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	Multivariate Statistics - ANCOVA Applications
		Because ANCOVA estimates an additional population parameter (the pooled population correlation), another degree of freedom is lost from the error term.
		A very controversial use of ANCOVA is to correct for initial group differences (prior to assigned to x) that exists on y among several intact, state variable groups.
		Remember that ANCOVA is simply a statistical method of accounting for a third variable; in experimental studies, the randomized blocks design is used to accomplish the same thing.
	www.uwsp.edu /psych/cw/statmanual/ancovaapps.html (779 words)

	NationMaster - Encyclopedia: ANCOVA
		ANCOVA, or analysis of covariance is an old-fashioned name for a linear regression model with one continuous explanatory variable and one or more factors.
		ANCOVA is a statistical technique of controlling extraneous variables in correlational studies.
		ANCOVA is a merger of ANOVA and regression for continuous variables.
	www.nationmaster.com /encyclopedia/ANCOVA (764 words)

	Multivariate Statistics - ANCOVA Overview
		ANCOVA allows you to remove from a dependent variable (y) irrelevant or error variance that can not be predicted from your independent variable (x).
		Linearity: Since ANCOVA is a general linear model procedure with much in common with multiple regression, it is also assumed that the covariate has a linear relationship with the dependent variable.
		Homogeneity of Regression: ANCOVA assumes that homogeneity of regression exists--that the correlation between y and z is equal for all levels of x.
	www.uwsp.edu /psych/cw/statmanual/ancovaoverview.html (564 words)

	Reading Statistics and Research (Schuyler Huck): Student Help
		ANCOVA studies contain at least one _____ variable in addition to the independent and dependent variables.
		In ANCOVA studies, the covariate variable ___ be different from the dependent variable.
		Suppose ANCOVA is used in a study on thin people to compare two different diets (A and B) on weight gain over a 4-week period.
	www.readingstats.com /fourth/quiz15_interactive.htm (830 words)

	Quasi-designs - Analysis of Covariance (Site not responding. Last check: 2007-10-25)
		ANCOVA assumes that the slopes of the regression lines are equivalent.
		In Figure 4 the ANCOVA indicates that the posttest differences between the two groups are significant, but that the treatment groups scores are higher than those of the control group.
		The effects of the independent variable in an ANCOVA are the effects attributed to the differences in the adjusted means.
	web.uccs.edu /lbecker/Psy590/ancova2.htm (2521 words)

	PA 765: Univariate GLM, ANOVA, and ANCOVA
		ANCOVA uses built-in regression using the covariates to predict the dependent, then does an ANOVA on the residuals (the predicted minus the actual dependent variables) to see if the factors are still significantly related to the dependent variable after the variation due to the covariates has been removed.
		ANCOVA is highly sensitive to outliers in the covariates.
		ANCOVA is sensitive to multicollinearity among the covariates and also loses statistical power as redundant covariates are added to the model.
	www2.chass.ncsu.edu /garson/pa765/anova.htm (16013 words)

	ANCOVA (Analysis of Covariance)
		ANCOVA is differentiated from the other two in that it is used when the researcher wants to neutralize the effect of a continuous independent variable in the experiment.
		ANCOVA is used to neutralize the effect of the more powerful, non-interacting variable.
		ANCOVA is applied correctly when the neutralized independent variable is measured on a continuous scale.
	www-users.cs.umn.edu /~ludford/Stat_Guide/ANCOVA.htm (438 words)

	Categorical and Continuous Models 2
		A secondary goal of using ANCOVA is to adjust (between) cell means for differences in the covariate.
		ANCOVA will let us do this, that is, to control for differences in cognitive ability to reduce the within cell variability.
		ANCOVA doesn't do its job if there is an interaction between the treatment (categorical variable) and the covariate (continuous variable).
	luna.cas.usf.edu /~mbrannic/files/regression/catcon2.html (2266 words)

	Statistics Solutions : Analysis of Variance (ANOVA)
		Analysis of covariance (ANCOVA) is used to test the main and interaction effects of categorical variables on a continuous dependent variable, controlling for the effects of selected other continuous variables which covary with the dependent.The control variable is called the "covariate." There may be more than one covariate.
		ANCOVA uses built-in regression using the covariates to predict the dependent, then does an ANOVA on the residuals (the predicted minus the actual dependent variables) to see if the factors are still significantly related to the dependent variable after the variation due to the covariates has been removed.
		Like other control procedures, ANCOVA can be seen as a form of "what if" analysis, asking what would happen if all cases scored equally on the covariates, so that the effect of the factors over and beyond the covariates can be isolated.
	www.statisticssolutions.com /ANOVA.htm (9826 words)

	ANCOVA
		ANCOVA is robust against violations of additivity but in severe violations the researcher may transform the data, as by using a logarithmic transformation to change a multiplicative model into an additive model.
		Note, however, that ANCOVA automatically handles interaction effects and thus is not an additive procedure in the sense of regression models without interaction terms.
		If the covariate is influenced by the categorical independents, then the control adjustment ANCOVA makes on the dependent variable prior to assessing the effects of the categorical independents will be biased since some indirect effects of the independents will be removed from the dependent.
	www.lehigh.edu /~wh02/ancova.html (953 words)

