The Effects of Type I Error Rate and Power of the ANCOVA<i>F</i>Test and Selected Alternatives Under Nonnormality and Variance Heterogeneity

Rheinheimer, David C.; Penfield, Douglas A.

doi:10.1080/00220970109599493

Cited by 44 publications

(43 citation statements)

References 18 publications

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“…For experiment 1, assumptions of normality were met, but equal variance was violated. Although the effect of violating these ANCOVA assumptions is a greater risk of accepting a false null hypothesis (Type I error) (Rheinheimer and Penfield 2001), we were able to reject H 0 for the interaction of interest (lake history 3 pH: see Results). For experiment 2, all assumptions were met except for homogeneity of regression slopes.…”

Section: Statistical Analysesmentioning

confidence: 76%

Adaptive Reversals in Acid Tolerance in Copepods From Lakes Recovering From Historical Stress

Derry

Arnott

2007

Ecological Applications

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Anthropogenic habitat disturbance can often lead to rapid evolution of environmental tolerances in taxa that are able to withstand the stressor. What we do not understand, however, is how species respond when the stressor no longer exists, especially across landscapes and over a considerable length of time. Once anthropogenic disturbance is removed and if there is an ecological trade-off associated with local adaptation to such an historical stressor, then evolutionary theory would predict evolutionary reversals. On the Boreal Shield, tens of thousands of lakes acidified as a result of SO2 emissions, but many of these lakes are undergoing chemical recovery as a consequence of reduced emissions. We investigated the adaptive consequences of disturbance and recovery to zooplankton living in these lakes by asking (1) if contemporary evolution of acid tolerance had arisen among Leptodiaptomus minutus copepod populations in multiple circum-neutral lakes with and without historical acidification, (2) if L. minutus populations were adaptively responding to reversals in selection in historically acidified lakes that had recovered to pH 6.0 for at least 6-8 years, and (3) if there was a fitness trade-off for L. minutus individuals with high acid tolerance at circum-neutral pH. L. minutus populations had higher acid tolerances in circum-neutral lakes with a history of acidification than in local and distant lakes that were never acidified. However, copepods in circum-neutral acid-recovering lakes were less acid-tolerant than were copepods in lakes with longer recovery time. This adaptive reversal in acid tolerance of L. minutus populations following lake recovery was supported by the results of a laboratory experiment that indicated a fitness trade-off in copepods with high acid tolerances at circum-neutral pH. These responses appear to have a genetic basis and suggest that L. minutus is highly adaptive to changes in environmental conditions. Therefore, restoration managers should focus on removing environmental stressors, and adaptable species will be able to reverse evolutionary responses to environmental disturbance in the years following recovery.

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Section: Statistical Analysesmentioning

confidence: 76%

Adaptive Reversals in Acid Tolerance in Copepods From Lakes Recovering From Historical Stress

Derry

Arnott

2007

Ecological Applications

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“…However, the main problem in literature is not the inappropriateness of ANCOVA, rather its misuse and misinterpretation. For example, Rheinheimer and Penfield (2001) investigated how the empirical size and power performances of ANCOVA are affected when the assumptions of normality and HOV, sample size, number of treatment groups, and strength of the covariate-dependent variable relationship are manipulated. They demonstrated that for balanced designs, the ANCOVA F test was robust and was often the most powerful test through all sample-size designs and distributional configurations.…”

Section: Introductionmentioning

confidence: 99%

A Comparison of Analysis of Covariate-Adjusted Residuals and Analysis of Covariance

Ceyhan

Goad

2009

Communications in Statistics - Simulation and Computation

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Various methods to control the influence of a covariate on a response variable are compared. These methods are ANOVA with or without homogeneity of variances (HOV) of errors and Kruskal-Wallis (K-W) tests on (covariate-adjusted) residuals and analysis of covariance (ANCOVA). Covariate-adjusted residuals are obtained from the overall regression line fit to the entire data set ignoring the treatment levels or factors. It is demonstrated that the methods on covariate-adjusted residuals are only appropriate when the regression lines are parallel and covariate means are equal for all treatments. Empirical size and power performance of the methods are compared by extensive Monte Carlo simulations. We manipulated the conditions such as assumptions of normality and HOV, sample size, and clustering of the covariates. The parametric methods on residuals and ANCOVA exhibited similar size and power when error terms have symmetric distributions with variances having the same functional form for each treatment, and covariates have uniform distributions within the same interval for each treatment. In such cases, parametric tests have higher power compared to the K-W test on residuals. When error terms have asymmetric distributions or have variances that are heterogeneous with different functional forms for each treatment, the tests are liberal with K-W test having higher power than others. The methods on covariate-adjusted residuals are severely affected by the clustering of the covariates relative to the treatment factors when covariate means are very different for treatments. For data clusters, ANCOVA method exhibits the appropriate level. However, such a clustering might suggest dependence between the covariates and the treatment factors, so makes ANCOVA less reliable as well.

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“…Our choice of ANCOVA is consistent with much of the literature on the analysis of pre-test/post-test designs (e.g., Dimitrov & Rumrill, 2003;Owen & Froman, 1998;Rheinheimer & Penfield, 2001;Wright, 2006). However, not uncommonly for classroombased research, the data did not meet two of the underlying statistical assumptions of ANCOVA: conditional normality (or normality of residuals) and homoscedasticity (equality of variances).…”

Section: Analytic Approachmentioning

confidence: 70%

Technology in the Classroom: Improving Automaticity in Mental-maths in Primary-aged Students

O’Rourke¹,

Main²,

Hill³

2017

AJTE

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The Effects of Type I Error Rate and Power of the ANCOVAFTest and Selected Alternatives Under Nonnormality and Variance Heterogeneity

Cited by 44 publications

References 18 publications

Adaptive Reversals in Acid Tolerance in Copepods From Lakes Recovering From Historical Stress

Adaptive Reversals in Acid Tolerance in Copepods From Lakes Recovering From Historical Stress

A Comparison of Analysis of Covariate-Adjusted Residuals and Analysis of Covariance

Technology in the Classroom: Improving Automaticity in Mental-maths in Primary-aged Students

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