Quantitative method VS. Qualitative method? Contribution to a Debate


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DOI:doi.org/10.24241/swrp.2015.rp

Abstract:

Our paper focuses on the analysis of the relationship between quantitative and qualitative method. It questions the theoretical foundations of each method in order to achieve the epistemological bases of each. In this perspective, our paper presents an essay of elucidation of the bases on which are erected the presuppositions of a process of knowledge production around a defined object in the social sciences. Because the two methods represent two different approaches for the production of scientific discourse on social reality, our paper also raises the question of whether they are necessarily in conflict or competitive relationship or on the contrary, the specificity of each mode of approach of social reality added to the complexity of the latter, requires them to be rather in an complementary order, in the sense that the weakness of one is reflected in the strength of the other and vice versa.

 

In practical terms, we are trying to grasp the theoretical and methodological issues included in the mixed method approach as it is used in SAHWA project.

Introduction

 

To the extent that every social phenomenon can be analyzed using the quantitative or qualitative analysis method (Becker.HS in De Singly.F 1992.23), it is useful to know what is the scope, cognitively, of the observations we do, in order to know whether to talk about the relationship between the qualitative and the quantitative method means,  necessarily, putting face-to-face two methodological perspectives or two methodological rationality (Groulx-Lionel.1997.3) of different backgrounds. Because with different methodological approaches this means, by implication, the production of two specific discourses revealing two particular ways of representing reality. It is from this starting point that arises or may take root tendency to the opposition between the two methods of analysis, qualified of ritual opposition by Marpsat.M (1999.1), and therefore removes or at least leaves little room for the hypothesis of complementarity. One issue that has given rise to extensive debate generating significant divisions among both specialists of methodological issues related to social sciences in general and the discipline of sociology in a special way, as well as those who have studied, circumstantially, the issue (Blanchet.A & Gotman.A.1992, Marpsat.1999 Alain léger.1993).

 

To this end, there are, on the one hand, advocates of qualitative method whose method after having long been marginalized and reduced to a straitjacket to literary trend and against-productive (Aubin.I. 2008.142) is actually finding nowadays, its pedigree. It is also through detecting limits of the quantitative method that the qualitative approach is experiencing a boom. The contribution of the latter is expressed in this context by Leger.A who said that its function was “... to add quivering flesh from experiences around the cold skeleton of statistics” (1999.5). On the other, the followers of quantitative analysis for whom the submission of social phenomena to statistical analysis and measurement are able to ensure the rigor required in the method to provide proof, in compliance with positivist paradigm designed on the basis of how scientific knowledge is acquired in the field of natural sciences.

 

As if to show the dominance of the quantitative method (Fekede.Tuli. 2010), its defenders are quick to show their "strength", built on the basis of the weakness known to the qualitative method concerning the criterion of scientificity after taking into account a limited number of cases. A fact which greatly limit the scope of the validation process of building scientific knowledge in addition to the fact of taking as an object the intersubjectivities of individuals and groups.

 

Thus, to try to elucidate what can differentiate the two methods is to conceptualize them. It is obvious that the question revolves around a common denominator : the concept of method, which refers to the rational and logical approach to the taking of evidence on the basis of known and recognized methods in the realm of production of scientific knowledge. Moreover, putting the problem in these terms between quantitative and qualitative method, we aim to understand whether we are dealing with two different visions of the social world or just two specific techniques? Questioning the method is often, for researchers from different backgrounds, (Groulx.Lionel.H, I Aubin. Medicine Aktouf.O social sciences, ...) an essential outcome when it comes to admitting (through proof) the results of their investigations.

At the source, a difference of reference paradigm:

 

The approach of social reality by means of methods and tools for providing evidences cannot be done outside of theoretical basic assumptions on which stands  the representation of the social entity, the behavior of individuals and social fact in general. This is what helps us understand why different search methods, namely quantitative and qualitative method produce different speeches on "the same reality." A priori, the explanation may come from the fact that each method makes the selection of a type of observations that comes from its own selection. But it becomes much more relevant to try to find out on what basis the logic of selecting observations is based.

 

A key question that has long intrigued and still continue to intrigue researchers in the fields of epistemology and methodology of the social sciences. To this end, Groulx.LH refers to the work of Guba.E Lincoln.Y in 1989 in the United States, who were among the first researchers, according to Kuhn's tradition, to uphold the hypothesis of irreducible separation between quantitative and qualitative method, estimating that each refers to a paradigm diametrically opposed to the other in accordance with three complementary levels of reading: the ontological, epistemologically and methodologically level. The quality of argument made by the two authors deserves some attention.

