FREE INQUIRY in Creative Sociology Volume 8 No 2 November 1980 213 A POISSON ANALYSIS OF ADOLESCENT'S seek guidance and advice from their par­ LOVE OF PARENTS ents.

Donald E. Allen ASSESSED CHANGE IN THE LOVE Oklahoma State University RELATION Susan Cavaness Columbus College Previous studies have shown that young children show a stronger affective tie to CHILD'S ORIENTATION TO THE PARENT the same sex parent, and that the affective tie persists through the adolescent years. In the child's orientation to the parent, The question then arises as to whether the the crucial issue is not the "objective relation is an increasing or decreasing situation," but the perception of the situa­ function of age. This study will examine tion as understood by the child. The child evidence as to whether there is a trend to will react as if his definition of the reduction of the adolescent's affective tie situation is accurate, and for him, his toward both parents. Such a trend could be definition represents reality. Assuming the inferred from the distribution of responses importance of the effect of parent-child to a Likert scale, if the pattern of the interaction on the development and future distribution could be shown to follow a orientation of the child, we hope that this we'u-recognized" form of mathematical dis­ study will help to interpret some of the tribution with reasonable consistency. The intervening elements of information about Likert scale should consist of an ordinal children and their relationships with their series of steps on a credible underlying parents. The relationship between children continuum. The scale intervals of the and parents influences the child's attitude Likert scale are often scored and analyzed about decision making and social relation­ mathematically as if they represented ships in his later life (Luckey, 1960) equal intervals, although this is not one of Several studies have concentrated on the the assumptions of the Likert scale. In the perception of parents by young children present study, the affective scale to record (Breznitz, 1965; Schvaneveldt, 1970), and the child's love for the parent was "Unlim­ by somewhat older children (Kagan, 1956; ited -- Very Strong - Strong - Not Very Duvall, 1969). This study will focus on Strong - Weak," and the scale for the older adolescents of high school age. A child's rating of the parent was "Excellent­ somewhat closer affective tie and expres­ Good - Average -- Below Average --Poor." sion of love has been found between chil­ Such scales have commonly been equated dren and parents of the same sex. College to "grade points" for the calculation of students reflected a higher affect for the overall academic performance in schools same sex parent in a study coding Parsons' and in universities. Admittedly, the scale "affective-neutral" pattern variable in con­ may not have! priori consistency, but in tent analysis of verbatim protocols (Allen, many applications it does operate with 1969). This supported an earlier study of apparent consistency. If the responses to a emotional behavior reported by boys and Likert scale were distributed in a regular girls in relation to the same sex parent pattern of increase or decrease from one (Droppleman, 1963). More detached emo­ end of the scale, a clear possibility of some tional behavior was reported by boys and prior process to create such a uniform girls in relation to the parent of the distribution would exist. opposite sex. The closer affective tie was In the relation of the child to the with the parent of the same sex. parents, many social bonds, conventions There appears to be a much higher level and processes combine to maximize the of sentiment and communication between child's affection and. regard in the pre­ parents and teen-age children than is im­ school period and in the early·school years. plied by the mass media. According to Among these are the child's extreme de­ Elkin (1955) the continuity of parental pendency for daily physical needs, the socialization for adolescents is more strik­ general absense of alternatives to the ing than the discontinuity. Much joint parents' influence and control, the child's participation in activities between parents response to the routine gratifications re­ and their adolescent children has been ceived from both parents, and particularly found, and adolescent children frequently the mother. The parents' great physical FREE INQUIRY in Creative Sociology Volume 8 No 2 November 1980 214 size and social authority, relative to that progress at predictable rates of transition. of the child impresses the child. He looks Coleman provides the following rationale: on them, not only as his only dependable (1964,291) resource for the present, but also as his ideal model for his own future growth. The The appropriateness of the Poisson pro­ modern nuclear family functions to inten­ cess for social phenomena lies not in its sify these effects due to its very small size empirical fit to social data; it lies and its extreme privacy. Living in a instead in the assumption on which the detached house, with little contact with distribution is based. It deals with neighbors or relatives, it is probably un­ numbers of elements, or proportions, and avoidable that the young mother, at home numbers of events. Therefore, contin­ all day with her preschool child, would uous variable measurements, which are intensify her influence on him, since nei­ rare in social sciences, are unnecessary. ther has such a constant and immediate The Poisson process occurs continuously social alternative. over time, rather than at discrete trials. According to this model, the