Multivariate analysis: types, examples, methods of analysis, purpose and results

2024 Author: Howard Calhoun | [email protected]. Last modified: 2023-12-17 10:16

Variance multivariate analysis is a combination of various statistical methods that are designed to test hypotheses and the relationship between the factors under study and certain features that do not have a quantitative description. Also, this technique allows you to determine the degree of interaction of factors and their influence on certain processes. All these definitions sound quite confusing, so let's understand them in more detail in our article.

Criteria and types of analysis of variance

The method of variance multivariate analysis is most often used to find the relationship between a continuous quantitative variable and nominal qualitative traits. In fact, this technique is a test of various hypotheses about the equality of various arithmetic samples. Thus, it canconsidered and as a criterion for comparing several samples. However, the results will be identical if only two elements are used for comparison. The study of the t-test shows that such a technique allows us to study the problem of hypotheses in more detail than any other known method.

It is also impossible not to note the fact that some types of analysis of variance are based on a certain law: the sum of squares of intergroup deviations and the sum of squares of intragroup deviations are absolutely equal. As a study, Fisher's test is used, which is used for a detailed analysis of intra-group variances. Although this requires the prerequisites for the normality of the distribution, as well as the homoscedasticity of the samples - the equality of the variances. As for the type of analysis of variance, the following are distinguished:

• multivariate or multivariate analysis;
• univariate or univariate analysis.

It is not difficult to guess that the second one considers the dependence of one feature and the value under study, and the first one is based on the analysis of several features at once. In addition, multivariate variance does not allow you to identify a stronger relationship between several elements, since the dependence of several values \u200b\u200bis investigated at once (although it is much easier to conduct the method).

Factors

Thought about the methods of multivariate correlation analysis? Then you should know that for a detailed study, you should study those factors that control the circumstances of the experiment and affect the final result. Also underfactors may imply methods and levels of processing values that characterize a particular manifestation of a particular condition. In this case, the figures are given in the ordinal or nominal measurement system. If there is a problem with grouping data, you have to resort to using the same numerical values, which slightly changes the final result.

It should also be understood that the number of observations and groups cannot be excessively large, because this leads to an excess of data and the inability to complete the calculation. At the same time, the method of grouping depends not only on the volume, but also on the nature of the variation of certain values. The size and number of intervals in the analysis can be determined by the principle of equal frequencies, as well as the same intervals between them. As a result, all received studies will be listed in the multivariate analysis statistics, which should be based on various examples. We will return to this in later sections.

Purpose of ANOVA

So, sometimes situations may arise when it is necessary to compare two or more different samples. In this case, it would be most logical to apply a multivariate correlation-regression analysis based on the study of the hypothesis and the relationship of various factors in the degree of regression. Also, the name of the technique indicates the fact that various components of the variance are used in the research process.

What is the essence of the study? ForFirst, two or more indicators are divided into separate parts, each of which corresponds to the action of a certain factor. After that, a number of research procedures are carried out to search for the relationship of various samples and the relationships between them. To understand such a complex but interesting technique in more detail, we recommend that you study several examples of multivariate correlation analysis given in the following sections of our article.

Example one

There are several automatic machines in the production workshop, each of which is designed to produce a specific part. The size of the produced element is a random variable, which depends not only on the settings of the machine itself, but also on random deviations that will inevitably occur as a result of the production of parts. But how can a worker determine the correct operation of the machine if he initially produces parts with defects? That's right, you need to purchase the same part on the market and compare its dimensions with what is obtained during production. After that, you can adjust the equipment so that it produces parts of the desired size. And it does not matter at all that there is a manufacturing defect, because it is also taken into account in the calculations.

At the same time, if there are certain indicators on the machines that allow you to determine the intensity of adjustment (X and Y axes, depth, and so on), then the indicators on all machines will be completely different. If the measurements turned out to be exactly the same, then the manufacturing defect can not betake into account at all. However, this happens extremely rarely, especially if the errors are measured in millimeters. But if the released part has the same dimensions as the standard purchased on the market, then there can be no question of any marriage, since in the production of the "ideal" a machine was also used, giving certain errors, which were probably also taken into account by the workers.

