It takes two to tango.

Once upon a time, in a distant town in a far away land, there was a regular ballroom dancing event every weekend, an Argentine Tango Spectacular.  Everyone in the town was invited, and since there wasn’t much else to do, nearly everyone turned up.    Now, in tango, as you know, you dance in couples, one man and one woman.  As the night wore on, some people danced over and over again with the same  partner.  Some did every dance with a different partner.  Some mostly just sat out and watched, and socialised. Some boycotted the whole event.

The King decided to commission a survey in all the towns in the country, asking people how many times they had danced tango in the past year and how many different people they had danced with.  In our town, the results came back showing that women had an average of 20.3 dancing partners and men had only 16.8. In most other towns, the survey had found that men danced with more different partners than women.

What can we conclude from this survey?  What does it tell us about who was calling the shots in dancing decisions? Does it mean that women liked more variety in their dancing partners?

Of course, we can’t conclude anything.  Every time a woman dances with a new man, that man is dancing with a new woman.  If the number of men and women in the town is close to equal, the average number of dance partners for men and women must be the same as a matter of simple arithmetic. All we learn about is the inadequacies of the survey.  Of course, this is just a story, and any resemblances to real statistical errors are almost entirely accidental.