Main effects and interaction factors - General Psychological Workshop

Basic effects and interactions of factors

Carrying out factor experiments allows us to obtain two main types of results: the main effects of factors and their interactions.

The main effects are the effect on the results of each independent variable studied separately. In fact, the ego is the results that could be detected in a conventional experiment with one independent variable.

Interaction is the joint influence of all studied factors on the results, expressed as the dependence of the influence of one independent variable on which levels other independent variables take. It reflects the degree of non-additivity of the factors. Results of this kind can not in principle be obtained in simple experiments. And it is the ability to detect interactions that ensures the specificity of the factorial plans.

Let's analyze the possible results of factor experiments in more detail.

The main effect is the effect on the dependent variable of a particular factor, i.e. Considering the influence of one independent variable, while all other independent variables are not taken into account. In the experiment, so many basic effects can be obtained, how many independent variables are to be studied. For example, in the 2x3 factorial plan, no more than two main effects can be obtained, in the plan 2 x 2 x 2 - no more than three main effects, etc. The main effect allows us to analyze whether the influence of each independent variable exists separately, while the values ​​of other variables are fixed.

Suppose we want to know how the size of a serving affects the perception of the taste of restaurant dishes, as well as the different types of food names. Two levels of the first factor ("portion size") are examined: a small portion (100 g) or a large portion (300 g). The second factor ("type of name") is also explored on two levels: a name with a listing of ingredients (for example, "Salad of tomatoes and cucumbers") or without such an enumeration (for example, "Spring" Salad). Both variables are presented intersubjectively.

The subjects are asked to evaluate how tasty the dish looked to them, on a 10-point scale. All subjects try the same dish, only the subjects of the first group get a small portion and read the name of the dish, which contains the list of ingredients; the subjects of the second group receive a small portion, but the readable name does not contain mention of the ingredients; the subjects of the third group try a large portion, and the readable name contains a listing of the ingredients; the subjects of the fourth group try a large portion, and the name of the dish that they read does not contain mention of the ingredients. Thus, the intergroup factor plan 2x2 is realized.

You can build various hypotheses about the results. For example, that a large portion will allow you to get fuller, and this will lead to a positive attitude and higher scores. Or that knowing what ingredients the dish consists of can also have a more positive impact on the perception of its taste.

Suppose, as a result, the data presented in Table 1 were obtained. 13.4. Subjects who tried small portions, and in the name of the dish were listed ingredients, on average, assessed its taste by 3 points; subjects who tried small portions, the ingredients were not listed in the names, on average they evaluated the taste for b bals, etc.

Table 13.4

Hypothetical results of the study of the influence of the size of a portion and the name of a dish on the evaluation of taste sensations

Serving Size

Title Type

Average

With ingredients

No ingredients

Small

3

6

4.5

Large

9

6

7.5

Average

6

6

6

If we want to analyze the main effect of the portion value variable, we should consider this variable as averaged at all levels of the second independent variable, i.e. irrespective of the effect of the variable "type of name". So, on average, subjects who tasted a small portion evaluated the taste of the dish by 4.5 points out of 10. Here we summarize the results in the line "Small portion" regardless of the variable type of title (ie, consider the average for all levels of the second independent variable).

Similarly, we consider the average taste score for subjects who have tried a large portion (but the "Big portion" line). On average, they appreciated the taste by 7.5 points. To understand whether the main effect of the portion value variable was detected, it is necessary to compare these two values. If the differences are statistically significant, the main effect is considered to be detected.

We will not conduct complex calculations, just assume that the difference between 4.5 and 7.5 in our fictional experiment is significant, which means that we managed to find the main effect of the variable "portion size". This effect consists in the fact that subjects evaluate large portions as more delicious. Such a result could be obtained using a simple one-factor experiment in which only the variable "size of the portion" would be studied.

Now we'll analyze the main effect of the type of name variable. To do this, we need to compare the results obtained for its different levels (the name with the list of ingredients and the name without listing the ingredients), regardless of the different levels of the second factor. That is, we need to calculate the average value for the With ingredients column and the No ingredients and compare these values. We see that in both cases the subjects evaluated the taste of the dish in the same way - by 6 points out of 10, which means that the main effect of the factor "type of name" not detected. Note that we could also get this result in a simple one-factor experiment.

