UNDERSTANDING ANALYSIS OF COVARIANCE (ANCOVA)In general, research is conducted for the purpose of explaining the effects of the independentvariable on the dependent variable, and the purpose of research design is to provide a structurefor the research. In the research design, the researcher identifies and controls independentvariables that can help to explain the observed variation in the dependent variable, which in turnreduces error variance (unexplained variation). Since the research design is structured before theresearch begins, this method of control is called experimental control.Research design – the science (and art) of planning procedures for conductingstudies so as to get the most valid findings. Called “design” for short. Whendesigning a research study, one draws up a set of instructions for gatheringevidence and for interpreting it. Experiments, quasi-experiments, double-blindprocedures, and correlated groups design are examples of types of research design(Vogt, 1999).Control for – to subtract statistically the effects of a variable (a control variable)to see what a relationship would be without it (Vogt, 1999).Hold constant – to “subtract” the effects of a variable from a complexrelationship so as to study what the relationship would be if the variable were infact a constant. Holding a variable constant essentially means assigning it anaverage value (Vogt, 1999).In addition to controlling and explaining variation through research design, it is also possible touse statistical control to explain variation in the dependent variable. Statistical control, usedwhen experimental control is difficult, if not impossible, can be achieved by measuring one ormore variables in addition to the independent variables of primary interest and by controlling thevariation attributed to these variables through statistical analysis rather than through researchdesign. The analysis procedure employed in this statistical control is analysis of covariance(ANCOVA).Statistical control – using statistical techniques to isolate or “subtract”variance in the dependent variable attributable to variables that are not the subjectof the study (Vogt, 1999).Analysis of Covariance (ANCOVA) – an extension of ANOVA that providesa way of statistically controlling the (linear) effect of variables one does not wantto examine in a study. These extraneous variables are called covariates, or controlvariables. (Covariates should be measured on an interval or ratio scale.) ANCOVAallows you to remove covariates from the list of possible explanations of variancein the dependent variable. ANCOVA does this by using statistical techniques(such as regression to partial out the effects of covariates) rather than directexperimental methods to control extraneous variables. ANCOVA is used inexperimental studies when researchers want to remove the effects of someantecedent variable. For example, pretest scores are used as covariates in pretest-posttest experimental designs. ANCOVA is also used in non-experimentalresearch, such as surveys or nonrandom samples, or in quasi-experiments whensubjects cannot be assigned randomly to control and experimental groups.Although fairly common, the use of ANCOVA for non-experimental research iscontroversial (Vogt, 1999).A one-way analysis of covariance (ANCOVA) evaluates whetherpopulation means on the dependent variable are the same across levels of a factor(independent variable), adjusting for differences on the covariate, or more simplystated, whether the adjusted group means differ significantly from each other.With a one-way analysis of covariance, each individual or case must have scoreson three variables: a factor or independent variable, a covariate, and a dependentvariable. The factor divides individuals into two or more groups or levels, whilethe covariate and the dependent variable differentiate individuals on quantitativedimensions. The one-way ANCOVA is used to analyze data from several types ofstudies; including studies with a pretest and random assignment of subjects tofactor levels, studies with a pretest and assignment to factor levels based on thepretest, studies with a pretest, matching based on the pretest, and randomassignment to factor levels, and studies with potential confounding (Green &Salkind, 2003).The analysis of covariance (ANCOVA) is typically used to adjust or controlfor differences between the groups based on another, typically interval level,variable called the covariate. The ANCOVA is an extension of ANOVA thattypically provides a way of statistically controlling for the effects of continuous orscale variables that you are concerned about but that are not the focal point orindependent variable(s) in the study. For example, imagine that we found thatboys and girls differ on math achievement. However, this could be due to the factthat boys take more math courses in high school. ANCOVA allows us to adjust themath achievement scores based on the relationship between number of mathcourses taken and math achievement. We can then determine if boys and girls stillhave different math achievement scores after making the adjustment (Leech,Barrett, & Morgan, 2005).STATISTICAL CONTROL USING ANCOVAAnalysis of covariance is used primarily as a procedure for the statistical control of anextraneous variable. ANCOVA, which combines regression analysis and analysis of variance(ANOVA), controls for the effects of this extraneous variable, called a covariate, bypartitioning out the variation attributed to this additional variable. In this way, the researcher isbetter able to investigate the effects of the primary independent variable. The ANCOVA F testevaluates whether the population means on the dependent variable, adjusted for differences onthe covariate, differ across levels of a factor. If a factor has more than two levels and the F issignificant, follow-up tests should be conducted to determine where there are differences on theadjusted means between groups. For example, if a factor has three levels, three pairwisecomparisons among the adjusted means can be