摘要
EcologyVolume 80, Issue 4 p. 1150-1156 Special Feature THE META-ANALYSIS OF RESPONSE RATIOS IN EXPERIMENTAL ECOLOGY Larry V. Hedges, Larry V. Hedges Department of Education, University of Chicago, 5835 South Kimbark Avenue Chicago, Illinois 60637 USASearch for more papers by this authorJessica Gurevitch, Jessica Gurevitch Department of Ecology and Evolution, State University of New York, Stony Brook, New York 11794 USASearch for more papers by this authorPeter S. Curtis, Peter S. Curtis Department of Plant Biology, Ohio State University, 1735 Neil Avenue, Columbus, Ohio 43210 USASearch for more papers by this author Larry V. Hedges, Larry V. Hedges Department of Education, University of Chicago, 5835 South Kimbark Avenue Chicago, Illinois 60637 USASearch for more papers by this authorJessica Gurevitch, Jessica Gurevitch Department of Ecology and Evolution, State University of New York, Stony Brook, New York 11794 USASearch for more papers by this authorPeter S. Curtis, Peter S. Curtis Department of Plant Biology, Ohio State University, 1735 Neil Avenue, Columbus, Ohio 43210 USASearch for more papers by this author First published: 01 June 1999 https://doi.org/10.1890/0012-9658(1999)080[1150:TMAORR]2.0.CO;2Citations: 2,549Read the full textAboutPDF ToolsRequest permissionExport citationAdd to favoritesTrack citation ShareShare Give accessShare full text accessShare full-text accessPlease review our Terms and Conditions of Use and check box below to share full-text version of article.I have read and accept the Wiley Online Library Terms and Conditions of UseShareable LinkUse the link below to share a full-text version of this article with your friends and colleagues. Learn more.Copy URL Share a linkShare onEmailFacebookTwitterLinkedInRedditWechat Abstract Meta-analysis provides formal statistical techniques for summarizing the results of independent experiments and is increasingly being used in ecology. The response ratio (the ratio of mean outcome in the experimental group to that in the control group) and closely related measures of proportionate change are often used as measures of effect magnitude in ecology. Using these metrics for meta-analysis requires knowledge of their statistical properties, but these have not been previously derived. We give the approximate sampling distribution of the log response ratio, discuss why it is a particularly useful metric for many applications in ecology, and demonstrate how to use it in meta-analysis. The meta-analysis of response-ratio data is illustrated using experimental data on the effects of increased atmospheric CO2 on plant biomass responses. Supporting Information Filename Description https://dx.doi.org/10.6084/m9.figshare.c.3297278 Research data pertaining to this article is located at figshare.com: Please note: The publisher is not responsible for the content or functionality of any supporting information supplied by the authors. Any queries (other than missing content) should be directed to the corresponding author for the article. Literature Cited Adams, D. C., J. Gurevitch, and M. S. Rosenberg . 1997. Resampling tests for meta-analysis of ecological data. Ecology 78: 1277–1283. Arnqvist, F. R. and D. Wooster . 1995. Meta-analysis—synthesizing research findings in ecology and evolution. Trends in Ecology and Evolution 10: 236–240. Cooper, H. M. and L. V. Hedges . 1994. The handbook of research synthesis. Russell Sage Foundation, New York, New York, USA. Cooper, S. D., S. J. Walde, and B. L. Peckarsky . 1990. Prey exchange rates and the impact of predators on prey populations in streams. Ecology 71: 1503–1514. Curtis, P. S. and X. Wang . 1998. A meta-analysis of elevated CO2 effects on woody plant mass, form, and physiology. Oecologia 113: 299–313. DerSimonian, R. and N. Laird . 