Generalized Eta and Omega Squared Statistics: Measures of Effect Size for Some Common Research Designs

Department of Educational Psychology, College of Education, University of Georgia, Athens, GA 30602-7143, USA.
Psychological Methods (Impact Factor: 4.45). 01/2004; 8(4):434-47. DOI: 10.1037/1082-989X.8.4.434
Source: PubMed

ABSTRACT The editorial policies of several prominent educational and psychological journals require that researchers report some measure of effect size along with tests for statistical significance. In analysis of variance contexts, this requirement might be met by using eta squared or omega squared statistics. Current procedures for computing these measures of effect often do not consider the effect that design features of the study have on the size of these statistics. Because research-design features can have a large effect on the estimated proportion of explained variance, the use of partial eta or omega squared can be misleading. The present article provides formulas for computing generalized eta and omega squared statistics, which provide estimates of effect size that are comparable across a variety of research designs.

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Available from: James Algina, Sep 29, 2015
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    • "Generalized eta 2 (Á 2 G ) was computed as a measure of the effect size (Olejnik and Algina, 2003). This statistic has two major advantages over the traditional eta 2 and partial-eta 2 : first, it provides measures of effect size that are comparable across a wide variety of research designs; and second, these effect-size measures provide indices of effect that are consistent with Cohen (1988) guidelines for defining the magnitude of the effect (Olejnik and Algina, 2003). These guidelines state that an effect size ≤0.20 is considered small, around 0.50 is considered a medium effect, and ≥0.80 is a large effect. "
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    ABSTRACT: Benthic diatoms are often used for assessing environmental conditions, such as water quality and habitat conditions in stream and river systems. Although laboratory experiments have shown that each diatom species have different levels of tolerance to different stressors, few studies have been conducted in laboratory settings that analyze the responses of the diatom assemblage to the effects of multiple simultaneous variables. The aim of this study was to evaluate some structural responses (such as species composition and diversity) of the diatom assemblage on a short time scale to the effects of the simultaneous increase in four variables that are directly linked to the environmental changes affecting the Pampean streams: tur-bidity, nutrients (phosphorous and nitrogen), water velocity and temperature. To this end we conducted a five-week laboratory experiment using artificial channels where we simulated two environmental conditions (LOW and HIGH) employing epipelic biofilm from a mesotrophic stream. The results obtained in the experiment show that the structure of the diatom assemblage in the epipelic biofilm is affected by the simultaneous modification of temperature, water velocity, nutrient concentration and turbidity. These modifications in the assemblage included moderate decreases in diversity, small decreases in the proportion of species sensitive to eutrophication and saprobity, moderate increases in the IDP (Pampean Diatom Index) values and moderate changes in the percentages of the stalked growth-forms. The relative abundance of species such as Luticola mutica, Navicula cryptocephala and Navicula lanceolata were negatively affected by both treatments; other species such as Planothidium lanceolatum, Caloneis bacillum, Encyonema minutum, Humidophila contenta, Luticola kotschyi, Nitzschia amphibia, Navicula veneta, Pinnu-laria subcapitata var. subcapitata were positively affected by the HIGH treatment; and Nitzschia fonticola was positively affected by both treatments. The results suggest that, in the very short term of the bioas-say conducted, the diatom assemblage can modify its structure to respond in a sensitive manner to the abrupt changes in multiple physical–chemical variables.
    Limnologica - Ecology and Management of Inland Waters 03/2015; 51:15-23. DOI:10.1016/j.limno.2014.10.004 · 1.80 Impact Factor
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    • "Many researchers have recommended that ESEs be reported alongside pvalues to more clearly describe findings (e.g., Cohen, 1992, 1994; Kirk, 1996; Thompson, 1999) because ESEs provide a sample size-independent assessment of the variance contributions of the factors in a model (Olejnik & Algina, 2003; Snyder & Lawson, 1993) and represent the extent to which a relation exists in the population (Cohen, 1988). Given that ESEs specify an effect's strength on a continuous scale, these statistics better illustrate the practical significance of a factor's contributions to performance outcome above and beyond the binary decision provided by NHST (e.g., Cohen, 1973; Huberty, 2002; Keppel & Wickens, 2004). "
