated quickly, but identifying the dead takes time. This hypothesis is consistent with the fact that there are fewer and fewer updates for children and women - as the war destroys more and more of Gaza the less resources the MOH has to update the statistics in a timely fashion. This argument is very reminiscent of that made by Covid skeptics during the height of the pandemic. As health authorities around the world updated their statistics, the tallies for some series went negative on some dates which was seen as very suspicious in some circles.

Note that Simpson, Stone, and Rose claims that the negative counts are -287, -372, and -796 and happens on December 2, December 5, and December 9. I can't find figure out what data they are using so I can't explain the discrepancy.

Claim 4 Wyner claims (if I understand him correctly) that more than 30% of the casualties should be men since most Palestinian militants are men. But this assumes that militants are killed at a higher rate than civilians, and that the number of militants is high enough to impact the casualty statistics. As airstrikes and shellings appear to have killed most Palestinians, these assumptions are questionable. Furthermore, the militants have access to non-civilian infrastructure (e.g tunnels) and intelligence. This extra protection against indiscriminate bombings may offset some of their increased risk of dying in hand-to-hand combat with Israeli soldiers.

Simpson, Stone, and Lewi make the argument that 70% of the casualties cannot be women and children since the fraction of male deaths registered at Gazan hospitals in 2023 was 40% (6088 / (6088 + 4659 + 4602)). They assume that the distribution of registered hospital deaths is similar to the distribution of casualties which may not be the case. Gaza is a patriarchial society so perhaps hospital care prioritizes wounded men, hospital statistics may also include gender-identifcation "lag", or perhaps badly mutilated corpses are identified by men as default. All of which would skew the distribution towards men. Simpson, Stone, and Lewi claim to have identified clear cases of "fraud" in the published data, but it is unclear to me what data they base this conclusion on.

Interestingly, Wyner has been embroiled in another statistical controversy. Namely the one over Mann, Bradley, and Hughes's Hockey stick graph (calling it a "controversy" is perhaps a stretch). This refers to a figure from Mann et al's 1998 paper (revised in 2008) that showed how northern hemisphere temperatures had rapidly risen since the start of the Industrial Revolution. In 2010 Wyner and his colleague McShane published A statistical analysis of multiple temperature proxies: Are reconstructions of surface temperatures over the last 1000 years reliable? alleging that the hockey stick was the result of improperly applied statistical methods which Wyner would later call "manipulative" and "misleading". This lead to a huge debate in the climatology community with some agreeing with at least some of Wyner and McShane's criticism and others claiming that it was they who had manipulated the data.

I used this dataset for the graphs: Daily Casualties