Spreadsheet simulation and trial and error methods in statistics Michael Wood University of Portsmouth, UK

Computer-intensive, “crunchy” methods Crunch out answers without dependence on sophisticated maths Rationale transparent Sometimes more robust in the sense of no dependence on unrealistic assumptions Often more general—can tackle problems with no convenient formula-based method Detailed step through for beginners Very brief overview of three possibilities

An aside … I am fairly critical of many applications of statistics: not the subject of this talk except that transparency makes problems more obvious

Regression and least squares models Spreadsheet to calculate MSE (mean square error), then use Solver to find parameters for least squares model Identical answers to standard formulae Obvious what’s going on and can be modified if required Single variable: pred1var.xls Multiple regression: predmvar.xls Can easily adjust method—e.g. ExerciseCurve.xls

Test of null hypothesis that two variables are unrelated Randomization test: Spreadsheet simulates no relationship hypothesis Obvious what’s going on with no technical statistical concepts Assumptions less restrictive and more obvious than t-test, etc Flexible – test difference between two means or two proportions, or correlation, etc Difference of two means: diffofmeanstest.xls General spreadsheet: resamplenrh.xls

Bootstrap confidence intervals One method for many different statistics –Use sample to set up a “guessed” population –Experiment drawing samples from guessed population to assess sampling error (resampling with replacement) Obvious what’s going on and when it’s not sensible! Confidence intervals are a subtle concept: simple bootstrapping avoids the mathematical problems but not the conceptual ones Many more complex methods - not simple!

Conclusion Active learning in that learners don’t have to take formulae on trust, but can act out methods and see how they work. And can often adapt to new problems.

References and website All spreadsheets files mentioned at (These all have a Read this sheet for a brief explanation) Approach explained in more detail in Wood, M (2003), Making sense of statistics: a non- mathemical approach, Basingstoke, UK: Palgrave.