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Using a Priori Contrasts for Multivariate Repeated-Measures Using A Priori Contrasts for Multivariate Repeated-Measures ANOVA to Analyze Thermoregulatory Responses of the Dibbler (Parantechinus apicalis; Marsupialia, Dasyuridae) Author(s): Philip C. Withers and Christine E. Cooper Reviewed work(s): Source: Physiological and Biochemical Zoology, Vol. 84, No. 5 (September/October 2011), pp. 514-521 Published by: The University of Chicago Press Stable URL: http://www.jstor.org/stable/10.1086/661637 . Accessed: 22/11/2011 19:59 Your use of the JSTOR archive indicates your acceptance of the Terms & Conditions of Use, available at . http://www.jstor.org/page/info/about/policies/terms.jsp JSTOR is a not-for-profit service that helps scholars, researchers, and students discover, use, and build upon a wide range of content in a trusted digital archive. We use information technology and tools to increase productivity and facilitate new forms of scholarship. For more information about JSTOR, please contact [email protected]. The University of Chicago Press is collaborating with JSTOR to digitize, preserve and extend access to Physiological and Biochemical Zoology. http://www.jstor.org 514 TECHNICAL COMMENT Using A Priori Contrasts for Multivariate Repeated-Measures ANOVA to Analyze Thermoregulatory Responses of the Dibbler (Parantechinus apicalis; Marsupialia, Dasyuridae) Philip C. Withers* physiological variables to a categorical factor and are especially Christine E. Cooper useful for repeated-measures ANOVA designs common to many Animal Biology M092, University of Western Australia, physiological studies. Stirling Highway, Crawley, Western Australia 6009, Australia; and Department of Environment and Agriculture, Curtin University, P.O. Box U1987 Perth, Western Australia 6845, Australia Introduction Accepted 5/16/2011; Electronically Published 8/24/2011 A priori contrasts provide a powerful tool to evaluate expected patterns with a categorical factor for ANOVA (Cohen 2008), Online enhancement: Excel file. univariate repeated-measures ANOVA (Potvin et al. 1990; Park et al. 2009), and multivariate repeated-measures ANOVA (Rencher 2002), because they examine specific hypotheses using an appropriate contrast matrix (e.g., Bock 1975; Hand and ABSTRACT Taylor 1987). For example, a simple contrast tests whether a Physiological studies often involve the repeated measurement control category is different from each other category. For or- of individuals over a range of ordered categorical conditions, dered categorical data, a Helmert contrast tests whether a cat- for example, varying ambient temperature. We illustrate here egory is different from all subsequent categories pooled to- the use of a priori contrasts for multivariate repeated-measures gether; a reverse-Helmert contrast tests whether a category is ANOVA by analyzing the thermal responses of various physi- different from all previous categories pooled. For ordered nu- Њ ological variables for a small marsupial, the dibbler (Parantech- meric categories (e.g., ambient temperature Ta measured in C), inus apicalis). Our analyses showed that dibblers conform closely a polynomial contrast examines whether there is a linear, qua- to the Scholander-Irving model of endothermy. Body tempera- dratic, or other polynomial relationship. A priori contrasts can 0.24ЊCat be more powerful than the overall ANOVA hypothesis (that all ע ture was constant at low air temperatures, was 36.3 thermoneutrality (30ЊC), and increased at 35ЊC. Metabolic rate means are equal) because they address more specific hypotheses decreased with increasing ambient temperature to a basal rate of than general post hoc tests and because they address fewer Ϫ1 Ϫ1 Њ ע 0.619 0.036 mL O2 g h at 30 C; it extrapolated closely to specific uncorrelated hypotheses (e.g., experimental groups dif- thermoneutral body temperature. Increased oxygen demand at fer from a control group, or there is a linear relationship for lower ambient temperature was met by increased respiratory ordered categories). However, contrast tests have not been minute volume, achieved by increased respiratory frequency and widely embraced by comparative physiologists despite their use- tidal volume; oxygen extraction was constant at about 19%. Evap- fulness for examining specific patterns in physiological data sets orative water loss and wet and dry thermal conductance increased and especially their particular value in overcoming the issue of markedly at high ambient temperatures but not sufficiently to an absence of post hoc tests for repeated-measures ANOVA. maintain constant body temperature. Relative water economy Many physiological studies involve the repeated measure- was similar to that of other small marsupials, increasing linearly ment of individuals subjected to different categorical