Tchau, USA!

This will be my last year teaching in Nashville. My wife and I have made the huge decision to relocate (with all three of our kids) to São Paulo, Brazil next summer, where we will both be teaching at Graded International School (http://graded.br) for at least two years. I will still be teaching high schoolRead More

How likely is any given study to be “true”? A conditional probability / inference exploration.

  An important point I try to get across to students is that statistics is real math, but by its very nature statistical techniques always have a possibility of error. Which means that sometimes an experiment will find a “statistically significant” result (and therefore, in a super-simplistic view, result in a publishable paper in a respectedRead More

Always Sometimes Nevers are the best

Last year, I semi-accidentally created my single favorite geometry activity of the year: class-collaborated Always/Sometimes/Nevers. You can read about my initial version of the activity here if you’d like. The post this year is in two parts. In the first one, I talk about what I love about Always/Sometimes/Nevers as a problem type and the type ofRead More

Bootstrap Confidence Intervals – not as reliable as their reputation!

Bootstrapping can be used to estimate confidence intervals. Start by resampling the original sample - that is, drawing samples the same size as the original sample WITH REPLACEMENT from the sample itself. This simulates taking many samples from a large population that looks exactly like the sample. This will create an approximate sampling distribution. By taking the middle C% of the data, you can estimate a C% confidence interval. Bootstrapping is the best way to estimate confidence intervals for most quantitative statistics, if a tool is available to perform the process.

I’ve been learning a lot about the deep details of statistics lately, motivated partially by interest and partially by a deep desire not to accidentally put something in the CPM Statistics book that is wrong! My current study is about bootstrapping confidence intervals. If you’ve never heard of bootstrapping, I’ll give you the introductory definition weRead More