Bad Stats on Innumeracy

In his recent post, The Innumeracy of the Media Has Not Been Greatly Exaggerated, the always reserved and subtle Barry Ritholtz writes “these shopper surveys and measures of foot traffic have in the past had no predictive value relative to retail sales”. He concludes with “A coin flip– 50/50 chance of getting it right — has much greater accuracy than these surveys.”

What does that even mean? When you write a post on others’ innumeracy you should not conclude with nonsensical statistical bluster that epitomizes the deficiency you criticize!

A coin flip has a binary outcome: Yes/No or On/Off or True/False, whatever. Green/Purple works too.

Well, how could we use a coin flip to predict retail sales “accurately”? Perhaps an over/under prediction – flip the coin to predict whether this holiday season’s retail sales will be higher or lower than some baseline such as last year’s(*)? Fine, but if such a coin flip has “much greater accuracy than these surveys”, then these surveys have some value as contrary indicators, which means they do have predictive value if properly interpreted.

His earlier Bloomberg article was better and more entertaining.

* Regardless of the actual binary outcomes profile, the coin flip has a 50% probability of being “correct” each time. So with repeated trials the expected profile is also 50% correct, 50% incorrect.

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