So, the main effect is the effect of each variable studied separately; the number of main effects that can be detected in a factor experiment is equal to the number of factors investigated. In order to determine the main effect of a particular variable, it is necessary to compare the mean values ​​obtained at its different levels, ignoring all other independent variables.

The effect of interaction of factors reflects the nonadditive effect of factors on the dependent variable. It is found in the case when the influence of one factor differs at different levels of another factor (or other factors), i.e. depending on the value of one independent variable, the effect of the second independent variable on the dependent variable will be different.

Let's return to our example with an assessment of the taste of dishes, depending on the size of the portion and the type of name (see Table 13.4). Analyzing the results obtained for different experimental conditions, we can see that although the main effect of the variable type of name It was not found, the presence or absence of ingredients in the names of dishes affects differently the taste of dishes with portions of different sizes. So, if the ingredients in the title are listed, then the small dish will be rated as less tasty (the average score in this condition is 3), while the large one will be rated as more tasty (the average score is 9). In this case, if the ingredients are not listed in the name of the dish, then the portion is not affected by the taste estimate; this is interaction. Depending on the level that one independent variable takes ("type of name"), the effect of the second independent variable ( portion size ) changes on the taste estimates.

In general, the result of this experiment can be described as follows: "Dishes with small portions as a whole seem less tasteful to the subject. The most dramatic this difference is in those cases when the name of the dish lists its ingredients. If the ingredients are not listed in the name of the dish, the portion size does not affect the perceived taste of the dish. "

Thus, if the researcher is asked if it is necessary to increase portions, so that restaurant visitors rate the dishes as more delicious, the answer should be: "It depends on what names are used in the menu. If they do not list the ingredients of the dish, the portion size will not affect the taste assessment. If the enumeration of ingredients in the name is used, the portion must necessarily be increased

Results of this kind could not be obtained in a simple one-factor experiment, because, by examining, for example, the influence of the "type of name", we would necessarily control the variable "portion size" as an auxiliary, leaving it the same for all cases. This would lead to the fact that the influence of the name of the dish on its perceived taste would not be revealed.

The interaction of factors is the main result of the factor experiment, so when it is detected it must be interpreted first and only then it makes sense to analyze the main effects if they were also detected.

For greater clarity, the results of the factorial plans are usually presented not only as a table that reflects the mean values ​​of the independent variable under different experimental conditions (similar to Table 13.4), but also in the form of specially organized graphs.

If we consider a simple two-factor case, the graphs are constructed as follows. The levels of one independent variable are located on the abscissa (the X axis), and the levels of the second independent variable are displayed as separate lines in the graph. The dependent variable is plotted along the y-axis (Y-axis).

In Fig. Figure 13.1 shows a graphical representation of the results presented in Table. 13.4.

Here, as we can see, two points corresponding to two levels of the variable "type of name" are plotted along the abscissa axis. (on the left there is a point corresponding to the presence of the list of ingredients in the name, and to the right - corresponding to their absence), and the two lines of the graph represent two levels of the variable portion size (the solid line corresponds to a small portion, and the dotted line corresponds to a large portion).

Fig. 13.1. Graphical representation of the hypothetical results of the experiment on the effect of the size of the portion and type of name on the taste of the dish

Thus, the graph reflects the results obtained in each experimental condition, and they can be traced for each independent variable separately.

It is important to understand that the image of the results of the factorial plan in the form of such graphs is simply a way of visualization and in fact has nothing to do with the functional dependence for which graphs are usually used in mathematics. This is due to the fact that on the axes X and U the data presented in different scales is postponed. On the vertical axis, Y is the estimate of taste measured in the ordinal scale. On the horizontal axis X the variable measured in the nominative scale is laid, i.e. just two points corresponding to different levels of one of the independent variables. In this case, the arrangement of points on a straight line can be chosen arbitrarily: we have a point on the left corresponding to the presence of the enumeration of the ingredients in the name, but we could arrange this on the right; we could arrange these points closer or further apart, and this would not affect the interpretation of the results obtained.

