DETERMINACY ANALYSIS The basic concepts, Statistical criteria, Applications in psychology

DETERMINACY ANALYSIS The basic concepts, Statistical criteria, Applications in psychology APPENDIX 2

The basic concepts of the Determinacy Analysis (DA) Analysis of data in psychology, sociology and other social sciences requires dealing with objects represented by vectors of values of variables. During experimental design the variables are chosen along with the sets of values for these variables. Let us assume now that we want to know how two variables x and y form the vector of all variables related to each other. Herewith we assume from our understanding of psychological process, that this relation is not just a mere correlation between them, but variable x has more depth than y, and x affects and determines y.Now we will give the basic concepts of the method of measure such determinations suggested by Russian mathematician Sergey Chesnokov. His articles and special soft is available in www.context.ru. Let us assume that variable x has a value of a, and variable y has a value of b. Then we will call the judgement If x=a then y=b the rule or the determinacy (if event x=a determines, explains event y=b, then the relationship between x=a and y=b obeys the rule) The valueaof determining variable x is an explaining attribute, The valueb of determined variable y is an explained attribute Each rule has two basic characteristics: Accuracy and Completeness. Accuracy I(a,b) is a proportion of cases when x=a and y=b among all cases when x=a (has range between 0 and 1) Completeness C(a,b) is a proportion of cases when x=a and y=b among all cases when y=b (has range between 0 and 1)

For better understanding let us see the Venn’s diagram (fig.1): U – universal set of all cases, S(U) – the square of U A – a set of cases having x=a, S(A) – the square of A B – a set of cases having y=b, S(B) – the square of B AB – a set of cases having x=a and y=b, S(AB) – the square of AB U A B AB Fig. 1. General relations between sets A and B Then I(a,b)=S(AB)/S(A) and C(a,b)=S(AB)/S(B)

If accuracy is equal 1 (100%), the explanation does not have exceptions: every time x=a, there is also that y=b (fig. 2). U B A Fig. 2 AB. I(a,b)=1

Completeness shows how well (complete) the rule explains the fact that y=b (how many cases when x=a and y=b are among y=b). If completeness is equal 1, then every time y=b, there should be x=a. (Fig. 3) U BA Fig. 3 BA. C(a,b)=1

Accuracy of this rule is calculated using the formula: (1) Accuracy is a measure of sufficiency x=a for presencey=b. Accuracy is one of the main criteria of practical value. The rules, which have accuracy close to 1, have the most values. If we have a sufficiently large sample we can say about the possibility of prognosis. For example, if accuracy is equal 1, then the forecast is correct: x=a with a hundred-percent guarantee entails y=b. Completeness shows what proportion of cases y=b among all can be predicted on the basis of x=a. Accuracy defines practical value of the rule. Accurate rules (having the accuracy equal to 1) have the greatest value for practice and sciences. They give faultless explanations, correct forecasts, and serve as extremely effective positive tests. Practical value of the rule depends also on its completeness. However, rules having completeness less then 1 also can have high prognostic values. In the situation of quantitative data analysis let us consider than S(U)=N – the number of all cases S(A)=N(a) – the number of cases having x=a S(B)=N(b) – the number of cases having y=b S(AB)=N(a,b) – the number of cases having x=a and y=b

Completeness of the rule is calculated using the formula: (2) Completeness is a measure of uniqueness of the rule, a measure of necessity x=a for presencey=b. The rule’s completeness is also the main criterion of the rule’s practical value. The rules with higher degree of completeness have more practical values. However, the presence of very high degree of completeness is not absolutely necessary. The third characteristics of the rule is an essentialityx=a in the rule If x=a then y=b for explanation of y=b or contribution of x=a in the accuracy of determinacy y=b. (3) The essentiality E(a,b) of an explanative feature is considered the most significant characteristics reflecting the correctness of its choice. This value shows to what extent the portion of cases possessing both x=a and y=b features among cases with the feature x=a is less or greater than the portion of cases with the feature y=b in the whole sample. Thus theoretically possible range of essentiality is from –1 to 1. If the essentiality of the given rule is equal to zero, x=a is not significant in the given rule. The comparison of accuracy, completeness and essentiality of different rules allows finding more important relations between variables. Variables used in the rules can be not only simple, but also complex such as variables obtained with rules of the Logical Algebra. (NOT),  (AND),  (OR). For example we can analyze how event{x=a&z=c}determines {y=b}, or {x=az=c}determines{y=b1y=b2& (w=d)}