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    ABSTRACT: Several years ago, the American Psychological Association began requiring that effect size estimates be reported to provide a better indication of the associative strength between factors and dependent measures in empirical studies (Publication manual of the American Psychological Association, 2010, Author, Washington, DC). Accordingly, developmental journals require/strongly recommend effect size estimates be included in published work. Potentially, this trend has important benefits for infancy research given some of the inherent difficulties in establishing conceptually strong findings when often facing highly variable performance in typically small samples. This study examined recent infant research from select journals for accuracy and interpretative value of effect size estimates. Demographics, sample size, design, and statistical data were coded from 158 published (2007–2012) articles presenting 878 effect size estimates from experimental findings with infants using behavioral methods. Descriptive and distribution statistics were calculated for the following variables: (1) statistical tests, (2) effect size parameters, and (3) effect size interpretations. Although partial eta squared () and eta squared (η2) were most common (49 and 42%, respectively), “η confusion” was apparent, and interpretation of effect size estimates was virtually nonexistent. Thus, effect size estimates are not impacting infant development research in spite of criticisms of sole dependence on null hypothesis (e.g. American Psychologist, 49, 1994 and 997). Suggestions for increasing accuracy of effect size estimate selection and interpretative effect size estimate cutoffs are offered to improve empirical clarity.
    Infancy 03/2015; 20(4). DOI:10.1111/infa.12078 · 1.73 Impact Factor
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    • "We calculated effect sizes for environmental and body size data using: x 2 ¼ SS treatment À df treatment 3 MS error SS total þ MS error where SS treatment is the sum of squares for a given parameter, df treatment is the degrees of freedom for that parameter, MS error is the mean square error, and SS total is the total sum of squares. These values were calculated from an analysis of variance to determine the proportion of explained variance of each parameter (Olejnik and Algina 2003). To determine the best regression model to predict R, we used an informationtheoretic approach using Akaike's information criterion (AIC) (Burnham and Anderson 1998 "
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    ABSTRACT: For many organisms, constraints on activity increase energetic costs, which ultimately reduce the suitability of a particular habitat. Mechanistic species distribution models often use estimates of activity to predict how organisms will respond to climate change. These models couple physiology and morphology with climatic data to estimate potential activity. In turn, the duration of activity is used to estimate the energetic balance of individuals at a given location. Whether individuals remain in positive net energetic balance determines if a given location is suitable for the species. However, because these models often assume that physiology does not vary across the species range, estimates of activity (and consequently energetics) are potentially misleading. To test the consequence of this assumption, we measured total resistance to water loss (R) within two species of lungless salamanders (Plethodon metcalfi and P. teyahalee) collected from locations along their elevational extent in southwestern North Carolina. Because hydration state constrains the activity of salamanders, increasing R would increase potential activity. Here, we leveraged the natural changes in environmental conditions along an elevational gradient to determine if salamanders modify R in different environments. We predicted that salamanders collected from low elevations would have higher R to compensate for the warmer, drier conditions at low elevations that may limit activity. We determined R in the laboratory using a flow-through system at two temperatures (12°C, 18°C) and at three vapor pressure deficits (0.20 kPa, 0.35 kPa, 0.5 kPa). For P. metcalfi, individuals collected from low elevations exhibited the highest R, suggesting either acclimatization or adaptation to local conditions. For P. teyahalee, individuals collected from high elevations exhibited the highest R, but these results may reflect alternative pressures due to differences in behavior. The results also suggest that salamanders might use temperature as a cue to increase R, but the capacity to do so depends upon the temperatures experienced in nature. Moreover, we show that variation in R has the potential to alter the duration of activity over the elevational ranges of these species, illustrating the importance of incorporating geographic variation of physiological traits for predicting a species’ response to climate.
    Ecosphere 01/2015; DOI:10.1890/ES14-00360.1 · 2.26 Impact Factor
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