Commentary on Bootstrapping Inferential Statistics with a Spreadsheet Alan M Batterham Sportscience 16, 16, 2012 (sportsci.org/2012/amb.htm) |
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This
article and associated spreadsheets represent a very valuable addition to the
suite of resources at sportsci.org, providing an excellent introduction to
bootstrap resampling methods. Particularly useful, perhaps, is the content relating
to modeling quadratic relationships to derive confidence intervals for X
values at either maxima or minima. I urge readers wishing to delve deeper
into the theory and practice of bootstrap resampling to consult the classic
text of Efron and Tibshirani (1993). Bootstrap resampling methods are
available in many commercial statistical software packages including IBM SPSS
(as an add-on module), Stata, SAS, and R. There is also specialized
resampling software such as Resampling Stats, available as a very flexible
Excel Add-in. However, I know of no other user-friendly, free-to-use
resources for resampling with the flexibility of the spreadsheets at
sportsci.org. From an educational perspective, I applaud the open nature of
the spreadsheets that allows readers to access the formulae and get into the
"black box" between data input and results output. This
characteristic of the resources provides a very powerful learning tool. The
spreadsheets construct confidence intervals using a simple percentile method
which, as stated in the resources, is adequate for most purposes given a
large enough original sample size and a reasonably well behaved distribution.
However, in some circumstances the percentile method can lead to confidence
intervals with unsatisfactory coverage properties (too narrow), as it cannot
address either bias with respect to the original effect estimate or a
standard error that varies with the value of the estimate. In short, the
percentile method can underestimate the tails of the distribution. To address
these issues, the bias corrected and accelerated (BCa) method was developed
to improve coverage. The BCa bootstrap adjusts for both bias and skewness in
the bootstrap distribution (Efron and
Tibshirani, 1993), and is available as an option in
the software packages mentioned above. In most cases, however, the coverage
properties and associated magnitude-based inferences derived from the simple
percentile method will be correct with sufficient N and appropriate
transformation of severely skewed data. Efron B, Tibshirani RJ (1993). An Introduction to the Bootstrap. Chapman and Hall: London Published July 2012 |