Flip a coin

I often gets questions about gambling and the lottery. Just the other day I was asked to figure the odds of a tossed coin landing on 'heads' after 9 'heads' were tossed in a row.

I explained and the person still does not believe the answer. I told him that if a fair coin is tossed and heads comes up 9 times in a row it has no effect on the next toss. A coin has no memory so there is still the usual 50-50 chance of tails or heads. The previous 9 or 900 tosses have nothing to do with that next toss.

The confusion is about the probability of tossing 10 'heads' in a row. That's a whole 'nother smoke.

The probability of one head in a row is 1 out of 2 (.5), the probability of 2 heads in a row is 1 out of 4 (.5 x .5), 3 heads is 1 out of 8 (.5 x .5 x .5) and so on. So the probability of 10 heads in a row is 1 out of 1024 (.5 to the 10th power) or .0009765625.

In a real world case where someone tosses 9 heads in a row I would be concerned about the fairness of the coin. 

Statistics Done Wrong - Book Review

Author Alex Reinhart's s bio says "I’m a PhD student in statistics at Carnegie Mellon University, after previously earning my BSc in physics at the University of Texas at Austin while doing research on statistical methods to detect unexpected radioactive sources using mobile detectors. (I preferred to call it “finding radioactive people at football games.”) I now work on statistical models to understand and predict where crimes occur."

He obviously know his stuff - it just wasn't the stuff that I expected when I picked up the book.

As a mathematician I like to read books on various math disciplines especially topology, set theory and so on but also some applied topics such as probability and stats. I wrongly assumed that Statistics Gone Wrong would be about how methods and theorems of applied stats can lead to inaccurate results. The book is more for people who analyze data and make statistical predictions.

Don't get me wrong. The author does a very complete job in demonstrating how using stats can lead to inaccurate and even false conclusions. He starts with defining p values and gives examples of how they can lead to inaccuracies.

The use of examples is interesting such as the published results of the "Right turn on Red" data.

The author writes "If you’re a practicing scientist, you probably use statistics to analyze your data. From basic t tests and standard error calculations to Cox proportional hazards models and propensity score matching, we rely on statistics to give answers to scientific problems. This is unfortunate, because statistical errors are rife.

Statistics Done Wrong is a guide to the most popular statistical errors and slip-ups committed by scientists every day, in the lab and in peer-reviewed journals. Many of the errors are prevalent in vast swaths of the published literature, casting doubt on the findings of thousands of papers. Statistics Done Wrong assumes no prior knowledge of statistics, so you can read it before your first statistics course or after thirty years of scientific practice."

It's a good, solid book. Just don't expect it to be about probability and statistics. It is about the errors that can be made in analyzing data.