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=bthe 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 value a of determining variable x is an explaining attribute,The value b 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 UA – a set of cases having x=a, S(A) – the square of AB – a set of cases having y=b, S(B) – the square of BAB – a set of cases having x=a and y=b, S(AB) – the square of AB

Fig. 1. General relations between sets A and BThen I(a,b)=S(AB)/S(A)and C(a,b)=S(AB)/S(B)

U

AB

AB

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

Fig. 2 AB. I(a,b)=1

U

BA

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)

Fig. 3 BA. C(a,b)=1

U

B A

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 thanS(U)=N – the number of all casesS(A)=N(a) – the number of cases having x=aS(B)=N(b) – the number of cases having y=bS(AB)=N(a,b) – the number of cases having x=a and y=b

Accuracy of this rule is calculated using the formula:

)(),(),(

aNbaNbaI (1)

Accuracy is a measure of sufficiency x=a for presence y=b.Accuracy is one of the main criteria of practical value. The rules, which have accuracy close to 1, have the most values.

Completeness of the rule is calculated using the formula:

)(

),(),(

bN

baNbaC (2)

Completeness is a measure of uniqueness of the rule, a measure of necessity x=a for presence y=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 essentiality x=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.

N

bNbaIbaE

)(),(),(

(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=az=c} determines {y=b1y=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 1Essentialities of determinations of types of attitudes to

modern Russian history by respondents’ political orientation and age

DeterminantsTYPE

I II III IV

Political orientation:

Democrats –0.08 0.04 0.03 –0.06

Communists 0.21 0.00 – 0.00

National patriots –0.05 – –0.02 0.20

Age:

under 20 –0.06 –0.07 0.09 0.04

from 20 to 30 –0.09 0.01 0.03 –0.01

from 30 to 45 0.04 0.13 –0.05 0.00

from 45 to 55 0.09 –0.03 –0.06 0.10

over 55 0.11 – –0.03 0.02

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

Determined feature: I support male candidate Volume: 1872

  Determining feature

Rules’ attributes

  Sex Accuracy Completeness Number of application

Number of confirmation

Rule 1 1. Male

Essentiality 0.01 0.78 0.42 1021 793 0,020

Rule 2 2. Female

Essentiality -0.01 0.76 0.58 1417 1079 –0,028

Total 0.77 1.00 2438 1872

- Non significant

Table 3.2

Determined feature: I support female candidate Volume: 1068

  Determining feature

Rules’ attributes

  Sex Accuracy Completeness Number of application

Number of confirmation

Rule 1 1. Male

Essentiality -0.04 0.40 0.38 1021 409 –0,068

Rule 2 2. Female

Essentiality 0.03 0.47 0.62 1417 659 0,071

Total 0.44 1.00 2438 1068

- 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.

1. Supporters of planned economy and communist ideology (as seen in the model provided by the former USSR)

2. Positive attitudes towards western-oriented liberal reforms in the economy. 3. Positive attitudes towards western-oriented society oriented reforms in the

economy. 4. 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).

5. Positive attitudes towards western-oriented society oriented reforms in the economy with a greater extent of regional economic independence.

6. 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:

095.0740

6.632

01.0|| N

For level of significance p<0.05 the threshold is:

072.0740

3.842

05.0|| N

Table 4Determinations of political attitudes types

The first type: Supporters of planned economy and communist ideology

Rules Essentiality Accuracy Completeness

From 40 till 55 0.16 0.29 0.34 0.202

Older then 55 0.17 0.29 0.26 0.182

University or college degree 0.05 0.17 0.66 0.144

Very Low income 0.12 0.24 0.21 0.126

Engineers and Technologists 0.21 0.33 0.17 0.166

Retired to pension, Housekeepers 0.30 0.42 0.23 0.245

Russian Folk Movement 0.21 0.33 0.04 0.079

The Communist Party of the RF 0.61 0.74 0.36 0.471

The Liberal Democratic Party of Russia 0.15 0.27 0.06 0.076

Most essential determinant for the respondents of the 1st type is age; mainly these are people over 40 y.o. with very low material conditions, engineers and technicians, retired to pension and housekeepers, low qualified workers, voting for the Communist Party of the Russian Federation.

- significant with p<0.01

The second type: Positive attitudes towards western-oriented liberal reforms in the economy

Rules Essentiality Accuracy Completeness Medium income 0.05 0.15 0.51 0.120

Specialists in science, education, health care 0.09 0.19 0.27 0.122

Representatives of free, creative professions 0.12 0.22 0.14 0.104

Women of Russia 0.32 0.42 0.14 0.198

Kedr 0.12 0.22 0.22 0.133

The Party of Economic Freedom 0.17 0.27 0.08 0.099

The second type is mainly people with middle income, sometimes politically engaged scientists and the representatives of creative professions voting for “Democrats”.

The third type: Positive attitudes towards western-oriented society oriented reforms in the economy

Rules Essentiality Accuracy Completeness Very High income 0.33 0.35 0.60 0.444

Managers-Partners 0.21 0.24 0.60 0.351

In the third type men, assessing their own material position as very high, are slightly domineering, having their own businesses.

- significant with p<0.01

The forth type: Positive attitudes towards liberalism in the economy on the basis of traditional patriarchal Russian values

Rules Essentiality Accuracy Completeness From 25 till 40 0.04 0.06 0.80 0.173

Men 0.02 0.05 0.80 0.113

University or college degree 0.02 0.04 0.80 0.117

Ph.D. (or equivalent) 0.08 0.11 0.20 0.113

High income 0.25 0.28 0.80 0.182

Muscovites 0.01 0.03 1.00 0.101

Managers-Partners 0.37 0.40 1.00 0.618

The fourth type is composed mainly of the representatives of the second age group (from 25 to 40 years old.), chiefly men with higher education, the majority of them having high income, many of them being Muscovites. They are in opposition to all parties, although they regard themselves as democrats and think that none of the existent parties are really democratic. It’s interesting to note that the 4th type comprises businessmen and the representatives of big business belonging to the third type.

- significant with p<0.01

The fifth type: Positive attitudes towards western-oriented society oriented reforms in the economy with a greater extent of regional economic independence

Rules Essentiality Accuracy Completeness

Under 25 years old 0.03 0.05 0.88 0.158

High school education 0.02 0.05 0.88 0.124

Low income 0.04 0.06 0.88 0.184

Students 0.08 0.10 0.88 0.264

Yabloko 0.04 0.06 0.25 0.086

The fifth type consists mainly of democratically oriented students and young graduates working in their specialty, and if voting (though few of them go to the polls) then for Yavlinsky. We should note that poor students are engaged in politics to a greater extent. However, this is not the cause, rather the effect, for the majority of students highly assessing their income are to a greater degree anxious of their small businesses and think little about politics.

- significant with p<0.01

The sixth type: Supporters of combining social-democratic values with achievements of the Soviet system

Rules Essentiality Accuracy Completeness

Older then 55 0.04 0.05 0.40 0.119

University or college degree 0.01 0.02 0.80 0.082

Specialists in science, education, health care 0.04 0.06 0.60 0.143

Serving staff 0.08 0.09 0.20 0.121

Women of Russia 0.07 0.08 0.20 0.113

To the sixth type belong mainly people over 55, with university or college degree, working in science, health care, education. They connect their hopes for the transformations with “The Women of Russia” party.

- significant with p<0.01