Commentary on bootstrapping inferential statistics with a spreadsheet.
Confidence intervals (Analysis)
|Author:||Batterham, Alan M.|
|Publication:||Name: Sportscience Publisher: Internet Society for Sport Science Audience: Academic Format: Magazine/Journal Subject: Health Copyright: COPYRIGHT 2012 Internet Society for Sport Science ISSN: 1174-9210|
|Issue:||Date: Annual, 2012 Source Volume: 16|
|Topic:||Computer Subject: Spreadsheet add-on; Spreadsheet software|
|Product:||SIC Code: 7372 Prepackaged software|
|Geographic:||Geographic Scope: United Kingdom Geographic Code: 4EUUK United Kingdom|
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-touse 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
Alan M Batterham
School of Health and Social Care, University of Teesside, Middlesbrough TS1 3BA, UK. Email.
|Gale Copyright:||Copyright 2012 Gale, Cengage Learning. All rights reserved.|