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

**What is analysis of covariance (ANCOVA) and how is it used in scientific research?**

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).**.

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

## Applied statistics

Statistics is the science that encompasses all the knowledge, strategies and tools that make it possible to collect, organize, present, analyze and interpret a series 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 engage in research.

**This science aims to describe the results obtained in a research, as well as to analyze them or to help us**and analyze them or help us to make decisions. In psychology, it is usually 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 extracts information about the population).

One type of technique widely used in statistics is the analysis of covariance. **analysis of covariance, 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.

## 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 in statistics make it possible to analyze factors within a population. They also allow to quantify the extent to which two variables are independent.

The acronym ANCOVA stands for "ANalysis of COVAriance". In fact, ANCOVA combines two types of strategies: Analysis of Variance (ANOVA) 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 variance.**Thus, in addition to being an error control technique, it uncovers the influence of the treatments.

Analysis of covariance is also a statistical technique, but more complete than ANOVA; like ANOVA, it is used to reduce experimental error, but it also applies 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 extraneous variables), since they can alter the results and lead us away from the true changes we are looking for. Thus, experimental error includes those deviations in the results with respect to the true value of the quantity being studied.

**The techniques that seek to reduce experimental error can be of two types**The two types of techniques are: a priori techniques (used before applying the treatments and collecting the data) and a posteriori techniques (used once the data have been 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 it is possible to eliminate the heterogeneity that appears in the data. **the heterogeneity that appears in the variable that we are studying (being a dependent variable** (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 are, how they can alter the results of an investigation, and why analysis of covariance is useful in these cases.

## Function

The theoretical basis of the analysis of covariance is as follows (or "steps" to be followed): first an analysis of variance is applied to the data (ANOVA), and then a multiple linear regression is applied to the same data, **a multiple linear regression is applied to the data; this involves**This involves removing the effect that the covariates (independent variables) had on the dependent variable (i.e. the variable under study).

**Covariates (X) are characteristics or measurements of each experimental unit or participant, which do not depend on the treatments (X).**that 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 are not due to the treatment.

This means that when X varies, Y also varies; moreover, this variation in 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.**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 of a treatment on the outcomes we are studying.

## What is it useful for? Objectives

Analysis of covariance is used for the following purposes: on the one hand, to eliminate any systematic errors that may bias the results of an investigation (these errors generally occur because they are outside the researcher's control), and on the other hand, **to establish differences in the responses of research participants that are due to their personal characteristics.**.

This is why covariance analysis is used to establish differences 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 extraneous variable has been subtracted.

Analysis of covariance makes it possible to **to increase the precision of the experiments and to eliminate the effects of variables that have nothing to do with the treatment, but are nevertheless related to it.**but which are nevertheless 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

Analysis of covariance **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 can be used varies, and can be educational, clinical, agricultural, health, etc. research.

### 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 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 tomatoes (covariate) and the yield per hectare of our orchard (dependent variable) according to the variety of tomato (different treatments).

(Updated at Mar 28 / 2023)