At university, I remember a tutor using the following example of a statistic:
90% of patients who took this medication fully recovered.
The tutor pointed out that this statistic has zero meaning without additional information, such as:
- What percentage of people who did not take the medication fully recovered?
- What happened to the 10% that did not fully recover (for example did they die unexpected horrible deaths?)
Yated Neman has a column by By Rabbi Moshe Boylan which is a wonderful example of how to cherry-pick quotes and to quote meaningless statistics. Rabbi Slifikin of Rational Judaism has some good examples of how the column selectively quotes the Emek Davar and the Netziv to mis-represent their opinions, and if you look at the comments on Rational Judaism you'll see some great examples of how Rabbi Boylan mis-represented the Status-Quo agreement on which he basis a lot of the column.
But one of the best mis-uses of statistics is this gem:
In a recent article, Yonason Rosenblum quoted Rabbi Melamed, a religious leader in the Dati Leumi community, as saying that 25% of the Dati Leumi people who enter the Israeli army ultimately become chilonim.I have no idea whether the quote is accurate or the statistic is realistic (it is also hearsay - I heard someone say that someone else said that he heard that...) , but even if it is true that "25% of the Dati Leumi people who enter the Israeli army ultimately become chilonim", this tells me NOTHING AT ALL about the Israeli army.
For the statistic to become meaningful, we would need additional information such as:
- What percent of Dati Leumi people who do not enter the army become chilonim? (For example what percentage of Modern Orthodox youth in the US become less observant at the age of 18-25).
- What percentage of Chredim become non-observant, either with or without army service?
- Of the 75% of Dati leumi solders who do not "ultimately become chiloni", what percentage have their religious observance strengthened by their army service?
- What percentage of non-religious soldiers become observant as a result of their exposure to Mitzvot like Kashrut and Shabbat in the army (not to mention their interaction with religious solders)?
- What does "ultimately become chilonim" mean? If a man in his 30s gives up religion 15 years after leaving the army, is this connected to his army service?
- In what framework do the soldiers who become less observant serve? Are they with religious units such as Hesder or Nachal HaCharedi, are there differnet statistics for those units?
- How observant were these 25% of soldiers before they went into the army? The term "Dati leumi" encompasses a large spectrum of religious observance - from Charedi Leumi (such as Merkaz) through to people who are nominally religious, but are lax in the observance of many halachot. There are also many teenagers from religious families who become less observant well before they are drafted into the army, although it may be more visible when they are in the army as this is often the first time that they are outside their parent's house and are free to express themselves.
There may be good reasons for Cheredim not to serve in the army, unfortunately putting a series of mis-quotes and meaningless statistics together as Rabbi Boylan does in Yated has done does not strengthen their argument, it just gives the Chredi camp the appearance of having no legitimate sources for their argument and makes rational discussion that much more difficult.