FACTOR EXPERIMENTS, General Characteristics of Factor...


As a result of studying this chapter, students will: know

• Basic planning principles and types of factor experiments;

• concepts of basic effects and interaction of factors;

• types of interactions;

be able to

• correctly interpret the main effects of independent variables and their interactions;


• a general methodology for planning and evaluating factor experiments;

• The skills of applying statistical methods in assessing the main effects and the interaction of independent variables in factorial plans.

General Characteristics of Factor Plans

In the previous chapter, we learned how to build experiments with one independent variable. This approach to research is simple and convenient. However, modern experimental psychology has gone much further, and today research is mainly based on more complex schemes - within the framework of one experiment, the influence of several independent variables is studied. Experimental plans that allow one to study the effect of more than one independent variable are called factorial. This name is due to the fact that, in order to designate the variables whose influence is to be investigated, in addition to the term independent variable Another synonymous term is used - factor & quot ;. In the framework of this approach, the simple experiments considered before will be called single-factor experiments.

The number of independent variables in the factor plans can potentially be arbitrarily large, but in practice, usually no more than two or three variables are considered, and more rarely four. This is due to the fact that as the number of analyzed factors increases, not only the complexity of the organization of research increases, but also the complexity of interpreting the results; at some point it becomes simply impossible to adequately analyze the data.

With rare exceptions, practically all modern experimental studies are carried out with a factor scheme, because its application allows obtaining more rich results, testing more complex hypotheses, controlling possible side variables, increasing the internal and external validity of the experiment.

For example, G. Bauer in a series of studies of the influence of emotions on the processes of memory was interested in how the effectiveness of memorizing the emotional state of information experienced at the time of its perception varies with the emotional content of information. Subjects read a text that described the life of two students, one with positive events and one with negative ones. Before reading the story, the subjects with hypnosis caused either a joyful or sad mood.

The next day, the subjects had to remember the story, being in a neutral state. It turned out that the subjects who read the story in a cheerful mood remembered more events in the life of the student with whom positive events took place, while the subjects who read the story in a sad mood remembered more sad events from the life of the second student. The result obtained in this and similar experiments allowed Bauer to detect the effect of congruence of mood in memory, which consists in the fact that during the memorization the advantage is obtained of information of emotional content coinciding with the emotional state of a person at the moment of perception of this information.

Note that such an effect could not be detected using a simple experiment if the researcher manipulated only the emotional state of the subjects or only the emotional content of the memorized information.

Factor plans are usually designated with the help of a special system that allows to reflect in a concise form the general structure of the experiment: indicate the number of independent variables being studied, as well as the number of levels considered in each of them. The experiment described above can be designated as 2x2.

The number of digits in this notation indicates the number of independent variables (factors), and each digit, in turn, reflects the number of levels on each of them.

Thus, the 3x4 designation will say that two independent variables (two numbers in the notation) are examined, the first of which takes three levels, and the second one - four. The notation 3 x 2 x 5 will say that three independent variables are being studied, the first of which takes three levels, the second one takes two, and the third one is five.

When describing the structure of the selected experimental plan, it is customary to write in reports and publications: "The research used a 2 x 3 factorial plan," and then decipher which independent variables were studied and which levels they took.

In the above Bauer study, the 2x2 factorial plan was used, with the emotional state of the subject at the time of memorization (joyful or sad) being the first independent variable, and the emotional coloring of the information (positive or negative) as the second independent variable.

When it used to be about research with one independent variable, the term experimental condition was synonymous with the term independent variable level & quot ;. For factor experiments this is not the case, since each experimental condition is specified by a combination of different levels of several independent variables.

The number of experimental conditions in the factorial plans is not equal to either the number of independent variables, or the number of levels of each of them separately. It corresponds to the number of all possible combinations of all levels of all independent variables and can be calculated by multiplying the numbers indicated in the designation of the experiment.

Thus, in experiment 2x2, four conditions are studied which are obtained due to a combination of each of the two levels of the first independent variable with each of the two levels of the second independent variable. This is clearly shown in Table. 13.1, where the first independent variable is denoted by the letter A with the levels A 1 and A 2 strong> In 2 (located in the columns of the table).

