Analysis of covariance (ANCOVA): what it is and how it is used in statistics

The field of statistics uses 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).

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

• Related article: "Analysis of Variance (ANOVA): what it is and how it is used in statistics"

applied statistics

Statistics is the science that encompasses all the knowledge, strategies and tools that allow collecting, organizing, presenting, analyzing and interpreting a series of data. It is used especially in research contexts.

In psychology, it is studied more and more throughout the degree, since it is considered a very interesting tool to know, and especially useful, if we want to dedicate ourselves to research.

This science aims to describe the results obtained in an investigation

, as well as analyze them or help us make decisions. In psychology, it is often used to study and develop different treatments and therapies.

Statistic Types

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

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

Analysis of covariance: what is it?

The analysis of covariance (ANCOVA) is a technique used in statistics, and specifically it is a parametric test. Parametric tests within statistics allow you to analyze factors within a population. In addition, they allow quantifying to what extent two variables are independent.

The acronym ANCOVA stands for “ANalysis of COVAriance”. Actually, ANCOVA combines two types of strategies: Analysis of Variance (ANOVA) together with Regression Analysis.

Here we must remember that ANOVA is another statistical technique that segregates from the total variability of our results, the part due to sources of error; Thus, in addition to being an error control technique, it discovers the influence of the treatments.

For its part, the analysis of covariance is also a statistical technique, but more complete than ANOVA; Like her, it is used to reduce the experimental error, but in addition, it applies a multiple linear regression (statistical regression) to the results.

• You may be interested in: "Chi-square (χ²) test: what it is and how it is used in statistics"

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 us away from the true changes that we are searching. Thus, the experimental error includes those deviations in the results with respect to the real value of the magnitude that is being studied.

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

Specifically, the analysis of covariance consists of a statistical procedure by which manages to eliminate the heterogeneity that appears in the variable that 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 we will explain what covariates consist of, how they can alter the results of an investigation and why the analysis of covariance is useful in these cases.

Functioning

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 later, a multiple linear regression is applied to them; this implies that the effect that the covariates (independent variables) had on the dependent variable (that is, 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 the 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 they are not due to the treatment.

This means that when X varies, Y also varies; Furthermore, this variation of X will also affect the influence that the treatments have on Y. All this makes us interested in eliminating these influences (experimental errors), because they alter the results; and this is achieved by 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 will correctly identify the impact that a treatment has on the outcomes that we are studying.

For serving us? Goals

The analysis of covariance is used for the following purposes: on the one hand, to eliminate any systematic error that may bias the results of an investigation (these errors generally occur because they are outside the control of the investigator), and by the other, establish the differences in the answers of the 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 that the analysis of covariance gives us is a corrected score from which the amount or value attributable to the foreign variable has been subtracted.

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

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

Fields of application

Analysis of covariance It is applied fundamentally in the field of applied statistics. That is why it is frequently used in research; however, the type of research in which it can be used varies, and it can be educational, clinical, agricultural, health research, etc.

Examples (applications)

Analysis of covariance allows us to study, for example, the relationship between age (covariate) and Anxiety levels (dependent variable) by states (treatments), within a psychology investigation clinic.

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