Summary: Introduction to ANCOVA, its relationship to ANOVA, and how it accounts for covariates.
Learning Objectives:
Understand the concept of ANCOVA and its purpose in statistical analysis.
Learn how ANCOVA extends ANOVA by incorporating covariates to improve statistical power.
Identify situations where ANCOVA is appropriate and how to interpret its results.
ANCOVA (Analysis of Covariance) is a statistical method used to determine if there is a significant difference between the means of three or more independent groups, similar to ANOVA. However, ANCOVA incorporates one or more covariates, which help in understanding how a factor influences a response variable while accounting for the covariate(s).
ANCOVA is commonly employed when there are baseline group differences, as well as in pretest/posttest analyses where regression to the mean affects the posttest measurement. It is also utilized in non-experimental research, such as surveys, and in quasi-experimental designs where random assignment of study participants is not possible. However, the latter application of ANCOVA is not universally recommended.
Similar to regression analysis, ANCOVA allows examination of how an independent variable acts on a dependent variable. It removes the effects of covariates, which are variables not of primary interest in the study. For instance, if the aim is to investigate how different levels of teaching skills affect student performance in math, it may not be feasible to randomly assign students to classrooms. In this case, systematic differences between students in different classes, such as varying initial math skill levels between gifted and mainstream students, need to be taken into account.
As an extension of ANOVA, ANCOVA can be used in two ways:
The assumptions for ANCOVA are essentially the same as those for ANOVA. Before conducting the test, it is necessary to ensure the following (Leech etal, 2013: 141)
Software tools can typically verify the following assumptions:
Example: Consider the previous example of splitting a class of 90 students into three groups, each using a different studying technique for one month to prepare for an exam. To account for the students' current grade in the class, their grade is used as a covariate in an ANCOVA. The aim is to determine if there is a significant difference in mean exam scores between the three groups. By conducting the ANCOVA, it becomes possible to examine whether the studying technique has an impact on exam scores after removing the influence of the covariate. Thus, if a statistically significant difference in exam scores is found among the three studying techniques, it can be concluded that this difference exists even after considering the students' current grade in the class.
Example 1: Assessing the Effect of a Teaching Intervention on Test Scores while Controlling for a Covariate
Suppose you are conducting a study to evaluate the effectiveness of a teaching intervention designed to improve student test scores in a mathematics class. However, you suspect that the students' prior mathematical ability, as measured by a pre-test score, may influence their post-test scores. To account for this potential confounding factor, you collect data on both the pre-test score and the post-test score for each student.
To analyze the data using ANCOVA, you would consider the post-test score as the dependent variable, the teaching intervention as the independent variable, and the pre-test score as the covariate. ANCOVA allows you to determine whether there is a significant difference in the post-test scores among the different teaching intervention groups, while adjusting for the influence of the pre-test scores. If the p-value is below a predetermined significance level (e.g., 0.05), you can conclude that the teaching intervention has a significant effect on the post-test scores, even after accounting for the influence of the pre-test scores.
Example 2: Examining the Impact of a Drug Treatment on Blood Pressure while Controlling for a Covariate
Let's say you are interested in studying the effect of a new drug treatment on blood pressure in patients with a specific medical condition. However, you suspect that age may be a confounding factor, as it is known to be associated with blood pressure. Therefore, you collect data on both the patients' blood pressure measurements and their age.
To analyze the data using ANCOVA, you would consider the blood pressure measurement as the dependent variable, the drug treatment as the independent variable, and age as the covariate. ANCOVA allows you to determine whether there is a significant difference in blood pressure among the different drug treatment groups, while adjusting for the influence of age. If the p-value is below a predetermined significance level (e.g., 0.05), you can conclude that the drug treatment has a significant effect on blood pressure, even after accounting for the influence of age.
In both examples, ANCOVA enables you to assess the relationship between an independent variable and a dependent variable, while controlling for the influence of a covariate. It helps you understand the effect of the independent variable on the dependent variable, while taking into account the potential confounding effect of the covariate.