Table 13.1

Factor matrix for the 2x2 plan



Level In 1

Level In 2


Level A 1

A 1 In 1

A 1 In 2

Level A 2

A 2 In 1

a 2 in 2

The number of conditions in this experiment corresponds to the number of combinations of each level of one independent variable with each level of the other, or the number of cells in this table. In total, four conditions are obtained: a combination of the first level of the factor A and the first level of the factor In (A1B1), factor A and the second level of the factor In (A 1 In 2 ), combination of the second level of the factor A and the first level of the factor In (A 2 In > and the combination of the second level of the factor A and the second level of the factor In (A 2 in 2 ).

In order to conduct the correct factorial experiment, it is necessary to investigate the independent variable in all possible conditions.

Table 13.1, reflecting all the experimental conditions, represents a itself factor matrix. The numbering of rows and columns in it is always carried out in a standard way: the lines list the levels of the first independent variable, and the columns for the levels of the second. Understanding how the cells of the factor matrix are numbered can be important when processing the results of factor experiments in some statistical programs.

If we similarly outline the 3 x 4 factor plan, we get the matrix shown in Table. 13.2. In this experiment there will be 12 conditions.

A similar image for a factorial plan with three independent variables will be more complex (in fact, it must be three-dimensional). For example, the 2x2x2 factor can be illustrated as two 2x2 matrices, one of which is for

one level of the third independent variable, and the other - for its second level (Table 13.3). The number of possible combinations of levels of variables (experimental conditions) here will be eight.

Table 13.2

Factor matrix for 3x4 plan



Level In x

Level B2

Level In 3

Level B,


Level A,

A, B,

A, B 2

AB 3

A, B,

Level A 2

a 2 in x

a 2 in 2

A 2 In 3

A 2 In 4

Level A 3

A 3 In 1

a 3 in 2

A 3 In 3

A 3 In a

Table 13.3

Factor matrix for the 2x2x2 plan

Factor From: level With x



Level In x

Level In 2


Level A,

A, B, C,

A, B 2 ,

Level A 2

A 2 BC

A 2 In 2 With

Factor From: level With 2



Level In 1

Level In 2


Level A,

A 1 In | C 2

AB 2 With 2

Level A2

A 2 In x With 2

a 2 in 2 with 2

It is important to understand that carrying out a factor experiment involves obtaining data for each experimental condition. Arbitrary choice of only a few of all possible conditions is incorrect. Therefore, the more independent variables you examine and the more levels each of them takes, the more complex your experiment will be. If, for some reason, the researcher refuses to study any one or more combinations of experimental conditions, then such factorial plans are called patchwork.

The use of factor experiments not only allows a deeper approach to the study of the questions under study, but also imposes higher demands on the experimenter's skill, leading to the need to more carefully plan the research. The researcher must:

1) select all independent variables that will be studied;

2) determine the number of levels of each of these variables;

3) decide how best to present each of them - but within a sub-object or intersubject scheme;

4) to anticipate and eliminate possible threats to internal validity.

All the features, pluses and minuses described in the previous chapter with regard to single-peak experiments related to the number of levels and schemes of primary control of intra-entity and inter-group plans remain relevant for factor experiments, only now all this should be thought out for each factor.

If the variable is intergroup, it is necessary to solve the problem of creating equivalent groups of subjects that will work at different levels (use random distribution or pairwise selection procedures). If the variable is intrasubject, suitable positional equalization methods should be implemented for it to level the effects of the sequence. The definition of how each independent variable will be presented must be in accordance with its specifics.

As in single-factor plans, in factorial experiments the methods of presenting independent variables will directly affect the required number of subjects, the duration of their work, and so on. Depending on how the independent variables are used, the factor plans can be divided into several types.

If all the investigated independent variables and their levels are presented separately for each group of subjects, then such factorial plans are called intersubjects. In each experimental condition, different groups of subjects will participate. The total number of groups of subjects will correspond to the product of all levels of all independent variables (factors), and the total number of participants will correspond to the number of conditions multiplied by the number of subjects of each group.

As an example of an intergroup factorial experiment, we present D. Linder's study with colleagues to study the effect of the amount of remuneration for upholding positions that contradict human attitudes toward changing these attitudes. In his study, Linder wanted to separate the two concepts of the relationship between reward and change in settings.

Within the theory of reinforcement, it is assumed that the more significant in such a situation the subject will be rewarded (usually as compensation was used as compensation), the more his opinion on the key topic will change. In other words, it is assumed that the more fees there are for defending opposing views, the stronger will be the reinforcement of the change in one's own position and the sooner it will change.

