## Multilevel experimental plans

## Features and Planning Principles

In addition to classifying experiments using the method of presenting the levels of an independent variable, they can also be classified by the number of these levels, highlighting simple two-level experiments and more complex multi-level ones. Multileveled are the experiments in which more than two levels of the independent variable are studied.

Two-level experiments are simple in implementation and processing, their results are easy to interpret, and they are indispensable in cases of pilot studies that are conducted to determine whether it is worthwhile to study this independent variable. They are also good for conducting critical experiments in which the suitability of two alternative theoretical explanations of the studied reality is studied. However, the results obtained in them have a number of limitations, and in fact the overwhelming majority of modern experiments are built on a multilevel scheme, since this will enable us to more accurately study the influence of the independent variable on the dependent.

In spite of the fact that from the organizational point of view, carrying out a multilevel research is more complicated (it is necessary to attract more testees, implement more complicated equalization procedures, spend more time performing experiments, and also apply more complex statistical methods of processing results), all these disadvantages are compensated by the advantages that the study of the dependent variable gives on more independent levels. Multilevel experiments are more informative, allow testing more complex experimental hypotheses, and the conclusions that can be drawn as a result of their conduct will better describe the subject matter under study.

The main and most significant advantage of multilevel experiments is the ability, with their help, to verify in more detail the relationship between the independent and dependent variables. So, only multilevel plans are suitable for detecting nonlinear effects when the independent variable is quantitative.

In quantitative independent variables, the operationalization of levels can be expressed in quantitative relationships. Values of such variables are given in strong metric scales - equal intervals and relations. For example, the distribution of exercises over time can be operationalized as a repetition every 30 seconds, every two minutes, every half hour, and so on. The independent variable here, in fact, is a continuum, and as its levels for the study, its various manifestations from smaller to larger can be chosen.

In contrast, qualitative independent variables are operationalized in a nominative or ordinal scale (for example, different ways of studying an object or different methods of psychotherapy). These variables can not be expressed quantitatively, their levels differ not by the gradient of the gradient, but by qualitative, not expressed in numbers, parameters.

Sometimes it turns out that variables, which at first glance appear to be qualitative, are in fact quantitative. Even in the example of ways of memorizing poems, an independent variable can be considered as a quantitative one. We discussed two of its levels - the repetition of one quatrain before full memorization (the method of short passages) or the repetition of half a poem to its full memorization (the method of long passages). At the same time, this is, in fact, the operationalization of how much information is suggested to be memorized simultaneously: one quatrain or one half of the poem at a time. At the same time, in our fictional research, we ignored other possible variants: a repetition of two quatrains, three quatrains, etc.

It is quite possible that with more, more fractional, consideration, it would appear that with the increase in the number of simultaneously memorized quatrains to a certain level, the memory efficiency increases, and after it begins to fall. When we select only two variable levels of a variable, we can not detect effects of this kind. But since our imaginary research is of an applied nature, and its purpose is not so much to discover the connection between the amount of simultaneously learned information and the speed of remembering the entire amount of information, but simply finding out which of the two proposed methods is more effective, then for us it is not fundamentally that we can skip some effects.

However, in the conduct of scientific experiments, the researcher is interested in the possible more accurate establishment of the relationship between the independent and dependent variables, because an insufficient number of conditions under investigation can affect conclusions. And especially important this requirement is in cases where the relationship between variables is nonlinear.

Consider, as an example, the classic study of R. Yerkes and J. Dodson, on the basis of which a well-known psychological law on the optimum of motivation was formulated, which states that in solving problems of high and medium complexity, the most effective is the average level of motivation, while as with too high and too low motivation, the efficiency will be lower.

The researchers trained mice to distinguish between black and white. For this purpose, a special labyrinth was created, which began with an entrance chamber, from which it was further possible to pass into one of the two boxes, one of which was black and the other of white color. If the mouse went into the box of black, she received an electric shock, if the mouse went into the white box, there was no electric shock. The black and white boxes could be located either to the right or to the left, for each sample the position of the boxes was determined randomly and was the same for all mice.

It was studied the effect of the current intensity, applied when entering a black box, on the speed of formation of the skill of entering only in the white box. In the experiment, problems of three different degrees of complexity were used (in terms of color discrimination), and for each of them, their levels of electric shock power were used.

To simplify the presentation, we present the results of a series with an average degree of complexity of the discrimination problem, in which three intensity of electric shock was used: 125, 300 and 500 conventional units (cu). Without going into the details of the study, we say that the results for a complex problem turned out to be similar to those that we describe, and for a simple problem by others, so the Yerkes-Dodson law does not apply to simple problems.