	XLSTAT, Statistical software für MS Excel - Statistik und Datenanalyse mit Excel : Einführungen : Wie mache ich eine ...
		Using the Analysis of Covariance (ANCOVA), we want to find out how the weight of the children varies with their gender (a qualitative variable that takes value f or m), their height and their age, and to verify if a linear model makes sense.
		The ANCOVA method belongs to a larger family of models called GLM (Generalized Linear Models) as do the linear regression and the ANOVA.
		The specificity of ANCOVA is that it mixes qualitative and quantitative explanatory variables.
	www.xlstat.com /de/support/tutorials/anco.htm (1120 words)

	BioMed Central \| Full text \| Parametric versus non-parametric statistics in the analysis of randomized trials with ...
		ANCOVA was generally superior to Mann-Whitney in most situations, especially where log-transformed data were entered into the model.
		ANCOVA appears to be unbiased where the treatment effect is a shift.
		It has been argued [19] that ANCOVA with baseline scores should not be used for non-randomized trials on the grounds where baseline scores are not expected to be equivalent.
	www.biomedcentral.com /1471-2288/5/35 (4344 words)

	ANCOVA
		ANCOVA is used to increase power in a one-way or two-way ANOVA by adding a second or third variable as a covariate.
		The error term thus is broken into the amount of variance by the covariate X and the residual, smaller error (eij) that doesn't depend on the covariate.
		In ANCOVA, the dependent variable is adjusted statistically to remove the effects of the portion of uncontrolled variation represented by the covariate.
	carbon.cudenver.edu /~lsherry/rem/ancova.html (715 words)

	The International Electronic Journal of Health Education
		Analysis of covariance (ANCOVA) was used to test whether levels on the independent variables (friendship variables) differed with respect to the dependent variables (physical activity variables).
		The following variables were used as covariates and statistically controlled for in ANCOVA tests: grade, age, mother’s highest level of education, father’s highest level of education, urban or rural residence, subjective family affluence, times vacationing with family in the past year, and family car ownership.
		ANCOVA testing was also conducted to determine whether boys differed from girls on dependent measures.
	www.aahperd.org /iejhe/template.cfm?template=2005/page.html (4182 words)

	ANCOVA (Site not responding. Last check: 2007-10-25)
		That is, in ANCOVA we look at the effects of the categorical independents on an interval dependent, after effects of interval covariates are controlled.
		ANCOVA assumes sphericity, which is when the variance of the difference between the estimated means for any pair of different groups is the same as for any other pair.
		Sphericity is tested because ANCOVA repeated measures designs are sensitive to this violation of assumptions -- that is, to a spherical within-subjects covariance matrix.
	www.public.asu.edu /~hyanik/as/ancova.htm (1168 words)

	ANCOVA — AFNI and NIfTI Server for NIMH/NIH/PHS/DHHS/USA/Earth
		There are basically three assumptions in ANCOVA: (1) linearity of regression- linear relation between percent signal change and the covariate; (2) exact measurement of the covariate; (3) the covariate is independent of all factors (independent variables), and does not correlate highly with other covariates.
		To account for subject variability in group analysis, it is recommended the user run a one-way ANCOVA for each contrast or simple effect separately, similar to its counterpart of two-sample t test or one-sample t test with 3dttest.
		Without this variable added in the model ANCOVA would bear an assumption of homogeneity of regression in which two parallel lines are separated vertically by the main effect of each group.
	afni.nimh.nih.gov /sscc/gangc/ANCOVA.html (1278 words)

	PROPHET StatGuide: Examining ANCOVA results to detect assumption violations
		The resulting ANCOVA loses some power compared to the corresponding one-way ANOVA using only the group levels, due to the loss of a degree of freedom for the estimate of the common regression slope.
		You should bear in mind that a nonsignificant P value for the test of all slopes equal to 0 does not guarantee that the slopes are in fact equal to 0.
		The one-way ANCOVA's test of equality of intercepts tests the hypothesis that all the treatment (group) means are the same, given that the slopes of the treatment (group) regression lines are equal.
	www.basic.northwestern.edu /statguidefiles/ancova_exam_res.html (1331 words)

	ANCOVA
		ANCOVA (ANalysis of COVAriance) spája prvky analýzy rozptylu (ANOVA) a viacnásobnej regresie.
		ANCOVA si kladie rovnaké poiadavky ako ANOVA a viacnásobná regresia.
		Tradièná ANCOVA okrem toho predpokladá, e regresný koeficient β je rovnaký vo vetkých skupinách, teda neexistuje interakcia intervalového a nominálneho faktora.
	rimarcik.com /navigator/ancova.html (320 words)