 

a)    The ontological level or the relationship individual / society :

 

Sociology is the study of phenomena largely dependent on the way we define the nature of human being himself and in his relationship to society. This fundamental issue tends to divide social scientists in determinism enthusiasts who believe that social reality is independent of individual’s will and those of constructivism, for whom reality is the result of complex social processes and the main purpose is to grasp the meaning.

For the positivist attitude which stands at the basis of the quantitative method, the ontological principle is verified by the fact that the social world has an existence independent of men’s will. It obeys to laws; therefore the aim of scientific activity is to discover them.

The systematization of what can be called scientific knowledge is built on the core principle of reproducibility of the facts.

 

Contrary to this conception that takes its roots in natural sciences, for the constructivists, reality is socially constructed and therefore actors play an essential role. They are the builders of knowledge.

Highlighting the actor’s role in the production of knowledge appears clearly within the qualitative approaches namely phenomenology, symbolic interactionnalism, ethnomethodology, methodological individualism... The objective in this work behind describing social realities is to be able to access to the understanding of value systems, belief and culture that form the basis of behavior, forms of action and thought of men in society.

As far as research focuses on the intelligibility of meanings and significances which assigne players to their acts, then they cannot be reduced to simply quantifiable and measurable attributes.

 

b)    The epistemological level or scientificity criterion :

 

For quantitativists, human behaviour can be analysed in accordance with the discovery of the laws. An epistemological stance taken from the field of research in the natural sciences. In the course of this view, social facts exist outside the control of individuals. Social facts must be analyzed as things, because they have an objective existence. This is the essence of the positivist posture for the analysis of social behaviour that must be conducted according to a logical deductive interpretation, based on the identification of causal relationships between variables. The centrality of the principle of measurement is carried by the statistical theory.

 

Positivist principle applied to research in the social sciences proceeds by identifying discriminating variables based on the theoretical deductive approach in accordance with the detection of recurrences and regularities of the facts, based on the multiplication of cases by conducting analyses on relatively large statistical samples.

In contrast, the qualitative method sees the social world as a universe constructed according to the meaning which the actors give to social facts. The objective of  the research is not in the explanation of the observed phenomena, but it is rather to understand them, without pretending to generalisation. Understanding of the facts requires a contrary attitude to the idea of externality, as to grasp the meaning actors allow to their actions.

Since the meaning of social action figure as ultimate goal of qualitative investigations, it follows that the actor is seen as the author of his own story; the same relationship as may be established with the researcher himself tends to deepen thinking, insofar as the action on the actor’s subjectivity requires a system of "decrypting" the meanings.

 

Also, the qualitative method is the method of investigation based on the inductive approach device in the sense that the production of meaning of the action requires the construction of a dynamic process described in detail, i.e. ethnographic studies. So, the construction of the whole context from which the action derives its meaning, legitimates consideration of a limited number of units of analysis while taking into account a wide range of attributes.

 

c)    The methodological approach or level of evidence:

 

The method is a concept commonly used in circles of all scientific disciplines. It means the device, the method or process by which one reaches what is thought to represent reality and truth. According to the principle of the scientific method, it reflects the strategy of providing evidence in accordance with the assumptions dictated by the ontological and epistemological                                                     dimension.

Thus, the paradigmatic anchorage of positivism claims objectivity in research evidenced by the control of the roles of different variables within the hypothesis testing process. To do this, the comparison device is appropriate in the causal approach of social phenomena. In this framework, statistical tool grants the best mean to prove by numerical analysis and measurement.

 

In the opposite perspective, the qualitative method is itself driven by the constructivist paradigm, which assumes that the meaning attributed to social facts is not the fact of theoretical frameworks of interpretation, but based on the experiences of actors mediated by researcher’s perception, whose job is to fully grasp the meaning and significance of the social actions. From there, it becomes easy to grasp the opportunity of the concept of understanding the phenomena rather than their explanation.

The philosophical origin of the interpretive and understanding attitude goes back to the German tradition, through the work of the philosopher Dilthey.W for whom sociology aim to understand phenomena through the meaning and significance given by individuals to their actions. For the German philosopher, what is nowadays called social sciences was much perceived as sciences of the mind as opposed to the natural sciences. Besides, it is this particular naming which made him mark his opposition to the positivist epistemology. To this end, the fact of taking into account the historical dimension in the analysis of social facts led him to make a clear separation between understanding and explanation. The second objective cited is particularly related to natural sciences.

