The field of statistics employs many techniques that allow us to analyze, control and adjust the data we obtain in an investigation. One of them is the analysis of covariance (ANCOVA) .

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This statistical technique uses, in turn, two strategies: analysis of variance (ANOVA) and statistical regression. It is part of the techniques for controlling experimental error. In this article we will know what it consists of and how it works.

Applied statistics

Statistics is the science that encompasses all the knowledge, strategies and tools that enable the collection, organization, presentation, analysis and interpretation of data. It is used especially in research contexts .

In psychology, it is increasingly studied throughout the career, as it is considered a very interesting tool to know, and especially useful, if we want to devote ourselves to research.

This science aims to describe the results obtained in an investigation , as well as to analyse them or help us make decisions. In psychology, it is often used to study and develop different treatments and therapies.

Types of statistics

There are descriptive statistics (where the information extracted is about the sample) and inferential statistics (which extract information about the population).

One type of technique widely used in statistics is covariance analysis, which allows us to eliminate the systematic error that is altering our results . But it is a bit more complex than this; we will explain it in detail throughout the article.

Covariance analysis: what is it?

Covariance analysis (ANCOVA) is a technique used in statistics, and specifically is a parametric test . Parametric tests within statistics allow the analysis of factors within a population. Furthermore, they allow quantifying to what extent two variables are independent.

The acronym ANCOVA comes from “ANalysis of COVAriance”. In fact, ANCOVA combines two types of strategies: Analysis of Variance (ANOVA) and Analysis of Regression.

Here we must remember that the ANOVA is another statistical technique that separates from the total variability of our results , the part due to sources of error; thus, in addition to being a technique for controlling error, it discovers the influence of treatments.

Covariance analysis is also a statistical technique, but more complete than ANOVA; like ANOVA, it is used to reduce experimental error, but in addition, it applies a multiple linear regression (statistical regression) to the results.

Error control technique

In research it is very important to control the sources of experimental error (which appear due to strange variables), since they can alter the results and move away from the true changes we are looking for. Thus, experimental error includes those deviations in the results with respect to the real value of the magnitude being studied.

The techniques that seek to reduce the experimental error, can be of two types : a priori techniques (used before applying the treatments and collecting the data) and a posteriori techniques (used once the data are obtained). Covariance analysis belongs to the second type, and is used when we already have the data from our research.

Specifically, covariance analysis consists of a statistical procedure by which manages to eliminate the heterogeneity that appears in the variable we are studying (this being a dependent variable; for example, anxiety levels), due to the influence of one (or more) independent variables, which are quantitative, and which we will call covariates (for example, therapy in different degrees of intensity).

Later on we will explain what covariates are, how they can alter the results of an investigation and why covariance analysis is useful in these cases.

Operation

The theoretical foundation of the analysis of covariance is the following (or “steps” to follow): first an analysis of variance is applied to the data (ANOVA), and then, a multiple linear regression is applied to the data ; this implies that the effect that the covariates (independent variables) had on the dependent variable (i.e., on the variable we are studying) is eliminated.

Covariates (X) are characteristics or measurements of each experimental unit or participant , which do not depend on treatments (independent variables), but are related to the measurement of interest (Y) (dependent variable). That is, they have an effect or influence on what we are studying, but are not due to the treatment.

This means that as X varies, so does Y; furthermore, this variation in X will also affect the influence that treatments have on Y. All this makes us interested in eliminating these influences (experimental errors) , because they alter the results; and this is achieved through the analysis of covariance.

A curious fact is that the more covariates we have, the less variability the data will have, and the more statistical power the test will have. Statistical power is the probability that a test correctly identifies the impact a treatment has on the results we are studying.

What’s it for? Objectives

Covariance analysis is used for the following purposes: on the one hand, to eliminate any systematic errors that may bias the results of a research (these errors generally occur because they are beyond the control of the researcher), and on the other, to establish the differences in the responses of research participants that are due to their personal characteristics .

This makes the analysis of covariance used to establish differences between treatments, for example.

The result given by the covariance analysis is a corrected score from which the amount or value attributable to the foreign variable has been subtracted.

Covariance analysis allows to increase the precision of the experiments and to eliminate the effects of variables that have nothing to do with the treatment , but that nevertheless are influencing the results.

In addition, it allows us to obtain more information about the nature of the treatments we are applying in our research. In short, it helps us to adjust our results to make them more reliable.

Areas of application

Covariance analysis is mainly applied in the field of applied statistics . This is why it is frequently used in research; however, the type of research in which it may be used varies, and may be educational, clinical, agricultural, health, etc. research.

Examples (applications)

Covariance analysis allows us to study, for example, the relationship between age (covariate) and anxiety levels (dependent variable) by states (treatments), within a clinical psychology research.

But, as we have seen, this technique can be used in other types of research, for example in agricultural research: a possible application of this technique would be if we want to study the relationship between the size of the tomatoes (covariate) and the yield per hectare of our orchard (dependent variable) according to the variety of the tomato (different treatments).

Bibliographic references:

  • Amon, J. (2006). Statistics for Psychologists II: Probability, Inferential Statistics. Madrid: Pirámide.
  • Badii, M.H., Castillo, J. & Wong, A. (2008). Use of Covariance Analysis (ANCOVA) in scientific research. Business Innovations, 5(1): 25 – 38.
  • Ferguson, G.A. (1989). Statistical analysis in education and psychology. Madrid: Anaya.