At the same time, within the framework of the theory of cognitive dissonance, it is assumed that when one defends an opinion contrary to one's own attitudes, a person experiences cognitive dissonance, the overcoming of which will occur due to a change in one's own opinion. The dissonance will be the greater, the smaller the board, and therefore, it is in the case of a low card that the change in installation should be the largest compared to the case when the card was high. Each of these explanatory approaches has received its empirical evidence in previous studies, which seems illogical.

Linder suggested that both models actually work, but which one will work depends on the ability for a person to choose: to defend or not to defend views contrary to his own.

The researchers conducted a factor experiment 2x2. where as the first factor the amount of remuneration was investigated (two levels - a high reward of $ 2.5 or a low of 50 cents), and as a second factor - the choice (which also took two levels - the subject could choose whether to defend his opposing views , or there was no choice, and he just had to do it according to the research conditions). Both variables were intersubject.

Students participated in the role of students from one of the American universities. The task was to write a convincing essay in support of a law that prohibits speaking in state institutions to Communists and defenders of the Fifth Amendment to the US Constitution. This topic was chosen by researchers because the possibility of introducing such a law in North Carolina was widely discussed at that time, and students opposed its adoption, as it limited their freedom of access to information. After writing the essay, students assessed their attitude to this law on a scale containing seven categories - from "the law is completely unjustified" before the law is fully justified.

In the condition of having a choice, the subject was additionally stressed that the task remains completely at their discretion. In the absence of a choice, the subjects simply reported what exactly they would need to do. After the participants decided to participate in the study, shortly before the start of the assignment, one part of the subjects was informed that in addition to the usual fee for participating in the study, the organization that allegedly spends it pays 50 cents and the other part - 2.5 dollars .

The results confirmed the hypotheses of the authors: in the absence of choice, the subjects who changed their attitude to the law most changed (which corresponds to the theory of reinforcement), and at the same time, students who paid less (which corresponds to the theory of cognitive dissonance).

If all the studied independent variables and their levels are presented to each participant participating in the experiment, then such factorial plans are called intrasubjects. Each subject will take part in each experimental condition. Obviously, in this case only one group of subjects is needed. The number of participants in such experiments will be minimal. This, as we already know, is the advantage of intrasubject schemes.

As an example of intrasubject factorial experiment, one can cite a study in which the authors sought an empirical confirmation of the thesis that simulation of movements is a simpler task than performing movements in accordance with symbolic descriptions or verbal instructions. To do this, the researchers developed a plan for the intra-subject 2x3 experiment.

Subjects should perform simple movements - move the index or middle finger of the hand, depending on the instruction instructions. The first independent variable was the type of instruction that should have been performed: the subjects either had to repeat the indicated finger movements or move one finger or another with the help of symbolic instructions (if the figure 1 was to move with the index finger, and if the figure 2 appeared average).

Instructions were presented to the examinees in the form of animated slides, the design features of which were the second factor. At the base level of this factor, the subject was shown either the movement of the fingers or the numbers (according to what type of instructions he should follow at the moment). In other conditions, the slide showed both finger movements and numbers simultaneously. In this case, the directions of these two combined instructions could either coincide (at the same time, the movement with the index finger and the number 1 or the movement with the middle finger and the digit 2 were indicated) or did not coincide (at the same time the movement with the index finger and the number 2 or the motion with the middle finger and the digit 1 were indicated)

Different types of slides were presented in random order. In the first block of tasks, the subjects had to simulate the movements of the hand, ignoring the appearing figures, and in the second, move one finger or the other, depending on which figure was presented, ignoring the simultaneously displayed movements. The sequence of execution of the blocks of tasks was balanced between the test subjects.

It was found that subjects react faster when they need to simulate movements, and this effect is not dependent on the type of slides to which it was necessary to respond. When the instructions were set with symbols, the subjects performed the task more slowly if the symbols on the slides did not coincide with the simultaneous movement of the hand and performed faster if the symbols coincided.

Factor experimental plans, in which both intra-subject and intersubject variables are studied, are called mixed. With this construction of the research, it will be necessary to use all possible ways to control the side variables, and the required number of subjects will depend on the number of levels of the intergroup variable.

When describing the plans for such experiments, it is necessary to separately specify which of the variables was considered as intrasubject, and which as an intergroup one.