The lines themselves also display the levels of the nominative variable. These lines in no case say anything about the linearity of the detected connection, and so on. The connection of lines on the graph is done purely for clarity and does not contain any mathematical meaning.

Such graphs are very convenient for analyzing the interaction, but with their help you can visually determine the potential presence of the main effects.

So, the possibility of detecting the interaction will be indicated by the fact that the lines on the graph intersect or tend to intersect, while the complete parallelism of the lines will indicate the lack of interaction. On our graph it is clear that the lines converge at the point on the right.

In order to determine the presence of basic effects, it is necessary to mentally select the average value of the factor of interest for each level, regardless of the second independent variable.

For example, to determine the presence of the main effect of the type of name variable, we need to present an average taste score for the left and right points on the abscissa. In Fig. 13.2. These averages are represented as bold dots, and the averaged values ​​are drawn into ovals (left and right, respectively). These points are on the same value but the ordinate axis (the value of the independent variable in both cases is 6), which indicates that there is no main effect for this variable.

Fig. 13.2. Illustration of the absence of the main effect for the name name variable

In order to determine the presence of the main effect for the variable "portion size", you need to find the average values ​​of the dependent variable for each of the levels of this factor (which are displayed using the graph lines). In Fig. 13.3, these averages are depicted as fatty dots. These points are at different values ​​along the ordinate, which indicates the possible presence of the main effect for this variable.

Fig. 13.3. Illustration of the main effect of the variable Serving size

What kind of independent variable should be displayed but the abscissa axis, and which - in the form of different lines on the graph, the researcher chooses himself based on considerations of clarity. From the point of view of content, this is completely unimportant, the main thing here is for the reader to be more comfortable in accepting the result. Therefore, the results of this hypothetical study can be depicted as shown in Fig. 13.4.

Fig. 13.4. The second variant of the graphic representation of the hypothetical results of the experiment on the effect of the size of the portion and type of name on the taste of the dish

This drawing, in fact, is similar to Fig. 13.1, simply independent variables are interchanged: quot; quot; serving size Now it is located on the abscissa, and the factor "type of name" is depicted as different lines.

In order to choose the most graphic chart, you can build all possible options and use one that, in your opinion, best illustrates the results. There is only one general recommendation. Variable, containing more levels, it is better to locate on the abscissa axis, because it is easier to perceive a greater number of points on the axis than the greater number of lines on the plane of the graph.

If the study uses three independent variables, then the graphs are constructed in such a way that one of the variables is displayed by placing its levels on the abscissa, the second by using different lines on the graph, and the third by using different graphs. The graphs will be represented as many as the levels used to study the third independent variable. Thus, it is rather difficult to graphically represent the interaction of three variables.

There is another way of illustrating the results of factor experiments - using a bar chart, the columns of which reflect the magnitude of the dependent variable in each experimental condition. This method is more correct from the mathematical point of view, however it can be less clear when mapping the interaction. The results of a fictional experiment described above can be represented graphically in this case as shown in Fig. 13.5. In this diagram, columns of different colors display different levels of the quot; quot; serving size & quot ;, and different factor levels title type are represented as two groups of columns. In this case, each column shows the average value of the dependent variable in the corresponding condition.

The preference for this or that type of graphical presentation of these factor experiments remains entirely at the discretion of the researcher.

Fig. 13.5. Image of the hypothetical results of the experiment on the effect of the size of a portion and the type of the name on the evaluation of the taste of a dish using a bar chart

Finding an interaction is a complex result that requires for the interpretation of serious theoretical training of the researcher and practitioner in conducting such experiments. And if the examples considered above with the study of two independent variables are rather simple cases (the interaction is either present or absent, and the graph and the results matrix can be fairly easily understood and described), then the picture becomes much more complicated when three and more factors. In this case, the interaction options can be more: first, it can be first-order interactions, when a single variable affects what dependence is found for some other variable. In addition, ego can be interactions of the second and higher orders, when the form of interaction of the others changes at different levels of one variable.