1986. Meta-analysis in clinical trials. Controlled Clinical Trials 7: 177–188. Downing, J. A., C. W. Osenberg, and O. Sarnelle . 1999. Meta-analysis marine nutrient-enrichment experiments: variation in the magnitude of nutrient limitation. Ecology 80: 1157–1167. Englund, G., O. Sarnelle, and S. Carpenter . 1999. The importance of data-selection criteria: Meta-analyses of stream predation experiments. Ecology 80: 1132–1141. Feller, W. . 1966. Introduction to probability theory and its applications. Volume II. John Wiley & Sons, New York, New York, USA. Fieller, E. C. . 1932. The distribution of the index in a normal bivariate population. Biometrika 24: 428–440. Geary, R. C. . 1930. The frequency distribution of the quotient of two normal variables. Journal of the Royal Statistical Society 93: 442–446. Goldberg, D. E., T. K. Rajaniemi, J. Gurevitch, and A. Stewart-Oaten . 1999. Empirical approaches to quantifying interaction intensity: competition and facilitation along productivity gradients. Ecology 80: 1118–1131. Gunderson, C. A. and S. D. Wullschleger . 1994. Photosynthetic acclimation in trees to rising atmospheric CO2: a broader perspective. Photosynthesis Research 39: 369–388. Gurevitch, J. and L. V. Hedges . 1993. Meta-analysis: combining the results of independent studies in experimental ecology. Pages 378–398 in S. Scheiner and J. Gurevitch, editors. The design and analysis of ecological experiments. Chapman & Hall, London, UK. Gurevitch, J. and L. V. Hedges . 1999. Statistical issues in ecological meta-analysis. Ecology 80: 1142–1149. Gurevitch, J., L. L. Morrow, A. Wallace, and J. S. Walsh . 1992. A meta-analysis of field experiments on competition. American Naturalist 140: 539–572. Hedges, L. V. . 1983. Combining independent estimators in research synthesis. British Journal of Mathematical and Statistical Psychology 36: 121–131. Hedges, L. V. . 1994. Statistical considerations in research synthesis. Pages 29–38 in H. Cooper and L. V. Hedges, editors. The handbook of research synthesis. Russell Sage Foundation, New York, New York, USA. Hedges, L. V. and I. Olkin . 1985. Statistical methods for meta-analysis. Academic Press, New York, New York, USA. Hinkley, D. V. . 1969. On the ratio of two correlated normal random variables. Biometrika 56: 635–639. Hinkley, D. V. . 1970. Correction. Biometrika 57: 683. Kimball, R. A. . 1983. Carbon dioxide and agricultural yield: an assemblage and analysis of 430 prior observations. Agronomy Journal 75: 779–788. Laska, M. S. and J. T. Wootton . 1998. Theoretical concepts and empirical approaches to measuring interaction strength. Ecology 79: 461–476. Marsaglia, G. . 1965. Ratios of normal variables and ratios of sums of uniform variables. Journal of the American Statistical Association 60: 193–204. Meier, P. . (1953). Variance of a weighted mean. Biometrics 9: 59–73. Osenberg, C. W., O. Sarnelle, and S. D. Cooper . 1997. Effect size in ecological experiments: the application of biological models in meta-analysis. American Naturalist 150: 798–812. Osenberg, C. W., O. Sarnelle, S. D. Cooper, and R. D. Holt . 1999. Resolving ecological questions through meta-analysis: goals, metrics, and models. Ecology 80: 1105–1117. Poorter, H. . 1993. Interspecific variation in growth response of plants to an elevated ambient CO2 concentration. Vegetatio 104/105: 77–97. Rao, C. R. . 1973. Linear statistical inference. John Wiley & Sons, New York, New York, USA. Rosenberg, M. S., D. C. Adams, and J. Gurevitch . 1997. MetaWin. Statistical software for conducting meta-analysis: fixed effect models, mixed effect models, and resampling tests. Version 1.0. Sinauer Associates, Sunderland, Massachusetts, USA. Sarnelle, O. . 1992. Nutrient enrichment and grazer effects on phytoplankton in lakes. Ecology 74: 551–560. Citing Literature Volume80, Issue4June 1999Pages 1150-1156 ReferencesRelatedInformation