Assumptions ANCOVA

The underlying assumptions for ANCOVA are fairly rigid and restrictive. 

One disadvantage of ANCOVA is that the modelling does involve a number of assumptions and if those assumptions are not valid then the approach could mislead. For example, it is assumed (usually) that the covariates affect outcome in a linear way there is invariably too little information in the data to be able to assess this assumption in any effective way. In contrast, with an adjusted analysis, assumptions about the way in which covariates affect outcome are not made and in that sense it can be seen as a more robust approach. In some regulatory circles adjusted analyses are preferred to ANCOVA for these reasons. 

The t-tests and their extensions ANOVA, ANCOVA and regression all make assumptions about the distribution of the data in the background populations. If these assumptions are not appropriate then strictly speaking the p-values coming out of those tests together with the associated confidence intervals are not valid. 

B observations in each of several centres) and also with more complex structures which form the basis of ANCOVA and regression. For example, in regression the assumption of normality applies to the vertical differences between each patient s observation y and the value of y on the underlying straight line that describes the relationship between x andy. We therefore look for the normality of the residuals the vertical differences between each observation and the corresponding value on the fitted line. 

In any study, it is important that researchers first establish whether or not their data demonstrate a relationship between POP tissue concentration and tissue lipid levels. This is seldom done, as it is typically assumed that such a relationship must exist for lipophilic contaminants. As is compellingly demonstrated by Hebert and Keenley-side47 in their paper To normalize or not to normalize Fat is the question , such assumptions can lead to lipid normalized POP concentrations that are completely at odds with measured wet weight POP values. Further, since factors other than total lipid (such as differences in lipid class, for example) can affect POP levels in organisms, simple ratios (e.g. ng POP/ng lipid) are often inadequate and may actually increase data variability. In many cases, analysis of covariance (ANCOVA) may prove to be a more appropriate method for lipid normalization of POP concentrations47. 

The assumptions made regarding data collection for ANOVAs and ANCOVAs are similar to those for /-tests— the samples have been randomly selected from the population, the population and populations of the samples are normally distributed, and the variances and standard deviations of the subgroups are homogeneous. As with /-tests, ANOVAs and ANCOVAs are relatively robust with respect to non-normality and are relatively robust to heterogeneity of variances when the sample sizes are the same within each subgroup 19). 

In order to assess the impact of contextual control variables on the endogenous constructs, an analysis of covariance (ANCOVA) was conducted for each dependent variable (customer orientation, domain-specific innovativeness, opinion leadership) and each model (with and without empathy as predictor variable), which results in six different analyses. All assumptions for conducting ANCOVAs were met (Keselman et al. 1998 Owen and Froman 1998). The models included the original, hypothesized relationships (covarlates) and control variables for firm and department affiliation (fixed factors 3 firms, 5 department groups (product management, sales, marketing, R D, other)). Only direct effects were modeled. The results of the analyses are shown in Table 20. 

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