Linear Models and Effect Magnitudes for Research, Clinical and Practical Applications Will G Hopkins Sportscience 14, 49-58, 2010 (sportsci.org/2010/wghlinmod.htm) Sport and Recreation, AUT University, Auckland 0627, New
Zealand. Email.
Reviewer: Alan M Batterham, School of Health and Social Care, Teesside
University, Middlesbrough TS1 3BA, UK. |

After presenting the Magnitude Matters slideshow recently in several workshops, I realized that it needed more on the role played by linear modeling in estimation of effects. The additive nature of the linear model is the basis of adjustment for the effects of other factors to get pure or un-confounded effects and to identify potential mediators or mechanisms of an effect. The additive nature of linear models also explains why we should use the log of the dependent variable to estimate uniform percent or factor effects. A consideration of the error term in a linear model provides further justification for the use of log transformation, along with the use of the unequal-variances t statistic or mixed modeling in analyses where the error term differs between or within subjects. Finally, the analyses for counts and binary dependent variables make little sense without understanding how the underlying linear models require such strange dependent variables as the log of the odds of a classification or the log of the hazard of a time-dependent event. The new slideshow addresses all these issues and more, using material from the recent progressive statistics article (Hopkins et al., 2009) and a book chapter on injury statistics (Hopkins, 2009). The slideshow hopefully represents a useful combination of theory and practical advice for anyone who wants to understand and estimate effects in their research. For more on the way we infer causality, deal with
confounders, and account for mechanisms in the relationships between
variables, see the slideshow/article on When it comes to actual data analysis, you will need extra help with the practicalities of the use of a spreadsheet or stats package. Peruse the article on comparing two group means and play with the associated spreadsheet to come to terms with simple comparisons of means and adjustment for a covariate (Hopkins, 2007b). The article on the various controlled trials and the associated spreadsheets are a little more advanced and also full of useful material (Hopkins, 2006). See my item on Sad Stats for an overview of some of the stats packages and for a set of files that are useful for SPSS users. If you already have some experience with the SAS package but need specific advice on Proc Mixed, Genmod or Glimmix, contact me. The reprint pdf contains this article with a printer-friendly version of the slideshow (six slides per page). Chinn S (2000). A simple method for converting an odds ratio to effect size for use in meta-analysis. Statistics in Medicine 19, 3127-3131 Hopkins WG (2006). Spreadsheets for analysis of controlled trials, with adjustment for a subject characteristic. Sportscience 10, 46-50 Hopkins WG (2007a). Understanding statistics by using spreadsheets to generate and analyze samples. Sportscience 11, 23-36 Hopkins WG (2007b). A spreadsheet to compare means in two groups. Sportscience 11, 22-23 Hopkins WG (2008). Research designs: choosing and fine-tuning a design for your study. Sportscience 12, 12-21 Hopkins WG (2009). Statistics in observational studies. In: Verhagen E, van Mechelen W (editors) Methodology in Sports Injury Research. OUP: Oxford. 69-81 Hopkins WG, Marshall SW, Batterham AM, Hanin J (2009). Progressive statistics for studies in sports medicine and exercise science. Medicine and Science in Sports and Exercise 41, 3-12. Link to PDF. Published July 2010 |