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Tag: media

Statistics on The West Wing

The United States decennial census features heavily in the sixth episode of The West Wing (S1E6, "Mr. Willis of Ohio"). In particular, the topic of sampling versus a door-to-door headcount is discussed at length. The episode is 45 minutes long, and would probably be appropriate for high school students and beyond. (Not to say that spending an entire class period on this one episode is the best use of time, but there is certainly value to knowing this episode exists even if it is just for interested students' knowledge.)

While sampling-versus-census is a central focus of the episode, there are other subplots. Some of the subplots may be uncomfortable for some viewers, particularly in the later part of the episode. You should watch the episode before recommending or assigning it and know your audience.

The episode is available for streaming on both Netflix and Amazon Prime.

Cast of The West Wing, © NBC
Cast of The West Wing, © NBC
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Prudential's "Stickers" Commercial

I spotted a dot plot while watching TV the other day:

It isn't too frequently that one sees a dot plot on TV, so this is a good opportunity to discuss something students might have encountered. Using this commercial might be a worthwhile topic of discussion in a statistics lesson.

The apparently constructed the dot plot by asking 400 people "How old is the oldest person you've known?" A few more details can be gleaned from the Prudential website and a "behind the scenes" video that was shot.

A few things that can be discussed with students come to mind:

  • What can we actually conclude from the dot plot?
  • The description of the YouTube video describes this as an "experiment" (as does the narrator in the behind the scenes video). Is this really an experiment?
  • What do we know about the sample?
  • What happens as we get older in terms of the oldest person "[we]'ve known"? (Children and adults with a wide range of ages are asked to place a sticker.)

There's a 30 second version of the advertisement, too.

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Statistics in the news (use and abuse)

In early October 2012, the media started running stories about how eating many servings of fruits and vegetables is linked with happiness. The study in question was an observational study of the eating habits of 80,000 Britons and did find that, controlling for other socio-economic variables, high levels of happiness were associated with eating 7-8 servings (2.8oz) of fruits and vegetables per day (Blanchflower, Oswald, & Stewart-Brown, 2012). The study made it clear (in both the abstract and text) that because of its observational nature causality could not be determined:

  • "Reverse causality and problems of confounding remain possible."
  • "This implies that, as in some other parts of the well-being literature, we cannot draw firm inferences about causality."
  • "... with caveats about the lack here of clinching causal evidence..."
  • "... it is sensible to emphasize, first, the need for extreme caution in the interpretation of this study’s findings..."

The authors repeatedly made appropriate statements about the interpretability of the study  and the potential for future controlled studies to determine causality — exactly what one should do. The importance of this work is not diminished because of its observational nature, and serves to fill a gap in the well-being literature and suggest areas for future research.

But then the media happened.

Of course, some sources got the story right:

References

  • Blanchflower, David G., Oswald, Andrew J., and Stewart-Brown, Sarah (2012). Is Psychological Well-Being Linked to the Consumption of Fruit and Vegetables? Social Indicators Research(in press).
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Hurricane Sandy and the gambler's fallacy

There are presently no shortage of articles being written about Hurricane (now Post-Tropical Cyclone) Sandy and what role climate change has played in the formation of the "Frankenstorm" that has left over 7.5 million people without power. I came across one article, however, that should be addressed: Hurricane Sandy: The Worst-Case Scenario For New York City Is Unimaginable (by Mike Tidwell, at ThinkProgress.org).

Much of the article is a traditional "worst-case scenario" description found commonly in the media for seemingly all combinations of disasters and major cities. Of note, however, is the following paragraph (emphasis added):

Another major storm struck in 1892, then another in 1938 when the borderline Category 4 “Long Island Express” passed through the outskirts of greater New York, inflicting widespread death and destruction across New York state, New Jersey and much of New England. But that storm, 68 years ago, was the last major hurricane (Category 3 or above) to strike the New York Metropolitan region. It’s now a matter of when, not if, a big hurricane will strike again, according to meteorologists. And history says “when” is very soon.

The bolded statement is a classic example of the gambler's fallacy. It seems as if hurricanes can be reasonably modeled by a Poisson process, a useful probability model (e.g. this website, this paper (pdf), and this paper (pdf)), and this assumption will be used throughout this post.

One of the important properties associated with this model is called memorylessness. Essentially, what this means is that at any given time period, the probability of an event occurring does not depend on the history up to that point. That is, it doesn't matter how long a system has been running, a 'success' is just as likely to occur at this time period if this is the first time period, if this is the 10th time period, or if this is the 76th time period.

For example, when playing roulette, the probability of spinning a 'black' are the same on every spin, irrespective of how many times you have previously spun the wheel. Even if there have been 999 'red' in a row, we are not 'due' for a black spin (assuming the wheel is fair, etc.).

Just because New York City hasn't had a major hurricane for a while does not mean that it is due or overdue for one. Each hurricane season is a new cycle and does not remember the previous years' hurricanes.

I am not an expert in the fields of research associated with most disasters, but this makes sense in terms of hurricanes (both from various sources and my life as a Floridian). For other disasters (e.g. volcanoes and earthquakes), my understanding is that pressure builds over time and therefore reasonable models for those systems should not have the memorylessness property, so perhaps talking about 'overdue' for a major disaster is warranted. Maybe not, but I do want to emphasize that this is specific to hurricanes.

(It might also be worth checking out these comics related to the gambler's fallacy.)

Satellite image of Hurricane Sandy (25 October 2012)
Satellite image of Hurricane Sandy (25 October 2012)
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Poorly displayed poll results

I've begun searching for news articles that either use statistics incorrectly (misunderstanding what a study means, making bogus claims, etc.), present data exceptionally poorly (misleading graphs), or other offenses against numeracy. I wasn't expecting to find much on Day 1. I was wrong.

The Alligator (UF's 'unofficial' school newspaper) has a daily online poll. Monday's question was "Have you eaten pizza this month?" with the results displayed as percentages and a bar chart. For example:

Online poll results from The Alligator on 24 September 2012.

A few problems:

  1. The responses are given numerically only as a percentage with no indication of sample size (either by category or total responses). We are left to guess the sample size from the bar chart.
  2. The bar chart doesn't show 0 and goes so far as to not display the observations from the "no" respondents! Based on the percentages and guessing that "yes" had 61 respondents (it is hard to tell), it seems like "no" should have 11 which is certainly not what the graph appears to show.
  3. It isn't visible in the above chart, but on different pages of The Alligator the poll results showed slightly different numbers  (85%/15% (picture) and 84%/16% (picture)). I could click back and forth between the pages and the numbers didn't change.
Overall, the online poll (powered by amCharts.com apparently) that The Alligator hosts does a woefully inadequate job of displaying the results.
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