The quantitative method: regular and statistical generalization

 

Therefore, we are made to understand that the epistemological foundation that sustain the quantitative method dictates that the approach of social phenomena is made in accordance with the idea of building experimental method device in the social sciences and therefore it is rather oriented toward the identification of the mechanisms of causality. To do this, all that can meet the cultural relativism is systematically reduced to its simplest expression in favor of the use of the comparative method based on measurable attributes. That’s why Bozon.M noted that "... demographers and sociologists always start with breaking phenomena to reduce them to the status of quantifiable variables or indicators." (1988 560). With this in mind, it is clear that the structure of comparison confirms harmoniously the way causality is built. With respect to this stand point, the use is made of the statistical tool as a mean to serve the construction of the protocol of proving. It is undoubtedly, the more appropriate instrument able to account for the impact of social  determinants on phenomena. Indeed, we note by way of illustration, in a study of familial mutations affecting a given society and in order to test the hypothesis of persistence of traditional forms of community life and culture within the family structure, it was noted that 41% of weddings took place in the context of family relationships. The reported percentage which is an order of magnitude significant within a preset and constant interval, it represents the equivalent of the necessary and sufficient condition by admitting the hypothesis. However, it remains to be said that this argument remains dependent on a theoretical and  methodological condition in that it is built on the prior theoretical stating that the nature of the relationship between spouses is an indicator which qualify (traditional / modern) family structure, and therefore measurement of change. This demonstrates the role given to the theoretical basis for this type of display or explanation, within a deductive logic.

 

Yet it remains to be said that the comparison in the quantitative method is applied in accordance with the principle of all things being equal otherwise, when the social phenomenon exists, by definition, in its entirety and is also irreducibly a historical phenomenon (Passeron.JC 1991). It is therefore understandable why the quantitative method is often blamed in the sense that, through its analytical model, it breaks down what is, à priori not decomposable or separable.

 

It must therefore be noted that the comments sociologists and social scientists generally make through experimentation, are totally dependent on the conditions under which the test procedure is conducted, namely the socio-historical circumstances.

 

Thus the application of the quantitative method which proceeds by linking variables to observe the co-variations, continues to show some shortcomings associated with the consequences related to making "cuts" in the social universe which tends to reduce to a few variables the determinants of a given phenomenon, when we see that social behavior is expressed in its entirety and complexity. Hence the question that arises whenever we mention the methodological principle of all things being equal otherwise. In fact, using this argument and even introducing the test variables that can go in the direction of consolidation, in a given direction, the primary relationship found between a dependent variable and an independent variable, the determination of the independent variable can never be definitively proven to the extent that it remains dependent in turn by social and historical circumstances in which it exist. It follows that the search of the determination, or causes of phenomena can in no way be achieved completely and permanently, precisely because  the  primary  relationship  can  be  understood  in  a  relationship  of determination between two variables that can be itself the product of the determination by another independent variable when we recognize that all things being equal, when in fact they are not, or at least until we produce the necessary and sufficient evidences; this is the result of an illusion or an artfact. On the contrary, we note with Boudon.R that, the relationship between variables produces meaning in a causal model, which is the result of theoretical and conceptual construction, taking on its own prioritization of indicators. The causal model which is the result of the introduction and analysis of the effect of varying tests, has the advantage of specifying all the dimensions that contribute to the occurrence and recurrence of social determinants. Taking into account the specificity and complexity of social phenomena, it is clear that it is quite misleading to try to capture the "pure effect of a variable" (De Singly.F 1992.108).

 

The qualitative method: the centrality of the actor

 

For quite long, quantitativist option in the social sciences and specifically in sociology was the dominant option, built on the unsaid that "anything that is not counted does not count" where many authors relegated qualitative approach to the rank of method unable  to assume the generalization of research results, mainly because of the numerical weakness of its cases studied. An approach which is described as such is often associated speculative, subjective and emotional qualifiers. This kind of mistrust given to qualitative research is often illustrated by the way the writings of methodology "deviate" or minimizes the qualitative perspective in their texts. In this regard, we note in the book of Combessie.J.C (1998), for example, although it is called the method in sociology, the presentation accomplished is mainly dedicated to the quantitative method and research centered around the terms of causality. Indeed, the author devotes 29 pages of his book to present technical and qualitative analysis when the quantitative method is offered twice (55 pages) of the number of pages. One is tempted to think, therefore, that the qualitative method is not affected by the construction of method of proof. It is also what, bitterly, Blanchet.A and Gotman.A, noted in the preamble of their book (1992 7).

