# 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 that we obtain in a research. One of them is analysis of covariance (ANCOVA).

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

## Applied statistics

Statistics is the science that encompasses all the knowledge, strategies and tools that allow us to collect, organize, present, analyze and interpret a series of data. It is used in particular in research contexts.

In psychology, it is studied more and more throughout the career, because it is considered as a very interesting tool to know, and especially useful, if one wishes to embark on research.

This science aims to describe the results obtained in a research, In addition to analyzing them or helping 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 relates to the sample) and inferential statistics (where information is extracted about the population).

One type of technique widely used in statistics is analysis of covariance, which eliminates the systematic error that affects our results. But it’s a little more complex than that; we will explain it in detail throughout the article.

## Analysis of covariance: what is it?

Analysis of covariance (ANCOVA) is a technique used in statistics, and more particularly it is a parametric test. Parametric tests within statistics are used to analyze factors within a population. In addition, they make it possible to quantify the extent to which 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 regression analysis.

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

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

## Error checking technique

In research, it is very important to control for sources of experimental error (which appear due to strange variables), as they can alter our results and stray away from the actual changes we are looking for. Thus, the experimental error includes these deviations in the results compared to the real value of the quantity studied.

There are two types of techniques which seek to reduce experimental error.: A priori techniques (used before application of processing and data collection) and a posteriori techniques (used once the data has been obtained). The analysis of covariance belongs to the second type and is used when we already have the data of our research.

More precisely, the analysis of covariance 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, e.g. anxiety levels), due to the influence of one (or more) independent variables, which are quantitative, and which we will call covariates (e.g. therapy at different degrees of d ‘intensity).

Later, we will explain what covariates are, how they can affect the results of a search, and why the analysis of covariance is useful in these cases.

## surgery

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

Covariates (X) are characteristics or measures of each experimental or participating unit, Which do not depend on treatments (independent variables), but which are linked to the measure of interest (I) (dependent variable). In other words, they have an effect or an influence on what we are studying, but they are not due to the treatment.

This makes that, by varying X, also varies I; moreover, this variation of X will also affect the influence of the treatments on Y. All this interests us in eliminating these influences (experimental errors), Because they change the results; and this is achieved by 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 of a treatment on the outcomes we are studying.

## What is it for us? targets

The analysis of covariance is used for the following purposes: on the one hand, to eliminate any systematic error that could bias the results of a survey (these errors generally occur because they are beyond the control of the researcher), and d ‘somewhere else, establish differences in the responses of research participants due to their personal characteristics.

This leads the analysis of covariance to be used to differentiate between treatments, for example.

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

The analysis of covariance allows increase the precision of the experiments and eliminate the effects of variables that have nothing to do with the treatmentBut they always influence the results.

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

## Application areas

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

### Examples (applications)

Analysis of covariance makes it possible to study, for example, the relationship between age (covariate) and anxiety levels (dependent variable) by condition (treatments), in the context of 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 the same would be if we want to study the relationship between the size of the tomato (covariable ) and the yield per hectare of our garden (dependent variable) according to the variety of tomato (different treatments).

#### Bibliographical references:

• Amon, J. (2006). Statistics for psychologists II: probability, inferential statistics. Madrid: Pyramid.
• Badii, MH, Castell, J. and Wong, A. (2008). Use of analysis of covariance (ANCOVA) in scientific research. Business innovations, 5 (1): 25 – 38.
• Ferguson, GA (1989). Statistical analysis in education and psychology. Madrid: Anaya.