Second example

For the manufacture of a certain device that runs on electricity, it is necessary to use several types of different insulating paper: electrical, capacitor, and so on. In addition, the apparatus can be impregnated with resin, varnish, epoxy compounds and other chemical elements that extend the service life. Well, various leaks under the vacuum cylinder at elevated pressure are easily eliminated using the method of heating or pumping out air. However, if the master has previously used only one element from each list, various difficulties may arise in the production process using the new technology. Moreover, almost certainly, such a situation will be caused due to one element. However, it will be almost impossible to calculate which factor affects the poor performance of the device. That is why it is recommended to use not a multi-factor analysis method, but a single-factor one in order to quickly deal with the cause of the malfunction.

Of course, when using various tools and devices that track the influence of a particular factor onthe end result, the study is simplified at times, however, it will not be affordable for a novice engineer to acquire such units. That is why it is recommended to use one-way analysis of variance, which allows you to identify the cause of problems in a matter of minutes. To do this, it will be enough to set one of the most probable hypotheses in front of you, and then start proving it through experiments and analyzing the performance indicators of the device. Pretty soon, the wizard will be able to find the cause of the problems and fix it by replacing one of the selections with an alternative.

Third example

Another example of multivariate analysis. Suppose that a trolleybus depot can serve several routes during the day. On these same routes, trolleybuses of completely different brands operate, and 50 different controllers collect fares. However, the management of the depot is interested in how it is possible to compare several different indicators that affect the total revenue: the brand of the trolleybus, the efficiency of the route and the skill of the worker. To see the economic feasibility, it is necessary to analyze in detail the influence of each of these factors on the final result. For example, some supervisors may not be able to do their job well, so more responsible employees will have to be hired. Most passengers do not like to ride old trolleybuses, so it is best to use a new brand. However, if both of these factors go along with the fact that most of the routes are in high demand, then is it worth anything at all?change?

The task of the researcher is to use one analytical method to obtain as much useful information as possible about the influence of each of the factors on the final result. To do this, it is necessary to put forward at least 3 different hypotheses, which will have to be proved in various ways. Dispersion analysis allows solving such problems in the shortest possible time and obtaining maximum useful information, especially if a multiphase method is used. Keep in mind, however, that univariate analysis provides much more confidence in the influence of a given factor because it examines the sample in more detail. For example, if the depot directs all its efforts to analyzing the work of conductors, it will be possible to identify many unscrupulous workers on all routes.

One-way analysis

One-factor analysis is a set of research methods aimed at analyzing a certain factor for the final result in a particular case. Also, quite often, a similar technique is used to compare the greatest influence between two factors. If we draw an analogy with the same depot, then we should first analyze separately the impact of different routes and brands of trolleybuses on profitability, and then compare the results with each other and determine in which direction it would be best to develop the station.

In addition, do not forget about such a thing as a null hypothesis - that is, a hypothesis that does notcan be discarded and in any case it is influenced by all the factors listed to one degree or another. Even if we compare only the routes and brands of trolleybuses, the influence of the professionalism of the conductors still cannot be avoided. Therefore, even if this factor cannot be analyzed, the influence of the null hypothesis should not be forgotten. For example, if you decide to investigate the dependence of profit on the route, let the same conductor on the flight so that the readings are as accurate as possible.

Two-way analysis

Most often, this technique is also called the comparison method and is used to identify the dependence of two factors on each other. In practice, you will have to use various tables with accurate indicators so as not to get confused in your own calculations and the influence of factors on them. For example, you can run two completely different trolleybuses on two identical routes at the same time, neglecting the null hypothesis factor (choose two responsible conductors). In this case, the comparison of the two situations will be of the highest quality, since the experiment takes place at the same time.

Multivariate analysis with repeated experiments

This method is used in practice much more often than others, especially when it comes to a group of novice researchers. Repeated experience allows not only to be convinced of the influence of one or another factor on the final result, but also to find the mistakes that were made during the study. For example, most inexperienced analystsforget about the presence of one or more null hypotheses, which leads to inaccurate results during the study. Continuing the depot example, we can analyze the influence of certain factors in different seasons of the year, since the number of passengers in winter is very different from summer. In addition, repeated experience can lead the researcher to new ideas and new hypotheses.

Video and conclusion

We hope our article has helped you understand what the multivariate correlation analysis method is based on. If you still have any questions on this topic, we recommend that you watch a short video. It describes in detail the methods of analysis of variance using a specific example.

As you can see, multivariate analysis is a rather complex, but very interesting process that allows you to identify the dependence of certain factors on the final result. This technique can be applied in absolutely all spheres of life and can be effectively used for doing business. Also, the multivariate analysis model can be used to achieve breakthrough goals with simple methods.