	Directory of open access journals
		The objectives of this study were: a) to compare the relative power of Mann-Whitney and ANCOVA; b) to determine whether ANCOVA provides an unbiased estimate for the difference between groups; c) to investigate the distribution of change scores between repeat assessments of a non-normally distributed variable.
		ANCOVA was generally superior to Mann-Whitney in most situations, especially where log-transformed data were entered into the model.
		ANCOVA is the preferred method of analyzing randomized trials with baseline and post-treatment measures.
	www.doaj.org /abstract?id=124849&toc=y (267 words)

	Outcomes: ANCOVA vs difference scores
		If your results are not large and "robust" enough to test-out the same regardless how you test, then it matters that you can tell which Outcome is appropriate.
		Much of what you say about ANCOVA with heterogeneous slopes is correct.
		The reservation I have about your statement derives from what I perceive as excessive reliance on the F test for unequal slopes to decide about what model to use in approaching the data.
	www.pitt.edu /~wpilib/statfaq/97anocha.html (1498 words)

	Ancova #1
		The analysis of covariance (Ancova) is really nothing more than what we have been doing all along.
		Then when I ran my Ancova, I basically adjusted the Error means to what they would be if all subjects had the same NewDistract.
		An excellent discussion of Ancova, and the effects of group differences on the covariate, can be found in an excellent book by Huitema (1980) The analysis of covariance and alternatives.
	www.uvm.edu /~dhowell/gradstat/psych341/lectures/Ancova-Uneq/Covar1.html (2856 words)

	[No title]
		The homogeneity of variances/covariances assumption implies that we perform this regression analysis subject to the constraint that all regression equations (slopes) across the cells of the design are the same.
		General Regression Models: This chapter discusses the between subject designs and multivariate designs which are appropriate for stepwise regression as well as discussing how to perform stepwise and best-subset model building (for continuous as well as categorical predictors).
		Mixed ANCOVA and Variance Components: This chapter includes discussions of experiments with random effects (mixed model ANOVA), estimating variance components for random effects, or large main effect designs (e.g., with factors with over 100 levels) with or without random effects, or large designs with many factors, when you do not need to estimate all interactions.
	www.statsoft.com /textbook/stanman.html (5994 words)

	[No title]
		How to Enter Data for ANCOVA There should be one row of the worksheet for each observation, containing the values of each response variable, the level of each factor, and the values of each covariate.
		How to Specify the Model in ANCOVA The model on the ANCOVA line is exactly the same as in the ANOVA command.
		Errorterm is a term in the model to be used as the denominator for the F-test.
	www.uic.edu /classes/idsc/ids571/ids474/mtbhelp/ancova.txt (1084 words)

	TERMS.HTM (Site not responding. Last check: 2007-10-25)
		Most analysts would say the name ANCOVA should be used only when the model does not include interactions between the covariates and the factor of interest.
		Thus, a strict ANCOVA model is a "parallel slopes" model, so that the regression coefficients for the covariates are the same for all factor levels.
		When an author says that an ANCOVA model was fitted, assume no allowance was made for an interaction between the factor and covariates unless there is a statement to the contrary.
	www.tufts.edu /~gdallal/TERMS.HTM (334 words)

	st: ANCOVA for pre post designs
		It has been suggested that in a randomized clinical trial design with baseline (B) and followup (F) test measures comparing a control and treatment group (G), performing an ANOVA on the ratio pre/post is the worst choice of the 4 ways to deal with baseline differences:
		Then, method (4) says to analyze group difference by the regression (ANCOVA) model, prepulse = constant + b1startle + b2group, and in Stata, this would be "anova prepulse group startle, continuous(startle)".
		The usual ANOVA on %PPI by method (3) would be "anova ppi group".
	www.stata.com /statalist/archive/2003-12/msg00612.html (564 words)

	Global Market Research & Consulting, Growth Strategies - Full Service Research: RONIN Corporation
		To assess differences in the average number of hours spent on the Internet among PC owners in four countries, while controlling for access speed, ANCOVA would be an appropriate analytic tool.
		ANCOVA is particularly useful in research situations where a variable, such as income, gender, education, or age, can potentially obscure or bias the results.
		The method is useful for research studies where there are a variety of segments being assessed on a number of different measures, where one or more variables needs to be controlled for that may potentially bias the results.
	www.ronin.com /full_service_research.htm (1750 words)

	Analysis of covariance
		Analysis of covariance (ancova) is used when you have two measurement variables and one attribute variable.
		Using ancova is a statistical way of making it as if all the mussels were the same size, then comparing the mean AAM length of the average-sized mussel.
		The final test in the ancova is to test the null hypothesis that all of the Y-intercepts of the regression lines with a common slope are the same.
	udel.edu /~mcdonald/statancova.html (873 words)

	Multivariate Analysis UCR Sociology 203A ANCOVA
		The ancova model is a very frequently used tool, because models with both continuous and categorical independent variables are often necessary to analyze data arising from both experimental and non-experimental studies.
		Using ancova, we are able to test whether the treatment variable has significant effects on the dependent variable "adjusted" for differences between groups in covariates.
		The ANCOVA model can be expanded to any degree of complexity on the right-hand side, limited only by the data and the ability of the analyst to interpret the results.
	faculty.ucr.edu /~hanneman/soc203a/ancova.html (2982 words)

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