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The Wired has published article "The Sickeningly Low Vaccination Rates at Silicon Valley Day Cares", in which they claim ridiculously low vaccination rates in daycare centers associated with some of Silicon Valley's tech giants.

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However, Google and Cisco claim these numbers to be inaccurate, and claim to have no PBEs (personal belief exemptions).

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    The question shouldn't be "Do Silicon Valley tech workers' kids have low vaccination rates?" because some companies are great and some are poor, even not considering the suspect data. The intro point that compares "the strength of brains and imagination" with the supposed sense to get their kids vaccinated probably could not be backed; in any case not in this article since no demographics of the exemptions are discussed. The article might be OK for general consumption, but it gets a statistics D-.
    – user3169
    Feb 13, 2015 at 2:48

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TLDR: This is embarrassingly bad statistical analysis on Wired's part. Proper replacement headline options:

Child Vaccination Rates Follow Normal Distribution

or

Study Shows Silicon Valley Parenting Is Average

Now, on to dissection. A direct quote form the article:

Of 12 day care facilities affiliated with tech companies, six—that’s half—have below-average vaccination rates, according to the state’s data.

Full stop right here. Think for a moment on this question: what percentage of people have below-average intelligence?

What does average mean? Statistically, average is the typical, most representative score. In a normal distribution, approximately half the scores will be above the average while approximately half will be below.

So, how many day care facilities should we expect to have below-average vaccination rates? About half. And how many will have above-average rates? Um, about half. And what does the chart say?

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Quick, new headline:

The Amazingly High Vaccination Rates at Silicon Valley Day Cares

After all, half of all silicon valley day cares have above-average vaccination rates, right?

OK, perhaps I'm being overly harsh here about a minor...total demonstrated lack of understanding of statistics that should be part of the first four weeks of an undergraduate course in statistics. Maybe it's just a silly error.

Later they claim one terrible daycare has only a ~40% immunization rate, which is obviously a very significantly low score. Why is it that one so low?

But Google has a simple explanation—a representative chalked it up to old data. “In 2013-2014, these two childcare facilities had immunization rates of 98 percent and 81 percent,” says a Google spokesperson, emphasizing that immunization is important to the company. “The reported numbers for the current year are lower simply because many parents have not yet provided updated immunization records. We’ve asked them all to do this, so we can update the figures.”

If this claim is true, then the previous year immunization rate was extremely high and should have a headline of how great Google Parents are at vaccinating their kids. Yet the present rate has said to have fallen to half the previous year levels? That's not a statistical trend - that can only be explained by throwing out half the kids and getting a whole new set with extra-ordinarily low rates of vaccination. Is that claimed in the article?

No, and the writer of the article doesn't claim - or apparently investigate - if this perfectly reasonable sounding explanation is true or not.

Furthermore, there is another glaring error in the article - all throughout the article it cites information as being direct, these-kids-definitely-aren't-vaccinated - but that's not apparently the case! The data refers to the percentage of parents who have provided medical documentation establishing that their child has been vaccinated to their childcare facility. Big brother isn't in play here - Wired Magazine does not have access to private medical records. The report of evidence is not on child vaccination, but on paperwork.

So finally, I propose the best possible headline that this report and data as written can possible support:

Parents In Silicon Valley Don't Keep Up On Bureaucratic Paperwork That Does Not Clearly Impact the Safety Or Health of Their Children

or

Governmental Data Too Out Of Date And Incomplete To Draw Wide-Reaching, Judgmental, Damning Conclusions

Now there's an article I can get behind. I obviously have no future in journalism.

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    +1 Some nice points, however, I don't get why you'd make an assumption that it's Gaussian distribution. If it would indeed be truly random, it would be Poisson distribution. So you can't make assumption that mean == median. Also, 6 of 12 facilities they've mention are below state average, not below average of these 12 facilities. In fact if you'd assume that these facilities have similar number of kids, then if the data shown in the graph is correct, the mean average of these 12 facilities would be way below state average.
    – vartec
    Feb 14, 2015 at 1:38
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    Your argument is reasonable for 9 of the 12. It's the last three that look bad.
    – Loren Pechtel
    Feb 14, 2015 at 1:39
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    @vartec One need not assume the underlying distribution is Gaussian, but the sample taken - such as shown in the chart, which is a sample of 12 of all care centers - can be expected to be normal, by the Central Limit Theorem. Further, I assumed that the "average" was a properly computed average by the state. In statistics if the distribution is skewed, then an arithmetic mean average isn't just crappy - its absolutely inexcusably inappropriate. If the statistics reported by the government committed so base an error as using the wrong central tendency, full stop - throw it all out, it's junk.
    – BrianH
    Feb 14, 2015 at 1:56
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    @LorenPechtel That's very true - and 2 of the 12 are specifically addressed towards the end, as a different fundamental problem with the report. If you accept that the data reported was incomplete and out of date and correct the chart accordingly, suddenly Silicon Valley has 8 out of 12 mentioned child care centers as being above the State average - which means, on average Silicon Valley is more immunized than the State as a whole. The headline reversed, story ruined - and this doesn't even deal with the fact that the data is cherry picked to support the report to start with.
    – BrianH
    Feb 14, 2015 at 2:00
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    I'd like to +2 for “I obviously have no future in journalism.”
    – gerrit
    Feb 14, 2015 at 15:17

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