Is 2 better than 1?

Not a statistical image this time, but a scene from the espionage novel "The Gun Seller" by writer, actor, musician Hugh Laurie. He uses an old example with a misunderstanding of the probability of joint events. Consider two events B₁ an B₂ each occurring with the same probability P(B₁) = P(B₂) = p. If they occur together, their joint probability is denoted P(B₁ and B₂). We can think sequentially and consider

P(B₁ and B₂) = P(B₁)P(B₂ given B₁) and if they are independent 

P(B₂ given B₁) = P(B₂) = p. So that under independence 
P(B₁ and B₂) = p² , much smaller than p. Notice how he relates this below. 

There was a bomb scare on the flight out to Prague. No bomb, but lots of scare.We were just settling ourselves into our seats when the pilot’s voice came over theintercom, telling us to deplane with all possible speed. No ‘ladies and gentlemen, on behalf of British Airways,’ or anything like that. Just get off the plane now.

We hung around in a lilac-painted room, with ten fewer chairs than there were passengers and no music to play by, and you weren’t allowed to smoke. I was, though. A uniformed woman with a lot of make-up told me to put it out, but I explained that I was asthmatic and the cigarette was a herbal dilation remedy I had to take whenever I was under stress. Everybody hated me for that, the smokers even more than the non-smokers.When we finally shuffled back on to the aircraft, we all looked under our seats, worriedthat the sniffer dog might have had a cold that day, and that somewhere there was a little black hold-all that all the searchers had missed.  

There once was a man who went to see a psychiatrist, crippled by a fear of flying. His phobia was based on the belief that there would be a bomb on any plane he boarded. The psychiatrist tried to shift the phobia but couldn’t, so he sent his patient to a statistician. The statistician prodded a calculator and informed the man that the odds against there being a bomb on board the next flight he took were half a million to one. The man still wasn’t happy, and sat there convinced that he’d be on that one plane out of half a million. So the statistician prodded the calculator again and said ‘all right, would you feel safer if the odds were ten million to one against?’ The man said, yes, of course he would. So the statistician said ‘the odds against there being two, separate, unrelated bombs on board your next flight are exactly ten million to one against.’ The man looked puzzled, and said ‘that’s all well and good, but how does it help me?’ The statistician replied: ‘It’s very simple. You take a bomb on board with you.'

I told this to a grey-suited businessman from Leicester, sitting in the seat next to me, but he didn’t laugh at all. Instead, he called a stewardess and said he thought I had a bomb in my luggage. I had to tell the story again to the stewardess, and a third time to the co-pilot who came back and squatted at my feet with a scowl on his face. I’m never going to make polite conversation ever again. 

Perhaps I’d misjudged how people feel about bombs on aeroplanes. That’s possible. A more likely explanation is that I was the only person on the flight who knew where the hoax bomb call had come from, and what it meant.

 Of course no statistician would suggest such an action. Comic irony or real misunderstanding?

Sometimes Charts Don't Lie

Dave Blazek's Loose Parts.

So Young, So Old

Nathan Yau at Flowing Data has produced an interactive graphic to compare your age with others. What percentage of the US population is younger than you? What percentage is older? In the static image above the US median age appears to be about 37 years old. Based on a 5-year American Community Survey from 2014, his interactive graphs lets you slide the line to match any age and see the percentage of Americans older or younger.

Changing Wants

Research in the Journal of Family Issues by Boxer et al. was illustrated by Max Roser at Our World of Data in the graphic above. From survey results that date back to the 1930s, college students ranked the importance of 18 traits of a prospective mate, via datavizblog, via techinsider.

Here are the ranking results from Boxer et al.:

Their research questions wondered if more recent surveys from 1985, 1996, and 2008 showed increasing importance to men of "good financial prospect." It had only partial support. Their next question wondered if there was increasing importance among women for "good cook and housekeeper" and "desire for home and children". It had no support. Finally, they wondered if there would be decreasing importance among women for "good financial prospect". It had no support.

The graphic above takes their widest view of mate preferences where "mutual attraction - love", "education - intelligence", "sociability", "good lucks", and "good financial prospect" have increased in importance since 1939 for both sexes. "Desire for home, children" has increased for men but decreased for women. And for men "ambition and industriousness" has dropped since 1939. "Chastity" has decreased in importance for both sexes.

Semester's End

It's the end of the semester and I saw this Post-It Note graphic that shows exactly how many people, especially students, approach an assignment's deadline. From Instagrammer Insta-Chaz via Visual News.