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Today’s deep thought: Percentages vs. raw numbers

Here's the LA Times piece I quoted earlier about first responders who are out with COVID-19:

More than 1,000 police officers, firefighters and paramedics in the Los Angeles region were ill or at home quarantining on Tuesday after testing positive for the coronavirus.

....More than 500 employees of the Los Angeles Police Department — including 416 sworn officers — were at home quarantining....The Los Angeles Fire Department had 201 employees out due to the coronavirus as of Tuesday, while the Los Angeles County Sheriff’s Department had 573 employees out.

....Across the state, more than 1,230 state prison employees were infected, as were 712 incarcerated people, officials said.

I got curious about how this same report sounds if you express everything in percentages. Here it is:

A little less than 3% of all police officers, firefighters and paramedics in the Los Angeles region were ill or at home quarantining on Tuesday after testing positive for the coronavirus.

....About 3.8% of all employees of the Los Angeles Police Department — including 4.2% of sworn officers — were at home quarantining....The Los Angeles Fire Department had more than 5% of its employees out due to the coronavirus as of Tuesday, while the Los Angeles County Sheriff’s Department had about 3% out.

....Across the state, a little less than 2% of all state prison employees were infected, as were nearly 1% of all incarcerated people, officials said.

I guess regular people hate percentages? Maybe. It's just that I read stuff like this and the first thing I wonder is, "How big a number is that?" After all, very few us know off the top of our heads how many total cops and firefighters there are in Los Angeles.

Of course, if this story had used percentages in the first place, maybe I'd be griping that I wanted exact numbers, not these approximations. Maybe I'm just never satisfied.

32 thoughts on “Today’s deep thought: Percentages vs. raw numbers

  1. Jimm

    Percentages definitely the way to go, but the press has long been inconsistent about this, often including percentages and raw numbers in the same article, without any indication as to why in each case.

    But let's not forget, the press/media does not exist to calm us down, but to get our attention.

  2. iamr4man

    I would like to have seen the numbers as of mid-December for comparison.
    The elementary school where my daughter teaches currently has 5% of its students who have tested positive so far this week. It was less than 1% prior to the break. This thing is just getting started. The next couple of weeks will tell the tale as to whether this is going to amount to a staffing crisis in places like schools and Police Departments.

    1. Joseph Harbin

      School "closures" are a lightning-rod issue. But unless Omicron makes a quick about-face, I don't see how they are avoidable.

      Three days in (and with many schools not yet back from the holiday), this week already has the highest number of "disruptions" for this school year.
      https://twitter.com/BurbioCalendar/status/1478815484946563072?s=20

      We're beginning to see stories like this:
      More than 240 teachers, or nearly 20%, were absent Wednesday in the Parkway School District.
      https://twitter.com/blythebernhard/status/1478893449969553419?s=20

  3. cmayo

    Nope - once numbers/populations get large enough, it really needs to be all percentages, all the time. Maybe the raw number can be tossed in there as long as it's also with a percentage, but it's paramount that percentages are there so as not to be needlessly sensational.

    But this is the mainstream media we're talking about here. Needlessly sensational is kind of their whole thing.

  4. Dana Decker

    Do both:

    500 employees (3.8%) of the Los Angeles Police Department — including 416 (4.2%) sworn officers — were at home quarantining....The Los Angeles Fire Department had 201 (5%) employees out due to the coronavirus as of Tuesday, while the Los Angeles County Sheriff’s Department had 573 (3%) employees out.

    1. Leisureguy

      Exactly! I was going to make the same comment. There is zero reason not to use both, since both are of interest and the information each provides is different. That should be the standard.

  5. Joseph Harbin

    If the paper just quoted the percentage, it would sound wrong to me. The percentage is just a statistic. The actual number makes it easier to understand that people are affected, and I believe it's a good thing not to dehumanize the coverage of what's going on.

    Whatever they use, it would be more helpful to know the corresponding figure a month or six months ago. A number and a trend is more useful than a number alone.

    Also, if you say 3% are quarantining, my assumption is that a lot of officers et al. are infected by not quarantining. What percentage of the force has actually been tested?

  6. Salamander

    Everybody's read "How to Lie With Statistics." If you haven't, get hold of a copy; it's still in print after nearly 70 years.

    Want to make a point? Then select the statistical measure that's the most arresting. 3.8% is no big deal, but 500 officers? Now that will grab the reader. Particularly if the reporter doesn't cite the normal number of officers out for sickness, etc.

    Why do reporters do it? Clickbait.