Example 1. From: Petrenko V., Mitina O. Psychosemantic Analysis of the Dynamics of Russian Life Quality. European Psychologist 2001, 3. In 1995 a research project was conducted with the purpose of reconstruction of categorical systems, through which people perceive the life of society and assess various governments of the USSR and Russia in different periods of time from 1917 until 1995. The influence of respondents’ age and political orientation on their assessment of the past and present of the country was analyzed. Five hundred and fifty three respondents, with age span from 17 to 70, took part in the survey. Psychosemantic analysis allowed obtaining and describing four groups of population according to their attitudes towards Perestroika and reforms in the modern Russia. 1) Reject the economic and political reforms, 2) Constructively accept the reforms as a given reality, 3) Undoubtedly support the reforms, 4) With negative attitude towards the political aspects of the reform and more positive attitude towards its economic component. Table 1 contains the results of determinacy analysis.

Table 1 Essentialities of determinations of types of attitudes to modern Russian history by respondents’ political orientation and age

As shown in Table 1, the most significant determinants for the first type of respondents are their belonging to the supporters of the communists (the essentiality is 0.21) and age - over 55 (the essentiality is 0.11). The characteristics of the respondents of the second type are weakly determined by democratic convictions (the essentiality is 0.04) and to a greater extent by age. For instance, the most significant determinant (0.13) is the respondents’ belonging to the age group from 30 to 45, which is the most active in economic and political respect. For the third (“romantically optimistic”) type of attitude to perestroika and Eltsin’s ruling the most significant determinant (0.09) is the age of respondents (under 20). The inclusion into the fourth type is determined mostly by national-patriotic convictions of the respondents (0.20) and their belonging to the age group from 45 to 55 (the essentiality is 0.10). 0.00 implies that the given determinant doesn’t influence the inclusion of respondents in this type, “ – “ implies that the type doesn’t include respondents with the given determinant

Example 3. From: Petrenko V., Mitina O. Psychosemantic analysis political consciousness of Ukrainians before presidential elections in 1999. in printing The list of 12 possible candidates (10 males and 2 females, before official registration) was suggested to 2438 respondents. They were asked to rate certain statements about these candidates. For example, one of these statements was “I would vote for this candidate during the election”. One of the goals was to determine whether there was any correlation between the gender of the chosen candidate and the gender of the respondent. Tables 3.1 and 3.2 contain the results of determinacy analysis. Table 3.1 ↓ Table 3.2 ↓

Table 3.1  - Non significant

Table 3.2  - significant with p<0.01

Therefore one can conclude that when voting for a female candidate the gender of an elector determines the results of voting, but when voting for a male candidate the gender of an elector does not determine the results of voting. In other words, in the case of voting for a male candidate the proportion of supporting people among men is approximately the same as among women, but the proportion of women supporting a female candidate among all women is significantly larger than the proportion of men supporting a female candidate among all men. It is also possible to conclude that women do not give preference either to male or female candidates based on the gender alone, whereas men prefer male candidates.

Example 4. From: Petrenko V., Mitina O. Psychosemantic analysis of social consciousness in Russia. 1997 (in Russian) • The attitudes of Russian citizens toward economic and political reforms in the country were studied using psychosemantic techniques. On the basis of 740 respondents' answers a theoretical typologization of respondents by their attitudes toward the Russian life was constructed. • Supporters of planned economy and communist ideology (as seen in the model provided by the former USSR) • Positive attitudes towards western-oriented liberal reforms in the economy. • Positive attitudes towards western-oriented society oriented reforms in the economy. • Positive attitudes towards liberalism in the economy on the basis of traditional patriarchal Russian values (including the Russian Orthodox Church's values and the strong unified State). • Positive attitudes towards western-oriented society oriented reforms in the economy with a greater extent of regional economic independence. • Supporters of combining social-democratic values with • achievements of the Soviet system.

Table 4 contains significant results of determinacy analysis. Numbers in the cells are: essentiality, accuracy, completeness,  The threshold forwith sample size 740 and level of significance p<0.01 can be calculated as follow: For level of significance p<0.05 the threshold is:

Table 4 Determinations of political attitudes types  - significant with p<0.01

 - significant with p<0.01

DETERMINACY ANALYSIS The basic concepts, Statistical criteria, Applications in psychology