Big Data, Plainly Spoken (aka Numbers Rule Your World)

Tip #2 for reading business trends: filter out the noise

Another month, another unemployment report, another set of peanut-gallery reports from the business press. The August numbers apparently delighted quite a few: some headlines are "U.S. Stocks Advance After Employment Report Exceeds Estimates" (Bloomberg BusinessWeek); "Fewer Jobs Lost in August; Private Hiring Beats Forecast" (CNBC); "Private Hiring Surprises with 67,000 New Jobs" (Reuters).

The key reported results are: employment drop (-54,000) lower than expected, government jobs decreased due to end of Census, private sector jobs increased (+67,000), upward revisions for both June (+46,000) and July (+77,000).

In Tip #1, I already discussed the idiocy of including once-every-10-year Census jobs in any of these numbers.

In this post, we shall hone our ability to see through the "noise".

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First notice that the revisions from the last couple of months are in the same order of magnitude (tens of thousands) as the reported changes for the current months. This is a very strong sign that the reported changes for the current month are just noise. When the revision of the August numbers comes out in September, what would the -54,000 become? It could be comfortably above zero indicating an overall gain in employment, or it could be quite a bit more negative than reported today.

Now imagine that the revisions were of a different magnitude. Let's say instead of 46K and 77K, they were 5,000 and 8,000. Then, we could believe that the August numbers would be directionally correct even after future revisions, and we would have more confidence in those numbers.

What we have done here is to use historical fluctuations to get a mental picture of how accurate these estimates are, and then use that margin of error to judge how good the current estimates are. This is a very important skill to have when looking at numbers, especially when looking for trends.

In Chapter 1, I pointed out how important it is to know the variability around average values. Here, the reports only gave us average values. But by looking back in historical revisions, we can get a good sense of how variable the numbers are, and get the information denied us.

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A more rigorous way to do this is to look up the technical note for the margin of error. The width of the confidence interval is given as 100,000 at 90% confidence. What this means is that when they report -54,000, what they actually mean is that any number between +46,000 and -154,000 is consistent with the data that was observed. So in fact, the statisticians have no idea whether employment grew or shrank in August. This is the overall employment number; for individual breakouts (like private sector jobs or mining jobs), the margin of error will be even greater, and they have even less of a handle of the trend.

Technically, this happens because the government does not have data on every business in the U.S. All of these estimates are made based on survey samples.  For example, the so-called Establishment Survey is based on 140,000 businesses and government agencies (I think, minus the nonresponders). That's a very small proportion of millions of businesses in the U.S. and therefore some error in estimation is inevitable.

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This may be the shocker: if you take the margin of error of 100,000, and notice that almost every number in the employment report is smaller than that, then essentially you can conclude that the entire report is pure noise, and you'd be right. (We say none of the changes are statistically significant.) The original design for the sample survey was not intended to read changes of this scale.

Now that you know this, and as you look around, you will find it's very very noisy out there.

Story time, says these education journalists

No sooner had I written about "story time" than the LA Times journalists on the education beat announced "Story time!"

An article published recently on using test scores to rate individual teachers has stirred the education community. It attracted Andrew Gelman's attention and there is a lively discussion on his blog, which is where I picked up the piece. (For discussion on the statistics, please go there and check out the comments.)

In reading such articles, we must look out for the moment(s) when the reporters announce story time. Much of the article is great propaganda for the statistics lobby, describing an attempt to use observational data to address a practical question, sort of a Freakonomics-style application.

We have no problems when they say things like: "There is a substantial gap at year's end between students whose teachers were in the top 10% in effectiveness and the bottom 10%. The fortunate students ranked 17 percentile points higher in English and 25 points higher in math."

Or this: "On average, Smith's students slide under his instruction, losing 14 percentile points in math during the school year relative to their peers districtwide, The Times found. Overall, he ranked among the least effective of the district's elementary school teachers."

Midway through the article (right before the section called "Study in contrasts"), we arrive at these two paragraphs (my italics):

On visits to the classrooms of more than 50 elementary school teachers in Los Angeles, Times reporters found that the most effective instructors differed widely in style and personality. Perhaps not surprisingly, they shared a tendency to be strict, maintain high standards and encourage critical thinking.

But the surest sign of a teacher's effectiveness was the engagement of his or her students — something that often was obvious from the expressions on their faces.

At the very moment they tell readers that engaging students makes teachers more effective, they announce "Story time!" With barely a fuss, they move from an evidence-based analysis of test scores to a speculation on cause--effect. Their story is no more credible than anybody else's story, unless they also provide data to support such a causal link. Visits to the classes and making observations do not substitute for factual evidence.

This type of reporting happens a lot. Just open any business section. They all start with some fact, oil prices went up, Google stock went down, etc. and then it's open mike for story time. All of the subsequent stories are not supported by any data; the original data creates an impression that the author uses data but has nothing to do with the subsequent hypotheses. So be careful!