    1. Salamander

      ... and that's also why they generally won't bother to report compensating data, like total population or percentages. Unless these are the "scary" numbers.

  7. golack

    And what is the normal % out???

    The issue is tipping points. A lot of places are understaffed to start, so a loss of 2% more (above normal outages) means things start to fray if not collapse. But it's more that one location has an outbreak, so 5 to 10% are out. And when that's at a grade school that barely has enough people to cover on good days--you either have 10% of the kids unsupervised...or go virtual. Saying only 4% of employees are out misses the clusters.

  8. D_Ohrk_E1

    Well, that depends.

    0.25% of the US population has been counted as a COVID-19 death. 827K deaths over 2 years is kind of a lot.

    0.042% of the atmosphere is CO2, but if that number went up to 0.05% -- a 56% increase over early 1960s -- it would mark the catastrophic failure of mankind to stop a runaway climate change.

  9. Rich Beckman

    This always bugs me when airlines start canceling flights. A thousand flights were canceled today!!! OK. A thousand is a lot. But how many didn't get canceled? How many get canceled on a normal day? It seems like none of the media ever gives any context.

      1. iamr4man

        Everything is dependent on how you look at it. Note that in my comment above I said I’d like to the the number of officers out with Covid during mid-December. Right now the situation is a very severe spike in cases due to Omicron.

  10. Vog46

    Let a layman chime in here
    The sheer number is correct and the % is relatively low
    But think of it this way
    For a job that runs 9 to 5 M-F that would be a whole LOT of business productivity lost.

    Police run 3 shifts 7 days per week. So some shifts are gonna be short handed, by a lot. In a high crime area that small percentage could result in some hefty problems.
    The problem is in that office it could mean say 1 house doesn't get sold or you lose 3 leads.
    In the police department it might mean an increase in response time and/or a shooting that results in death.
    One gets headlines, the other does not

    1. bgsmith

      I seldom comment, but Vog46 has the correct view in my opinion. The raw number or percentage or both have limited value without setting the context in terms of what does this mean the vital public services these organizations perform? What is the reduction in operational capability expressed in terms that all of us can relate to. Of course, that is more nuanced and not as attention grabbing. as Vog46 notes.

      Best wishes

  11. royko

    Is it really that hard to report both numbers? Shouldn't the goal of good journalism be to tell you what happened and put it in some kind of understandable context?

  12. Caramba

    I noticed that the American public has in general an issue with numbers.
    Reporters are still reporting the stock market moves in points, nowhere seen elsewhere in the world.

  13. azumbrunn

    I don't think the main question here is not percent or absolute figures. It is: How big is the difference to the good old COVID-free times? This is how we find out the extent of the problem created by COVID.

    4% of cops out sick strikes me as high, given that cops are probably healthier than average Americans. But from the reporting I wouldn't know, percentage or otherwise.

  14. mistermeyer

    That's the LA Times for you. Our local paper, the Sacramento Bee, reran a story from the LAT this morning with this headline: "Thousands in US Military still refuse to get vaccine." And sure, that's technically true, but with almost 98% vaccinated, those "thousands" represent a mere handful. (And a good chunk of the remaining unvaccinated will eventually get the jab when their phony requests for a medical waiver are denied.) I've learned to double-check anything out of the LAT.

    1. HokieAnnie

      A large percentage of the military holdouts are member who were already planning to separate/retire from the military so they are in "why bother" mode. I suspect these are folks who will show up at future Proud Boy rallies. SIGH.

  15. modaca41

    When talking percentages and our divided country, why don't we ever hear what 40% of Republicans believe this or that really means? What percentage of voters /people /whatever are Republicans these days?

    For instance: Is 40% of Rs 40% of fewer than 50%? After all, 40% of 50% is 20%, but 40% sounds much scarier than 20%. Or is it 40% of 40%?

  16. rick_jones

    A somewhat timely anecdote for percentages versus absolute numbers:

    However, she [Solicitor General Elizabeth Prelogar] said, OSHA had the authority to act in a way that would "save 6,500 lives and prevent 250,000 hospitalizations in just six months."

    https://www.cnn.com/2022/01/09/politics/asa-hutchinson-biden-vaccine-mandate-supreme-court-cnntv/index.html
    Past performance does not guarantee future results of course, but in the last six months there have been over 220,000 deaths. (estimate based on July 9, 2021 through December 30, 2021 - I've not updated my spreadsheet in the new year) So that would be less than 3%. Not an especially compelling appeal to figures.

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