treatments at lower air temperatures with a point of relative water economy on an ordered scale, for example, measurement of a physio- of 20.3ЊC. We conclude that a priori contrasts provide a statis- logical variable at different ambient temperatures. Multivariate tically appropriate and powerful analysis that can be used rou- repeated-measures analysis of variance (MANOVAR) is an ap- tinely to statistically describe the pattern of response of propriate statistical analysis for such data, with the repeated measure (e.g., Ta) being the multivariate factor (Potvin et al. 1990; Rencher 2002; Park et al. 2009). However, a major lim- * Corresponding author; e-mail: [email protected]. itation of MANOVAR is that it does not have formal compar- Physiological and Biochemical Zoology 84(5):514–521. 2011. ᭧ 2011 by The ison tests equivalent to ANOVA post hoc tests (e.g. Tukey, University of Chicago. All rights reserved. 1522-2152/2011/8405-1014$15.00. Dunnett, Student-Newman-Keuls, etc). Consequently, it is dif- DOI: 10.1086/661637 ficult to statistically discern the pattern of the effect of a sig- Technical Comment 515 nificant repeated factor (e.g., the pattern of a Ta effect for a Respirometry physiological variable) within the MANOVAR model. The re- cent physiological literature includes various approaches to this Metabolic rate (oxygen consumption, Vo2; carbon dioxide pro- problem. Some repeated-measures studies simply do not eval- duction, Vco2) and EWL were measured by flow-through res- uate the pattern of the repeated measure (e.g., Beaupre and pirometry for individuals that had been fasted for 20 h before Zaidan 2001; Gomez et al. 2006), and some use a Bonferroni- the commencement of experiments. Dibblers were measured type adjustment for multiple comparison tests (e.g., Rezende for 5–9 h at each Ta during their inactive phase (day) until et al. 2004; Berg and Biewener 2008; Park et al. 2009; Wu et Vo2,Vco2, and EWL were stable and minimal; individuals were al. 2009; Dunlap et al. 2010) or post hoc ANOVA tests that do measured at only one Ta per day and not more frequently than not account for repeated measurements (e.g., McLean and every 3 days. Observations of dibblers in the metabolic chamber Speakman 2000; Gilmour et al. 2001; Zerm et al. 2004; Zhao by video indicated when dibblers were resting and asleep; these and Cao 2009; Dupont-Prinet et al. 2010). periods were easily identified in the continuous traces of phys- We illustrate here the use of a priori contrasts, by examining iological data and used for analysis, so we are confident that the thermoregulatory responses of the dibbler (Parantechinus our values are for resting, inactive dibblers. Tb was measured apicalis), a 40–100-g endangered dasyurid marsupial charac- when dibblers were removed from the chamber at the end of terized by a white eye ring and freckled fur (Woolley 2008). the experiment, using a plastic-tipped thermocouple (con- The dibbler’s current distribution is restricted to three small nected to a Radio Spares 611–234 thermocouple meter) in- islands near Jurien, Western Australia, and a few scattered serted ∼1.5 cm into the cloaca. mainland sites on the south coast of Western Australia, where Mass flow controllers (Aalborg GFC17 and Cole-Palmer it inhabits dense heath on sandy soils (Menkhorst and Knight 32708-26) regulated the flow of ambient air at a constant rate 2004; Cronin 2008; Woolley 2008). We characterize body tem- of 500–700 mL minϪ1 through cylindrical glass chambers (500 perature, metabolic rate, thermal conductance, respiratory ven- mL), located in a temperature-controlled cabinet. Individuals Њ Њ tilation, evaporative water loss, and relative water economy over were measured at each ambient temperature (Ta:9.4,15.3, a range of ambient temperatures and then examine the various 19.9Њ, 25.3Њ, 30.8Њ, and 35.3ЊC) in random order for indepen- patterns of Ta effects below and above thermoneutrality using dence of data from the order of measurement. Excurrent air a priori contrasts and MANOVAR (Rencher 2002), based on passed over a thin-film-capacitance relative humidity (RH) and the typical responses of endotherms (e.g., McNab 1980; Withers Ta probe (Vaisala HMP45A), with a subsample passing through 1992) and more specifically of other dasyurid marsupials (e.g., a column of Drierite (W. A. Hammond Drierite) and then an Dawson and Wolfers 1978; Morton and Lee 1978; Geiser 1986; oxygen analyzer (Sable Systems FoxBox or Servomex 574) and Geiser and Baudinette 1988; Hallam and Dawson 1993; Lar- a carbon dioxide analyzer (Sable Systems FoxBox or CA-2A). combe 2002; Schmidt et al. 2009; Cooper and Withers 2010; The data were recorded by a PC every 20 s throughout the Warnecke et al. 2010). We use polynomial contrasts to examine experimental period using custom-written
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