Consider what kinds of interactions can be detected for a three-factor experiment with independent variables A, B and C. First-order interactions will be interactions <-> A and B, variable A and variable C, the variable In and the variable C. In addition, the interaction of all variables can be detected A, B and C. Whatever data visualizations are used, explain the specifics of the effect of one variable, depending on the other, and the difference in this effect depending on the third variable can be an overwhelming task. That is why, in factorial experiments, more than three independent variables are usually not used, and most often preference is given to two-factorial plans.

In general, when using factorial plans as a result of the experiment, the presence or absence of the main effects from each independent variable being studied, as well as the interaction of factors, can be detected. In this case, the more independent variables are to be studied, the more interaction options can be found.

Consider, for example, all possible outcomes for a simple two-factor experiment 2x2. Suppose we studied the features of memorizing information of various types (verbal and nonverbal) by people of different professions - artists and mathematicians. The subjects were presented with a set of stimuli consisting of 30 words and 30 images. Thus, the variable type of information was intra-subject, and the variable profession - intersubject. The researcher wondered whether differences in the memorization of information of different types would be detected depending on the professional belonging of the subjects.

As a result of this type of experiment, 8 different outcomes can be obtained.

1. Only the main effect for the first independent variable ( information type ) can be detected. The results presented in Table. 13.5 and in Fig. 13.6, show that regardless of professional affiliation, all subjects better memorize verbal and not figurative information, and people of different professions do not differ in the characteristics of memory.

Table 13.5

The hypothetical results of the experiment, in which only the main effect of the "info information" variable

is found

Information type

Profession

Average

Mathematics

Artists

Words

22

22

22

Pictures

12

12

12

Average

17

17

17

2. Only the main effect of the second independent variable ( profession ) can be detected. The data in Table. 13.6 and in Fig. 13.7 show that mathematicians, in comparison with artists, better remember information regardless of its type, and the type of information does not affect the efficiency of its memorization.

Figure 13.6. A graphic representation of the hypothetical results of an experiment in which only the main effect of the information type (1 - words, 2 - pictures)

Table 13.6

The hypothetical results of the experiment, in which only the main effect of the variable "profession" is found

Information type

Profession

Average

Mathematics

Artists

Words

22

12

17

Pictures

22

12

17

Average

22

12

17

Fig. 13.7. A graphic representation of the hypothetical results of an experiment in which only the main effect of the variable profession (1 - words, 2 - pictures)

3. Both major effects can be detected immediately in the absence of interaction. For example, in general, verbal information can be remembered better by all subjects, and mathematicians remember more information of any type (Table 13.7 and Figure 13.8).

Table 13.7

The hypothetical results of the experiment, in which the main effects of both factors are found and no interaction is found

Information type

Profession

Average

Mathematics

Artists

Words

21

14

17.5

Pictures

14

7

10.5

Average

17.5

10.5

14

Fig. 13.8. Graphical representation of the hypothetical results of the experiment, in which the main effects of both factors are found and no interaction is found (1 - words, 2 - pictures)

4. The main effect of the first factor, as well as the interaction of factors, can be detected. For example, subjects generally better remember verbal information, but for mathematicians the difference between the number of stored images and words is greater than for artists. The main effect of the second factor is not, because mathematicians and artists showed approximately the same results (Table 13.8 and Figure 13.9).

5. The main effect of the second factor, as well as the interaction, can be detected. For example, artists in general remember more information of any type, but there are more differences in the number of memorized images for artists and mathematicians than in the number of memorized words (Tables 13.9 and 13.10).

Table 13.8

The hypothetical results of the experiment, in which the main effect is found for the factor "information type" and interaction

Information type

Profession

Average

Mathematics

Artists

Words

26

24

25

Pictures

16

20

18

Average

21

22

21.5

Fig. 13.9. A graphic representation of the hypothetical results of an experiment in which the main effect for the factor "information type" is found. and interaction (1 - words, 2 - pictures)

Table 13.9

The hypothetical results of the experiment in which the main effect for the factor profession and interaction

Information type

Profession

Average

Mathematics

Artists

Words

20

24

22

Pictures

16

26

21

Average

18

25

21.5

Fig. 13.10. Graphical representation of the hypothetical results of the experiment, in which the main effect for the factor profession and interaction (1 - words, 2 - pictures)

6. There can be an interaction of two factors, while their main effects are not detected. Data of this kind are given in Table. 13.10 and in Fig. 13.11, which shows the results showing that mathematicians better remember verbal information, and artists - imaginative.