young Thus for naturally occurring events, in child's affection and regard for his parents contrast to controlled experiments, would be maximally positive during his something akin to the Poisson process is earlier years. Social conventions and the often appropriate. It is a process appro­ expectations of others would serve to priate to social phenomena because it sustain such attitudes for a considerable constitutes a rational model whose as­ time. Regardless of the absolute quality of sumptions can mirror our assumptions the parental relation, the child, lacking any about actual phenomena. Thus it need comparative standard, would tend to eval­ not be simply an empirical frequency uate his own home and family in the most distribution like the normal curve. favorable terms. As children mature into the early adolescent years, the variable Assume that there is a large number of shocks of social experience begin to pro­ individuals and a certain kind of events vide extrafamilial criteria for judging par­ which can happen to them. The states of ents, home, the self, and other family these individuals may be labeled 0, 1, Z, ... members. In this process, som~ children representing the number of events which will begin to revise their evaluations in the have occurred. Initially each unit is in negative direction. Presumably, these state Zero, and is subject to the possibility downward revisions occur in a series of of a recurrent event. The likelihood of this small adjustments. If that is the case, we event happening in any unit of time is alike could expect a general tendency for most for all those individuals and can be esti­ children to remain in the more favorable mated by the total number of individuals to state of regard for parents, and for those which the event has happened, over the who do change to pass progressively span of time divided by the number of through all intervening states. Moreover, individuals to which the event has hap­ those children who do change might be pened. The resulting number is the transi­ expected to exert and to receive influence tion rate. After the event has happened to in association with other children like an individual, putting him in a new state, themselves, and thus to add an element of he is immediately subject to the same social contagion to the process of revising chance of a new event with no delay. their opinions of their parents in the These assumptions permit calculating the negative direction. expected proportion of persons to whom no events have occurred, those to whom one THE POISSON MODEL event has occurred, and so on. There is a great number of elements to which an The Poisson model provides a reasonably event can happen, and the transition rate good approximation to the social processes governing the occurrence of this event is which we have tentatively identified in the Alpha. Once an event has occurred for an development of the child's attitudes toward element, it continues to be affected by the his parents. The Poisson model describes a same transition rate as before. The Pois­ probabilistic or stochastic process involving son distribution is the distribution of ele­ a sequence of adjacent states through ments in each of the states of the ordinal which a population of individuals may sequence. FREE INQUIRY in Creative Socioloqy Volume 8 No 2 November 1980 215 If the transition rate is increased as a students returned usable questionnaires, result of the first transition from state 0 to and 18 questionnaires were spoiled, face­ state 1, due to reduced resistance after the tious, or incomplete. In the case of 3Z7 "first time," or due to increased social students, both parents returned the paren­ pressure, exposure, or experience, we have tal questionnaires regarding the children's a Contagious Poisson process. The Conta­ academic and personal characteristics. gious Poisson includes the basic transition The students' responses on love for each measure, Alpha, and a second contagion parent and the rating of each parent measure called "Beta," which marks the provide the sample for this analysis. Al­ added likelihood of the occurrence of the though Logan County is classified as "rural" event, due to "contagion" from others in only ZZ percent of all students indicated the same state at the same time. The that the family income derived from agri­ contagion factor, "Beta" applies only after cultural sources such as farm crops and an element has made the transition from livestock. The six high schools were small, state 0 to state 1. consolidated, community type schools. Fur­ The following formulas are used in cal­ ther consolidation reduced the number of culating the two forms of Poisson distribu­ high schools to five at the end of 1968, the tion in Tables 1 and Z. year the survey was taken. The students in the subsample come from complete nuclear Terms: families with relatively cooperative par­ i is series of transition states. ents. Missing from the sample are students e is base of natural logs. who were ill, truant, or excused from class a = transition rate between states. to perform routine school services, and one b = added transition rate after i > O. student who refused to evaluate his par­ P = proportion expected in a state. ents, apparently due to a severe domestic pI: proportion observed in a state. disturbance in the family. The question­ m = estimated mean proportion of series. naires were explained and administer~d by sZ= estimated variance of proportions. regular classroom teachers in English classes (required for all students), using i -a written instructions prepared by the re­ a e Simple Poisson: Pi = '::""i"'"[=-- search