At each level of the independent variable, i.e. with negative reinforcement of different current strength, four mice (two individuals of male and female) were examined. Training of mice was carried out in a mode of 10 attempts every day. The learning criterion was the behavior of the mouse when, for three days, it chose the correct box each time (ie, it performed 30 unmistakable attempts). The dependent variable was calculated as the number of attempts that the mice made before reaching the learning criterion. For example, if the mouse has learned to correctly distinguish colors (and therefore pass through the labyrinth) on the fifteenth day, then it took 140 attempts.

It was found that the minimum number of attempts was needed for mice that experienced an incorrect choice of an average electric shock (300 cu), in cases of too weak or too strong a shock, the mouse was trained worse. This dependence is shown in Fig. 12.3. Thus, for the most effective learning, the level of motivation should be optimal: not too high and not too low.

It is absolutely obvious that it would be impossible to obtain such results if a simple two-level experiment is used. Moreover, depending on which levels of the independent variable were used, the researchers would come to completely different conclusions.

* Fig. 12.3. *

**Graphical representation of experiment results**

** Yerkes-Dodson **

Imagine three researchers who could conduct a similar experiment using only two conditions.

The first researcher, as a low level of reinforcement would take 125 cu, and as high-500, as a result, it would be found that in both conditions the learning speed is approximately the same, which would make it a paradoxical conclusion about the absence influence of the strength of negative reinforcement on learning (Figure 12.4).

* Fig. 12.4. *

**Graphical representation of the results of a hypothetical study in which only the current is used**

** at 125 and 500 cu **

Another researcher could compare the levels of the independent variable to 125 (low) and 300 (high level). and would come to the conclusion that with increasing motivation, the effectiveness of training increases (Figure 12.5).

* Fig. 12.5. *

**Graphical representation of the results of a hypothetical study in which only the current is used**

** at 125 and 300 USD **

The third imaginary researcher could take as a low level a current of 300 cu, and as high as 500 cu, and would come to the conclusion that as the motivation increases, the learning rate decreases (Figure 12.6) .

* Fig. 12.6. *

**Graphical representation of the results of a hypothetical study using only the current strength**

** at 300 and 500 cu **

Note that from the point of view of designing and carrying out experiments, all three researchers could have done excellent research using the correct methods of combating side variables, but because of the insufficient number of levels of the independent variable studied, the conclusions to which they could come turn out to be invalid.

In general, considering more levels of an independent variable helps to produce better results, since it approximates the experiment to an ideal in which all possible values of the independent variable are studied. In other words, using as many of the conditions as possible will increase the internal validity of the experiment with a quantitative independent variable.

However, conducting a multilevel experiment with a quantitative independent variable, it is equally important to correctly approach the choice of the levels studied. Our imaginary experimenters might not have an effect, even using a multilevel experiment, if we chose the levels of the independent variable that are not sufficiently spaced apart from each other (for example, a current of 140, 150 and 160 cu). The spread must be large enough for the effect to be detected. Sometimes, in order to more accurately select the levels of an independent variable, several pilot studies are needed.

In the above example, one can also well consider the problems associated with interpolation and extrapolation of results obtained in experiments with quantitative independent variables. Usually, as a result of such experiments, the researcher wants to get an idea of the functional relationship between the variables. Since it is impossible to study the dependent variable on the entire variety of potential independent levels, researchers based on the results obtained in the experiment try to predict the relationship also for those levels of the independent variable that in reality were not subject to study. When the number of conditions studied is small, it is very easy to make mistakes by extrapolating the results of the study (ie, by extending them to levels that are outside the range studied in the experiment) or by interpolating them (ie, by extending to independent variable levels within the range studied, but not subject to investigation directly).

Two-level experiments are most susceptible to such errors. For example, an imaginary researcher No. 1, showing his results as shown in Fig. 12.4, would have made the interpolation error by presenting that the relationship between the variables is linear.

Only carrying out multilevel experiments can allow us to more confidently describe the form of the relationship between variables. The more levels will be used, the more detailed information about the form of communication will be obtained.

Thus, for quantitative independent variables, the advantage of multilevel experiments is that they enable us to detect nonlinear effects and increase the internal validity of the experiment due to a better representation of the independent variable in the experiment.

With regard to qualitative independent variables, multilevel research also allows us to make a more correct view of the reality being studied and, in addition, to test alternative hypotheses within the same experiment, which makes the results more convincing and clear.