 

All seem to indicate that the qualitative method is reduced to a secondary role which cannot go beyond the exploratory phase in studies because not generating systematic and systematized hypotheses. The quantitativist hegemony that succeeded to the influence of the Chicago School, was denounced by Sorokin who in the 70s already, has spoken out against what he called the quantophrénie (in Gerard. 1998). Since particularly the 80s, the qualitative analysis is harnessed to enhance the base of its legitimacy as an approach to social reality. Thus, Groulx.LH rightly remarked that the manual Gauthier.B book is well within this perspective by saying, "... In the manual Gauthier (1992) and the report of the working group, we puts quantitative research as one way of representing reality and considers legitimate knowledge produced or generated by qualitative research that has its own logic and its requirements "(1997.47). By partnering with the response of social scientists to the hegemony of the positivist paradigm, Mucchielli.A, meanwhile, flashed his active contribution to the promotion of qualitative methods in 1996, claiming to describe all the methods and techniques in the context of knowledge of the meaning of human facts set majestically in his dictionary of qualitative methods in the social sciences.

 

In the construction of scientific discourse, it is required of qualitative analysis, which through its specific analytical instruments and its protocol, to account for a fact or aspect of the fact that the quantitative method cannot reach (Gerard. 1998.4-5). It will be appreciated, a little further, that it is the basis, in part, of the legitimacy of its methodological rationality.

 

Thus the scope of the qualitative approach is taking shape in the demonstration of the complexity  and  diversity  of  social  phenomena  through  the  analysis  of  individual’s experiences. In this sense, the specific methodological perspective of the qualitative approach stand as the opposite of that of the quantitative approach which assume that the essence of social facts must be conducted independently of the representations of those who live them. Thus the philosophical basis on which stands the qualitative method is that of phenomenology and symbolic interactionism. Two methodological postures whose foundations dictate to take into account the views of stakeholders and the senses as the starting point of any analysis of social phenomena (Bryman.A. 1984.78). In fact, it means opting for the centrality of the actor in the construction of the object of analysis. In this design, it is unworthy to conceive or think the individual as a social agent undergoing domination effects of structures and contexts, but as a conscious actor and that the point is to fully grasp the meaning that he attributes to the facts. All the analysis is based on the meanings given to the actions and behavior by actors including their own actions and behaviors. It is understood by this that any research effort wanting to grasp the reality of social facts must strive to highlight the meaning and significance individuals give to actions. The iteration and recurrence of actor’s experiences are not on the agenda, given the fact that the identification of the statistical dimension is of no use in highlighting the complexity that characterizes processes by which facts take place.

 

It is for this fundamental reason that the method of qualitative analysis of social facts is basically an interpretivist and constructivist method in so far as the ultimate goal is to unravel the social phenomena providing the modes from which the actors give them sense. Obviously, the intelligibility of the facts as the source is the perception that makes social actors.

 

Now, the set of qualitative techniques: participant observation, interviews, focus group, life- stories ... are used to enable the capture of the interpretative process of the meanings that social agents allocate their actions, behavior and practices. Hence, the search is for uniqueness and dissimilarity in the qualitative analytical protocol. Nevertheless critics may be done to qualitative analysis method to carry on the dispersion under the two criteria mentioned above. An orientation that is not to advocate its scientific potential, insofar as it does not satisfy the principle of convergence of minds, according to the Cohenniene design held to be the major goal of scientific practice.

 

Yet displaying such an attitude is actually denying the qualitative method "strike force" which is reflected particularly, not exclusively, in the descriptive, exploratory and monographic scientific research stages, and which, in inductive terms, means identify individual’s attributes through the selection of a small number of cases, even single  case. As can also the qualitative method be criticised concerning the weakness in the generalisation of research results. A perceived weakness as a kind of transgression of which almost unanimously made the rule of scientificity : generalisation.

The necessary complementary methods:

 

After the presentation of the respective paradigmatic logic on which each method lies, it is clear that it is incorrect and insufficient to charge the method from a purely technical aspect in the process of producing the conditions of proof. However, what seems more relevant is the fact that each method is associated with theoretical assumptions of ontological and epistemological perspective. For this reason, the writings of Lincoln and Guba weigh their weight.