team. These teachers had been fully briefed on the content and format of the questionnaires. According to teacher Contagious Poisson: reports, the students readily understood -a -b i _ a (a+b) ••• (a+(i-l)b) e (l-e ) and responded to the instrument. p. - . I iI bI POISSON APPROXIMATION OF LOVE RE­ SPONSE m 1: i po' = I Based on the observed values in Tables 1 and Z, the responses of boys are almost identical to t20se of girls relative to love of mother (X = ~.3, df = 4, P = .66) and love of father (X = 1.1, df = 4, P = .91). The predicted numbers are calculated from The rather regular pattern of rapid decline the Poisson proportions. The chi squared in frequency of observed responses in all statistic is calculated to measure the dif­ four tables suggests that a negative expo­ ference between observed and predicted nential function could consistently describe numbers. A low chi squared value with a the distribution. If such were the case, we high probability indicated a good agree­ might be in a position to develop certain ment between observed and predicated insights into the nature of the underlying values. dynamics of the child's love for his parents. The attempt to fit the observed distri­ SAMPLE CHARACTERISTICS butions with the simple Poisson was not very successful. In the eight applications The sample included all students attend­ of the simple Poisson for boys and girls for ing high school in Logan County, Oklahoma both parents for love and rating as a on the day of the survey. A total of 763 parent, four comparisons of observed and FREE INQUIRY in Creative Sociology Volume 8 No 2 November 1980 216 TABLE 1 - SIMPLE AND CONTAGIOUS predicted values indicated substantial dif­ POISSON ANALYSIS OF CHILD'S ESTI­ ferences by the significant chi squared MATED LOVE FOR MOTHER values. The single transition rate could not adequately account for the shifts from the Boys' Love Observed Predicted Poisson higher, more approbative state to the Simple Contagious adjacent lower state. The Contagious No limit n 64.8 68.6 Poisson was far more successful for pre­ Very strong 39 51. 7 47.3 dicting the observed distribution. In all Strong 25 20.7 19.5 applications, the chi square values were Not strong 6 5.5 6.3 sufficiently low to demonstrate that Weak 2 1.1 1.7 chance variation could account for the Total 144 143.8 143.0 differences. This suggests that the distri­ bution can be described consistently by an exponential function incorporating two Girls' Love transition rates, one of which operates as a basic transition function for all elements No limit 88.1 93.6 96 over all states. The second is probably a Very strong 45 57.4 50.0 contagion factor, and it does not operate Strong 21 18.7 17.9 until an element has shifted from the Not strong 4.1 5 5.3 initial state 0 to state 1. Elements in the Weak 2 .7 1.4 initial state are influenced only by the Total 169 169.0 168.5 basic transition rate, and the elements in all lower states are influenced by two Boys, Girls (B,G) BGB G transition rates, which tends to draw a alpha .80 65 .74 .59 larger portion of the population down into b~a .15 .20 the tail of the distribution. Instead, the X 4.5 2.6 4.4 .8 impact of the social environmental events probability .35 .63 .36 .94 accounts for the basic transition rate, here indicated by Alpha. The contagion factor, Beta, derives from the increased readiness TABLE 2 - SIMPLE AND CONTAGIOUS of those who have made one shift between POISSON ANALYSIS OF CHILD'S ESTI­ adjacent states to make an additional shift. MATED LOVE FOR FATHER In part, it could be influenced by associa­ tion among those who have made a shift, Boys' Love Observed Predicted Poisson but the present data offers no evidence on Simple Contagious that point. No Limit 74 64.7 69.3 A review of the Alpha values indicates Very strong 42 57.8 52.8 the transition rates regarding evaluation of Strong 30 28.5 24.0 the father are substantially higher than the Not strong 7.7 8.4 9 Alpha values for the mother, and that there Weak 3 1.7 2.5 may be more resistance to reevaluating the Total 158 157.7 157.0 mother among both groups. The fact that the bulk of the ratings in all four applica­ Girls' Love tions are retained in the two most favor­ able evaluation levels in the late adoles­ No limit 84 71.2 80.1 cent period indicated a strong conservation Very strong 44 61.5 52.1 of regard for parents. The assumption that Strong 27 26.6 23.4 those who have responded with lower eval­ Not strong 8 7.1 8.9 uations must originally have been in the Weak 6 1.7 3.1 state 0, the most favorable state, implicit Total 169 168.7 167.6 in the application of the Poisson formula­ tion has no firm support from this data, and therefore rests solely on face validity. It (B,G) Boys, Girls B G B G seems reasonable to think that those who alpha .90 .82 .86 .75 place a low evaluation on their parents b~a .16 .28 must have reached such an attitude level X 6.2 3.3 15. 3.4 only after a series of reevaluations. Of probability .18 .51 .01 .50 course, other formulations of the Poisson (Concluded on page 222) FREE INQUIRY in Creative Sociology Vo I ume 8 No 2 November 1980 222 general moral position (Erskine 1963 Childhood & 1972-1973). The moderating of the Society. 2nd ed. New York earlier anti-war attitudes indica­ .Gross Francis L 1978 Intellectual ted in the later sample illustrates deve Iopmen tin the u ndergradua te. the marked shifts in public opin­ Unpub I i shed paper ion as their perception of the situ­ • Koh Iberg Lawrence 1958 Deve Iop­ ation shifts. ment of Modes of Thinking and Choice in the Years Ten to Six­ REFERENCES teen. 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