Suppose you need to evaluate the effectiveness of use for normalization of a state in stressful situations such ways of appeasement as listening to calm music and conducting meditation. You can select people who have just been exposed to stress, measure their anxiety level, and then one part of them offer half an hour listening to calm classical music, and with another part to spend a half-hour session of meditation. After that, the alarm level is again measured.

Perhaps, as a result of this research, you will see that for the group listening to music, the alarm decreased, say, $ 7, or points - not as much as for the group that participated in the meditation session (they have an anxiety decreased, say, by 12 points). And you can conclude that meditation is a more effective means of fighting anxiety, and recommend it to those who are often prone to stress.

However, an increase in the number of levels of an independent variable could clarify the results. For example, you can add a control group of subjects who also underwent stress, but with whom there were no special effects to soothe. With them, just after half an hour, a second measurement would have been carried out. Suppose, it would be found out, that their anxiety also decreased by 12 points.

Such a result radically changes the conclusions that you can draw from the study. It turns out that half an hour after stress, the condition of the subjects without any influences stabilizes to the same extent as if they meditated for half an hour, while if during the same time they listen to classical music, then the state will be more slowly normalized. Having received such results, you most likely will no longer recommend listening to music as a way of appeasement. Thus, the presence of additional conditions helps to make the research results more accurate.

Multilevel experiments can be carried out both on the intra-sub-, and intersubjective scheme of presenting conditions. At the same time, the threats of internal validity, specific to these types of experiments, and their control schemes remain.

With multilevel intergroup plans, the same methods of creating equivalent groups are used, as for two-level ones, you just need to create more groups. This can complicate the study if the equivalent groups in it are created using the equalization procedure.

For multi-level intrasubject experiments in the same way as for simple ones, positional equalization is realized. However, preference is given to cross-individual schemes, since the more levels of the independent variable is used, the longer the sequences need to be used for qualitative intra-individual control, which may be inconvenient in terms of the duration of the subject's work. As a result, it is more convenient to present a single independent variable to each subject of each level with full control of the effects of the sequence at the sampling level.

Conducting intrasubject multilevel experiments with procedures of cross-level equalization may be accompanied by the appearance of specific problems leading to undesirable shifts in the results.

One such problem is the centration effect, which is the effect on the results of the experiment of the range of variants of the independent variable used. This is characteristic of quantitative independent variables, when many levels are studied that can be represented as a successively increasing or sequentially decreasing series. The effect is that the level of the independent variable, which is the average of all the investigated (middle of the series), can gain advantages over other levels, i.e. the results of the subjects can be improved for this level of the independent variable. At the same time, if the same value of the independent variable level is used in another series where it will not be an average, the results for it will decrease, and the best results will be found at the level that appears in the middle of the new series.

As an example of such an effect, an experiment is often given, in which the relationship between the height of the working surface (table) and the productivity of labor was studied-the number of parts processed during the allotted time. The authors conducted two series of experiments on different groups. In each of them, six heights of the working surface were used, and the experiment was carried out according to the intrasubject scheme: each subject worked on each working surface of each height.

A Latin square was used for cross-individual adjustment. In total, in both series of experiments I study nine different heights of tables. In this case, for the first series, the six lowest ones were chosen, and for the second, the six highest. Thus, three average heights (for the entire range of nine studied) are present in each series, in one series they were the highest of six, and in the second - the lowest.

It was found that the optimal height of the table in two different series is different. Simplifying, it can be said that the most preferred, i.e. The one whose work was the fastest was the height of the working surface that was closer to the middle of the series used in the particular series.

Thus, the results of the experiment depend on which range of levels of the independent variable is used. Perhaps the independent variable levels, which are the middle of the series, gain the advantage of being preceded by an approximately equal number of levels with both lower and higher values. Also, on average, they are the least different from all others, which means that the features of the work developed under other conditions can be more easily transferred and used on them.

If it is suspected that centering effects may occur, it is recommended to use intergroup experimental schemes.

So, multi-level experiments have a number of undeniable advantages in comparison with two-level ones. The results obtained in them are more evident, they make it possible to make a clearer idea of the form of the relationship between the independent and dependent variables, and to exclude alternative explanations in the context of one study. However, when deciding how many levels to use, it is necessary to observe a balance between their quantity and the possible costs associated with its increase. To study too many levels that are slightly different from each other can be a pointless undertaking. It is necessary to try to take only such conditions that are really informative. Sometimes, in order to determine what conditions this should be, additional piloting experiments should be conducted.

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