Consider, as an example, a study conducted by American researchers III. Murphy and R. Zayonts. Zayonts was engaged in the study of emotional processes and defended the position of the primary affect, arguing that for the emergence of simple positive or negative affective reactions, cognitive evaluation is not needed. This position contradicts the popular cognitive theory of emotions, which states that for the emergence of emotions a primary cognitive evaluation is needed. This position of the primacy of cognitive factors in the emergence of emotions was advocated by R. Lazarus, with whom Zayonts mainly theoretically and empirically argued.

In support of his position, Zayonts conducted a large number of experiments, in a number of which he used the priming paradigm, i.e. presetting. This paradigm assesses the impact of the pre-stimulus (it is called stimulus-nrednastroika, or prime) on the perception and evaluation of the targeted stimulus. Zayonts suggested that if the affective primes presented for insufficient time for their awareness and cognitive evaluation will influence the evaluation of the attractiveness of subsequent stimuli, this will be confirmed by his concept of the affective advantage (the emergence of simple emotional reactions without the aid of cognitive evaluations).

During the research, a 2 x 4 factorial plan was used. As an intersubject variable, the exposure time of the prime appeared. For one group of subjects, it was insufficient for detailed recognition at the level of consciousness (4 ms), and for the other - sufficient (1 s). As vnutrisubektnoy variable used Prime's type, this variable takes four values: prime could be missing (zero condition) can be neutral (as Prime's were presented polygons) either negatively or positively emotionally charged (in this case, the image is a prime people expressing, respectively, , negative or positive emotions).

Chinese hieroglyphs were presented as target incentives. The task of the subjects was to assess on a five-point scale, as far as they like the image.

The researchers found that the evaluation of the hieroglyphs depended on which prime was presented to them (negative or positive), but only if the prime was presented for insufficient time to realize. These results Zayonts interpreted in support of the idea of ​​the primacy of affect.

As already, apparently, it became clear, for factor experiments with the same number of independent variables and the same number of their levels, a different number of subjects may be required depending on whether the variables are presented intra-subject or intersubject. For the simplest plan 2x2 (two factors of two levels each), if necessary, to investigate in each condition the five test subjects will proceed as follows. If both variables are intra-subject, only five subjects are needed, since they all pass through each condition. If both variables are intersubjective, 20 subjects are needed, since each condition will need its own group. If one variable is intrasubject and the other is intersubjective, then it will take 10 people, because each subject will take part in each of the two levels of the subject variable, and two separate groups will be needed for the intergroup variable.

As noted above, factor experiments can be used for different purposes.

First, instead of several studies with one independent variable, only one can be conducted, in which the influence of all the factors of interest will be determined at once. Simultaneous study of the influence of several independent variables within the framework of one research can allow revealing such effects that can not be detected in simple experiments.

Secondly, factor experiments are used to test complex, combined hypotheses that can not in principle be tested in simple experiments. These are hypotheses in which there is initially an assumption about possible differences in the influence of one independent variable at different levels of the other. The above examples of Linder's research with colleagues and Murphy and Zaionz are just illustrations of this type of hypotheses. Linder assumed that the amount of compensation will affect the change in the installation in different ways depending on the choice, whether to defend the views opposite to their own. Zayonts suggested that the absence of the possibility of cognitive processing of the primaries would lead to their affective influence, and in the opposite case would not.

Third, the introduction of additional independent variables can increase the internal validity of the study, allowing you to monitor possible side variables and at the same time verify the suitability of alternative explanations. In this case, the variables that are to be equalized in simple one-factor experiments can be included in the experimental plan on a par with the main factor of interest to the researcher, which will make the independent variable cleaner. In this case, the second independent variable is entered as a control variable. The researcher is not interested in its influence directly, however, its introduction into the experiment makes it possible to better clarify the relationship between the main studied factor and the dependent variable. Recall that such variables are called additional variables.

Fourth, factorial plans can be used to increase the external validity of the experiments, i.e. to answer the questions about the possibilities of generalizing the results obtained on one sample to other samples. For example, it is possible to introduce, as the second independent variable, such as the ethnicity of the subjects, their age or sex, and to investigate the effects of interest to us simultaneously for different groups. The detection of identical results for different groups will confirm the universality of the revealed regularities. Here again the second independent variable is not of interest to the researcher directly, but will allow us to answer the question of the prevalence of the detected effects. Such a variable is also considered as an additional variable.

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