Statistical resolutions

Can you believe the time for New Year’s resolutions has come again? Maybe this year you can add to the traditional “I’ll eat healthily”, “I’ll stop smoking” and “I’ll hit the gym regularly” a new one: “I’ll look at statistics carefully”. You can start with these five simple tips. 

  • Reported averages might be meaningless 
So who is average?

An arithmetic mean (sum of all values divided by the number of values), often reported as the average, in fact doesn’t say much about the average value.  

Imagine you’re describing humans to extraterrestrial visitors. How many legs does an average person have? Slightly less than two. It’s because unfortunately some people have lost one or two legs, while nobody has more than two. Probably the information that a vast majority of people walk on two legs would be more useful for our alien friend. 

What even is an average person?  In 2017 British women had on average 1.9 children. How many women with 1.9 do you know personally? Exactly. Average people don’t exist. 

  • Huge numbers often just sound alarming 
Plenty of money? It depends what we need it for.

In 2018/19 the health spending in England should reach about £122 billion. Too much, isn’t it! However, if we divide this enormous number by the population of about 56 million, it turns out that the cost per person equals approximately £2200; a much more manageable value. 

Also, remember that journalists love to report extremes. Headlines such as “Bitcoin could soar as high as $64,000 next year” stimulate imagination, but the phrase could […] as high as is the key. Could, but probably won’t; as we read further, $64,000 is just the end of the predicted range, while the most likely value of $36,000 is almost twice smaller.  

  • Effects in the data can result from regression to the mean 

Thanks to the regression to the mean our world doesn’t resemble Gulliver’s Travels Among the Lilliputians and the Giants. Children of very tall people tend to be shorter than their parents, while short parents usually can expect their child to outgrow them. Extremes are called that way for a reason: usually the next time we take the measurement it gets closer to the average. 

Every weekend in the winter season millions of Poles follow closely men’s ski jumping tournaments. The score of each competitor is influenced by his two jumps. Usually after the first excellent jump the second one is mediocre, and vice versa. We like to explain it with psychology, claiming that the initial success put the poor guy under too much pressure, or the failure relaxed him. However, the explanation is much more boring: an extraordinary jump is an extreme event followed by more average performance. 

  • Statistical significance doesn’t imply real-life significance 

Scientific articles abound in statistically significant results. In everyday language significant equals important. However, not in the science lingo. 

Statistical significance informs us that the studied effect probably didn’t occur by chance and it’s worth researching it further. For example, if we compare a new treatment for lung cancer with the standard one and obtain statistically significant results, it’s likely that the new therapy really increases the survival rates. However, it doesn’t tell us anything about the effect size. The potential improvements might be outweighed by costs and risks of introducing a new therapy. 

  • Relative and absolute changes: we need to know both 
Bacon isn’t great neither for your health nor for the planet, but it probably won’t give you bowel cancer.

Have you also heard that eating processed meat increases the risk of bowel cancer by 18%? Sounds scary! However, the right question to ask is: what is the base value? It turns out that about one in twenty people will develop bowel cancer at some point in their lives, which makes the lifetime risk 5%. If someone eats 50g of processed meat every day, this risk increases to 6%. Sounds a bit less scary than 18% increase, doesn’t it? Of course, I strongly encourage you to reduce the meat consumption, but bowel cancer risk isn’t the reason. 

By following these simple tips, you can avoid falling for fake news and pseudoscientific claims. Let’s make 2019 the year of good statistics! Happy New Year! 🙂 

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