Covariates ANCOVA

In studies in which there are important prognostic factors accounting for them as part of the analysis can be important in increasing the precision with which treatment effects can be estimated. Such analyses generally involve the use of an analysis of covariance (ANCOVA) type of approach. 

This technique is called analysis of covariance (ANCOVA) and size of the primary tumour is termed the covariate. Taking account of the covariate here has led to a much more powerful analysis than that provided by the simple unpaired t-test. Of course the main reason why we are seeing such an improvement in sensitivity is that the covariate is such a strong predictor of outcome. These improvements will not be quite so great with weaker predictors. 

A11 F values, except total cerebral volume, are for analysis of covariance (ANCOVA) using total cerebral volume as a covariate. Adapted from Kumra et al. (2000)... 

Equally important is the use of suitable quantitative statistical analyses, including more complicated models, because they can hold certain variables constant, control for artifacts, and provide supplementary information. Whatever statistics are used, they should be explicitly described in sufficient detail so the reader knows exactly what was done and can make a judgment about their appropriateness. For example, there are many different types of analyses of variance (ANOVA), analyses of covariance (ANCOVA), or multivariate analyses of variance (MANOVA), and some are not appropriate to the task at hand. If only the results of an ANOVA with a p < 0.001 are provided, the reader should be justifiably dubious, because this model may not be proper ( p is an estimate of the probability that the results occurred by chance). Sufficient details are required to clarify which model was used, because the p value may be invalid with an inappropriate model. 

Analysis of Covariance (ANCOVA) for Testing Similarity of Slopes The first step is determining whether or not the degradation rates for all batches behave in a similar fashion. The following hypothesis will be tested ... 

Analysis of covariance (ANCOVA) reverses drug-induced depression of the CNS. Statistical method to determine if two or more related dependent variables exposed to two or more related variables differ significantly from chance. 

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. 

Analysis of covariance (ANCOVA) employs both analysis of variance (ANOVA) and regression analyses in its procedures. In the present author s previous book Applied Statistical Designs for the Researcher), ANCOVA was not reported mainly because it presented statistical analysis that did not require the use of a computer. For this book, a computer with statistical software is a requirement hence, ANCOVA is discussed here, particularly because many statisticians refer to it as a special t5q>e of regression. 

In regression models, the independent variables are usually quantitative or continuous variables. When the independent variables consist of all qualitative (grouped or categorical) variables, the model is the ANOVA model. When the independent variables consist of both qualitative variables and quantitative variables, the model is the analysis of covariance (ANCOVA) model. The next section illustrates the ANOVA model. 

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. 

By analysis of covariance (ANCOVA), we evaluated the effects of sociodemographic variables on psychometric tests. 

---