# Computational procedures, A practical example - Mathematical...

## Computational procedures

As in the case of ordinary experiments, in principle it is possible to carry out multivariate analysis of variance by performing calculations without any special computing means. To do this, you must use specially adapted formulas. Such formulas can easily be found in old textbooks on experimental psychology and the application of statistical methods for their processing - see, for example, R. Gottsdanker [5]; V. J. Winer [28].

However, in modern conditions, the use of specialized statistical packages such as IBM SPSS Statistics or StatSoft is ideal for performing multi-factor analysis of variances. STATISTICA. In a number of cases, when it comes to the simplest two-factor experimental plans, you can confine yourself to an Excel analysis package built into the MS

The implementation of multivariate analysis of variance in statistical packages is quite simple. It essentially reduces to the definition of independent and dependent variables. Directly, the analysis routines are generally specified in the general linear models.

Let's take a closer look at a practical example of performing two-way analysis of variance using the IBM SPSS Statistics statistical package.

## Practical example

As an example, consider the emotional congruence effect .

In the thesis student of the Institute of Psychology. LS Vygotsky RSUH (branch of the second higher education) EV Fikina, conducted under the leadership of IE Vysokova in 2012/13 school year, among other things, the influence of the situational emotional state on the processes of remembering significant events of family life was investigated. The subject of the study was the congruence effect, which is expressed in the coincidence of the emotional background accompanying the extraction of knowledge from long-term memory, and the emotional evaluation of the remembered facts.

In one of the experiments of E. Fikina took part 40 subjects: 20 men and 20 women. All subjects at the time of the experiment were married, the length of marriage was from 2 to 39 years. Subjects with the help of a specially developed experimental procedure were put into a state of sadness or joy. In this state, they were asked to recall the most important and notable event in their family life and assess the extent to which it was joyful or sad. A seven-point scoring scale from -3 (very sad event) to +3 (very joyful event) was used.

Thus, the experimental plan included two independent variables-the modality of emotion (sadness and joy) and sex (men and women). Consequently, we are dealing with a two-factor experimental plan of 2 x 2. The variable sex is obviously fixed, the variable modality of emotion depending on the tasks of the experiment can be considered both fixed and random. In the latter case, the results obtained in the experiment can be extended to the whole variety of situational emotional experiences.

The results obtained in the experiment are presented in Table. 5.5.

Table 5.5

The results of emotional evaluation of the most significant event of family life by men and women in a state of joy and sadness

 Emotional Status Men Women Joy 2 1 2 3 1 2 2 1 3 3 2 1 2 2 3 1 1 1 3 2 Sadness -2 -2 0 -3 0 -2 -2 -2 1 -2 -2 1 -3 -3 -2 -3 -2 -1 -2 -1

We calculate the average values ​​of emotional estimates and present them in a visual form, as shown in Fig. 5.2. It is seen that in the situation of joy, both men and women recall a more joyful event as an example of the most important event of their family life, in a sad situation - more sad. At the same time, on the whole, men give a slightly higher rating to the events remembered than women, although the observed difference is not too great and, apparently, can be attributed to an experimental error. It is also evident that the factors studied by us act more additively, their interactions are not observed.

Fig. 5.2. Dependence of the evaluation of a family life event by men and women in a situation of joy and sadness

For a statistical evaluation of the observed effects, we use the method of multivariate analysis of variance. As a tool for calculations, we will use the module of general linear models IBM SPSS Statistics.

First of all, we prepare the data for analysis. The preparation is identical to the one we examined in Ch. 3. On the Variables create three variables: two independent - factors - and one dependent. We call the independent variables Emotion and Floor & quot ;, the dependent variable is denoted as Estimate & quot ;. We indicate the values ​​of the independent variables (Figure 5.3).

Fig. 5.3. Variables for variance analysis in IBM SPSS Statistics

Now go to the "Data" tab, enter the values ​​of the dependent variable, comparing them with the levels of our factors (Figure 5.4).

Fig. 5.4. Data for two-way variance analysis in IBM SPSS Statistics

On the Analysis select General Linear Models and then OLM-one-dimensional ... & quot ;. The window for setting up the variance analysis is opened (Figure 5.5). The left field of this window lists all the variables we have defined. To the right, we see five fields. In this case, we are interested in the first three. In the top field, you need to transfer our dependent variable - Estimate & quot ;. Considering our experimental factors "Emotion and Floor as fixed, we transfer them to the corresponding window.

Fig. 5.5. The Dispersion Analysis Settings window in IBM SPSS Statistics

Having determined the parameters we need, click "OK". We fall into the window of the output of the results. It includes a number of tables, the most important of which for our purposes is a table called "Estimate the effects of intergroup factors" (Table 5.6), consider it in more detail.

Table 5.6

The results of the variance analysis in IBM SPSS Statistics

Evaluation of the effects of intergroup factors

Dependent variable: estimate

 Source Sum of squares of type III Number degrees freedom Medium Square F Znch Adjusted model 124,100 3 41,367 38,185 0.000 Free member 0.900 1 0.900 0.831 0.368 Emotion 122,500 1 122,500 113,077 0.000 Sex 1,600 1 1,600 1.477 0.232 Emotion * Sex 0.000 1 0.000 0.000 1,000 Error 39,000 36 1,083 - - Total 164,000 40 Adjusted total 163,100 39

and R square = 0.761 (corrected R square = 0, 741)

Table 5.6 contains standard information regarding the results of variance analysis. The sources of the dispersion are listed on the left. Let's pay attention to those of them, which are connected with the action of our factors and their interaction. We will also cancel out the error factor. The following columns give the values ​​of the summed squares, the corresponding degrees of freedom, the average squares calculated on their basis, and the statistics F. As we can see, the effect of the modality emotion turns out to be highly sensitive - F (1, 36) = 113.08; p & lt; 0.001. The effect of sex, , as we have assumed, does not reach the level of statistical reliability - F (l, 36) = 1.47; p & gt; 0.10. The effect of the interaction of these variables does not appear at all.

Let's pay attention to the last fact noted by us. Since statistical analysis has not revealed the effect of interaction of experimental factors, the effects of random factors should also be evaluated with respect to the intra-group dispersion. In other words, in our case, there is no need to additionally perform statistical analysis, considering the factor of the modality of emotions as a random one, and, thus, we can extend the results to the whole general set of situational emotional experiences. Otherwise, it would be necessary to return to the previous step and move the variable "Emotion" in the field of random factors and again click the "OK" button.

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