- Pick up the book nearest you with at least 123 pages. (No cheating!)
- Turn to page 123.
- Count the first five sentences.
- Post the next three sentences.
- Tag five other bloggers.
The random noise is obtained by adding to each y value, a random number from a normal distribution with mean 0 and a standard deviation of 80.The author then goes on to demonstrate that, by increasing the number of samples, we can increase the sensitivity of the test. Very interesting illustration of a weakness of statistical significance as an indicator of the presence or absence of a correlation between two variables.
[I've left out the example code to execute in statistics software - see the book if you're interested.]
A simulation run will typically produce non-significant results, such as
[More code and output illustrating that the linear relationship is statistically invisible behind all the random noise.]
Although there is a linear relation between y and x - we built it into the data set ourselves - the amount of noise that we superimposed is so large that we cannot detect it.
Now, I am as sceptical as the next Humanist about the underlying validity of bibliomancy, but it can be a useful seed for meditation. And you have to admit that this selection bears on how we interpret the world around us as empirical beings. So before I tag the next bloggers, I'm going to share a thought or two triggered by the passage quoted above.
Some say that you can prove anything with statistics. In fact, you can only do that if you are dishonest or incompetent, and your audience does not understand statistics. None of us can force every number-quoting ideologue out there to be both honest and competent, but the critical skills needed to discern good statistics from misleading ones are within the reach of anyone who wants them.
Now who's next?
Dale, at Meming of Life
Hemant, the Friendly Atheist
Hugo, who Thinks Too Much
Sean, of the interesting Shore
Kathryn, and her Mindful Life