Linear models and effect magnitudes for research, clinical and practical applications

Saved in:
Bibliographic Details
Title translated into German:Lineare Modelle und Effektstärken für die Forschung, klinische und praktische Anwendung
Author:Hopkins, Will G.
Published in:Sportscience
Published:14 (2010), S. 49-57, Lit.
Format: Publications (Database SPOLIT)
Publication Type: Journal article
Media type: Electronic resource (online) Print resource
ISSN:1174-9210, 1174-0698
Online Access:
Identification number:PU201009007198


Effects are relationships between variables. The magnitude of an effect has an essential role in sample-size estimation, statistical inference, and clinical or practical decisions about utility of the effect. Virtually every effect in research, clinical and practical settings arises from a linear model, an equation in which a dependent variable equals a sum of predictor variables and/or their products. Linear models allow for the effect of one predictor to be adjusted for the effects of other predictors and for the modeling of non-linearity via polynomials. Effects and models used to estimate them depend on the nature of the dependent variable (continuous, count, nominal) and the predictor variables (numeric, nominal). A continuous dependent gives rise to a difference in a mean with a nominal predictor and a slope or correlation with a numeric predictor. Default magnitude thresholds for difference in a mean come from standardization (dividing by the between-subject standard deviation): 0.2, 0.6, 1.2, 2.0 and 4.0 for small, moderate, large, very large and extremely large. The same thresholds apply to a slope, provided the slope is evaluated as the difference for 2 SD of the predictor. Thresholds for correlations are 0.1, 0.3, 0.5, 0.7 and 0.9. Many effects and errors are uniform across the range of the dependent variable when expressed as percents or factors, and these should be estimated via log transformation. Non-uniformity of error arising from repeated measurement or from different subject groups should be addressed via within-subject modeling or mixed modeling, which also provide estimates of individual responses to treatments. Effects on nominal variables and counts are analyzed with various generalized linear models, where the dependent is the log of either the odds of a classification, the hazard (incidence rate) of an event, or the mean count. The effect is estimated initially as a factor representing a ratio between two groups (or per unit or per 2 SD of a numeric predictor) of either odds of a classification, hazards of an event, counts, or count rates. Effects involving common classifications or events can be converted to differences in percent risk and interpreted with magnitude thresholds of 10, 30, 50, 70 and 90. Thresholds for common events can also be derived from standardization of log of time to the event. Both sets of thresholds are similar and correspond to hazard ratios of 1.3, 2.3, 4.5, 10 and 100. For counts and rare events, a consideration of proportions attributable to an effect gives rise to ratio thresholds for counts, hazards, risks or odds of 1.1, 1.4, 2.0, 3.3, and 10. Proportional hazards regression is an advanced form of linear modeling for use with events when hazards change with time but their ratio is constant. Verf.-Referat