Table 13.10

Hypothetical results of the experiment in which the interaction of factors is found and no major effects are found

Information type

Profession

Average

Mathematics

Artists

Words

24

10

17

Pictures

10

24

17

Average

17

17

17

Fig. 13.11. Graphical representation of the hypothetical results of the experiment, in which the interaction of factors was found and no main effects were found (1 - words, 2 - pictures)

7. Both major effects and interactions can be detected. The results given in Table. 13.11 and in Fig. 13.12, show that the memory of mathematicians for all information tints is better than that of artists, and images get an advantage when memorizing in comparison with words regardless of professional memory.

However, the most important is that mathematicians are equally effective in remembering information of any type, whereas artists are better able to remember non-verbal information. In this case, the interpretation of the interaction is most important, because it gives a more significant result, against which the information obtained in interpreting the main effects turns out to be insignificant.

Therefore, when interpreting the results of factorial plans, the advantage is always given to the interaction, if it is detected along with the main effects. Interpretation of interactions should be carried out first.

Table 13.11

The hypothetical results of the experiment, in which the main effects from both investigated factors are discovered, and also their interaction

Information type

Profession

Average

Mathematics

Artists

Words

24

10

17

Pictures

24

24

24

Average

24

17

21.5

Fig. 13.12. Graphical representation of the hypothetical results of the experiment, in which the main effects from both investigated factors are discovered, as well as their interaction (1 - words, 2 - pictures)

8. A variant unfavorable for the researcher is also possible, when as a result of the research neither basic effects nor interactions are detected. In this case, it is necessary to state that the factors chosen for study do not affect the dependent variable, i.e. in our example it may turn out that the efficiency of memorization is not affected either by the type of presentation of information or by the professional affiliation of the person (Table 13.12 and Figure 13.13).

Table 13.12

Hypothetical results of an experiment in which no major effects or interactions are found

Information type

Profession

Average

Mathematics

Artists

Words

20

20

20

Pictures

20

20

20

Average

20

20

20

Fig. 13.13. Graphical representation of the hypothetical results of the experiment, in which neither the main effects nor interactions (1 - words, 2 - pictures) are found

As you can see from the examples above, the types of interaction can vary greatly: in some cases, it is expressed in the fact that the effect of one independent variable is stronger for one level of the second independent variable and weaker (or absent) for another (cf. Figures 13.1, 13.9 and 13.10). At the same time, the interaction may consist in the fact that the direction of influence of the first variable is reversed under the influence of the second independent variable, as shown in Fig. 13.11.

Different types of interactions will be displayed in different ways on the charts. In the first case, the lines will converge, tend to intersect or intersect, and this intersection will vanish when constructing a graph with a different arrangement of independent variables on the abscissa and the plane of the graph. In the second case, the crossing will be distinct, and regardless of which factor is located on the abscissa axis, and which one is represented as segments, this crossing will persist.

Understanding the specifics of interaction is very important, because, depending on its type, the meaningful conclusions of the study will differ. When the interaction is detected, it is not enough to simply limit its presence. It is necessary to identify and analyze its specifics, and the use of graphs will prove to be a very convenient tool.

When interpreting the interaction, it is also important to consider that it can be explained in different ways. In the case of a two-factorial plan, there are two possible interpretations with equal probability:

- depending on which levels the factor A takes, the factor In affects the dependent variable in different ways;

Depending on which levels the B, factor is, the A factor affects the dependent variable, differently.

The choice of this or that interpretation should be based on theoretical notions about the phenomena being studied or on considerations of common sense. The existence of different possibilities to explain the interaction and leads to the fact that it can be quite difficult to interpret it.

We emphasize that it is impossible to draw an exact conclusion about the presence or absence of interaction, or the main effects in the general population, simply from the table and the figures from the table representing the average values ​​of the dependent variable in each experimental condition. To find out what the results really are, it is necessary to perform a statistical analysis of the data, and only on its basis to draw conclusions about the results of the study.

Also We Can Offer!

Ошибка в функции вывода объектов.