We publish the translation of this interesting analysis that was reported to us by a reader. This is a work published by a university professor of statistics in the United States, hosted on Tablet Magazine. The article in question highlights how the data on deaths in Gaza, released in the first days of the conflict, were manipulated by Hamas. Through in-depth statistical analysis and the use of graphs, the author demonstrates the inconsistencies in the numbers provided by Hamas, suggesting that they do not reflect the reality of the facts. This study not only raises questions about the veracity of official figures but also opens a broader discussion on the importance of data integrity in conflict contexts.
The first place to look is the reported “total” number of deaths. The graph of the total number of deaths by date increases with an almost metronomic linearityas shown in the graph in Figure 1.
This regularity is almost certainly not real. One would expect a notable variation from day to day. In fact, the daily count of reported victims during this period averages 270 plus or minus 15%. This is a surprisingly small change. There should be days with double the average or more and others with half or less. Maybe what is happening is that the Gaza ministry is releasing false daily numbers that vary too little because they don’t have a clear understanding of how the numbers behave naturally or that the details of the daily counts make the numbers suspicious.
Similarly, we should see a change in the number of child victims that follows the change in the number of women. This is because the daily variation in death counts is caused by variation in the number of attacks on residential buildings and tunnels which should result in considerable variability in totals but less variation in the percentage of deaths between groups. This is a fundamental statistical fact about random variability. Consequently, on days with many female victims there should be a large number of child victims, and on days when only a few women are reported killed, only a few children should be reported. This relationship can be measured and quantified by the R-squared (R2) statistic which measures how correlated the daily death count for women is with the daily death count for children. If the numbers were real, we would expect R2 to be substantially larger than 0, trending closer to 1.0. But R2 is 0.017 which is statistically and essentially no different from 0.
This lack of correlation it is the second circumstantial evidence which suggests that the numbers are not real. But there’s more. The daily number of female victims should be highly correlated with the number of non-women and non-children (i.e., men) reported. This is also expected due to the nature of the battle. The coming and going of Israel’s bombings and attacks should cause the daily count to move together. But that’s not what the data shows. Not only is there no positive correlation, there is a strong negative correlationwhich makes no sense and establishes the third piece of evidence that the numbers are not real.
Consider some additional anomalies in the data.
Taken together, what does all this imply? While the evidence is not definitive, it strongly suggests that a process unconnected or weakly connected to reality was used to report the numbers. Most likely, the Hamas ministry arbitrarily decided on a daily total. We know this because the daily totals are increasing too steadily to be real. Then they allocated about 70% of the total to women and children, dividing that amount randomly from day to day. Then they filled the number of men set by the pre-established total. This explains all the observed data.
Taken together, Hamas is reporting not only that 70 percent of victims are women and children, but also that 20 percent are fighters. This is not possible unless Israel is somehow avoiding killing non-combatants, or Hamas is claiming that almost all the men in Gaza are Hamas fighters.
Are there better numbers? Some objective commentators have acknowledged that Hamas’ numbers in previous fighting with Israel were more or less accurate. However, this war has nothing to do with the previous ones in terms of scale or scope; international observers who were able to monitor previous wars are now completely absent, so the past cannot be considered a reliable guide.
The fog of war is especially thick in Gaza, making it impossible to quickly determine total civilian casualties with any precision. Not only do official Palestinian death counts fail to distinguish soldiers from children, but Hamas places the blame for all the deaths on Israel even if caused by their own randomly fired rockets, accidental explosions, deliberate assassinations or internal battles.
The truth cannot yet be known and probably never will be. The total civilian casualty count is probably greatly overestimated. Israel estimates that at least 12,000 fighters have been killed. If this number turns out to be even reasonably accurate, then the ratio of noncombatant to combatant casualties is remarkably low: at most 1.4 to 1 and perhaps even 1 to 1. By the historical standards of urban warfare, where combatants are integrated above and below in civilian population centers, this is a remarkable and successful effort to prevent unnecessary loss of life while fighting a relentless enemy that protects itself with civilians.
*Abraham Wyner is a professor of statistics and data science at the Wharton School of the University of Pennsylvania and co-director of the Wharton Sports Analytics and Business Initiative.
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