Analysis of Covariance (ANCOVA)

Research Design

The simplest application of this model involves one grouping variable (G) having two levels (e.g., a herbal supplement treatment vs. a placebo), a single outcome variable (Y) (e.g., blood pressure) and a single nuisance variable, referred to as a covariate (X) (e.g., body mass index [BMI]) measured before the formation of the groups or before the start of the treatments. While the application of the model is identical when groups are formed using a random or nonrandom process, the primary purpose and the interpretation of the results are substantially different. When the formation of the groups is based on a random process (e.g., use of random numbers matched with participant identification numbers to assign individuals to [Page 16]treatment levels), the research design is referred to as an experiment and is often represented as follows:

where R represents the random assignment of units to the treatment groups; X is a covariate; G1 and G2 represent intervention and placebo groups, respectively; and Y is the outcome of interest. When group formation is based on a nonrandom process (e.g., self-selection) the research design is referred to as a quasi-experiment and is often represented as follows:

where terms are defined as above.

Data Example

Suppose a sample of 12 overweight patients having high systolic blood pressure volunteered to investigate the usefulness of a herbal supplement over a 2-month trial period. Half of the volunteers are randomly assigned to receive the herbal supplement, while the other half are given a placebo. Before beginning the investigation, each individual's BMI is computed. When the treatment period ends, systolic blood pressure is assessed. Table 1 presents hypothetical data along with means and standard deviations (SDs). These data will be used to demonstrate the use and interpretation of the ANCOVA model.

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