 

As far as our reasoning is concerned, we reach a first important result split in two points:

  1. The research method has at its base the theory that bases its conceptually logical demonstration in terms of internal validity and external validity.

 

    2. Each individual methodological logic follows a conceptualisation of social reality.

 

In this case, the method is a time of the theory, as it is indeed the fact of two methodological rationalities for specific purposes and in turn determines the protocol for selecting cases.

 

Everything leads us to believe therefore that it would be foolish to support the hypothesis of narrowing between the two methods under insurmountable constraint drawn up by the "ontological-epistemological veto." If this were true, we are very annoyed and irritated to explain a fact that tends to attract consensus among researchers and methodologists, that on the one hand it is difficult, even risky, to talk of quantitative or qualitative of pure state (Leger.A 1993) on the other hand each method has its strengths and weaknesses and by inference the weaknesses of one is the force of the other (Denzin et al. Groulx in 1989. LH 1997 7).

 

In the context of this posture Bryman supports the idea of integrating the two methods by referring to the differences that characterise them in terms of advantages and disadvantages and it is therefore useful for research to combine (1984.86).

 

In the same way, Gerard.H concludes that "Far from being opposed; qualitative and quantitative approaches are complementary. We need donations combine "(1998 7). So the search goes to the methodological pluralism in strict compliance with the epistemological principle. The first does not lead necessarily the second. Besides, Bryman.A in his article in the British Journal of Sociology, asks the question whether within the debate between quantitative and qualitative research should be focused around a question of method or epistemology? He said in this regard: "As part of a study, a researcher may perceive areas where a useful contribution could be made by both quantitative and qualitative methods, but it cannot be inferred from this that the epistemological positions presented by the debate between the two methods are ipso facto reconciled "(1984 87). This is a warning that clearly dictates that any attempt at integration, in the course of a mixed method, must be performed within the epistemological constraint.

 

However, in the course of carrying out research, it is common to find that researchers make use of elements of both methods without this would invalidate the approach of their logic of evidence. In reality, it is because of the complex nature of social facts; it often appears that a single method alone is incapable to cover all dimensions that the analysis of social phenomena requires. It is at the implementation of one or the other method for the investigation of a particular social fact that the need of conciliation is most resented and not at a philosophical or theoretical level.

 

Methodological pragmatism dominates all other considerations, because as Groulx.LH remarked "... the epistemological discourse expresses normative requirements rather than acts of research prescriptions ..." (1997, 51). It will be a consequence of not losing sight of the positivist or interpretivistes origins of each method, but at the same time to effectively meet the needs of a more general method, a hybrid method that aims to complement the respective deficiencies.

In fact, the purpose is to provide a theoretical reason to even make it possible and acceptable to overrun or bypass the epistemological obstacle and will have the advantage to comfort the methodological aspect of research, without questioning the first. In fact, it looks like searching to achieve a balance between epistemological pre-requisitions and enhancement need of the method through its "pluralisation".

 

This has the advantage of increasing the level of validity of the analysis by means of a multiplicity of angles of observation in so far although the approach seems the most convincing explanation as to his level of satisfaction of the condition of external validity of research results, the fact remains that it still has the disadvantage arising from the inability to restore the social fact as a socio-historical process and therefore do not concern only the co-variations a predetermined number of variables in the specific time limits. For this reason, the intervention protocol that combines understanding the experiences of social actors is of some use. This is what led Combessi.JC to assume that "Neither the qualitative or quantitative one hand, nor the broad approach or comprehensive approach on the other hand have a monopoly on heuristic virtues or validation power "(1982, 12). In other words, validation requires a plurality of angles of observation, given the fact that in social sciences neither method has supremacy by holding a monopoly on validation criteria. The trend in the United States to overcome the handicap of quantitative and qualitative techniques has generated the application of the technique of triangulation (Marspat.M.1999. 79), based on the approach to cross-check search results. This represents an additional argument in favor of complementary research methods in social sciences. Further reflected in the posture and Boudon.R & Fillieule.R who gave the example of the work of Thomas and Zaniecki about the famous and expansive survey of the early 20th century on the Polish Peasant who immigrated to the United States. Fieldworks are qualitative in nature according to the techniques used: life story, technical autobiographical content analysis of letters, ethnological description of social relations, conflicts etc ... and when they noticed that, "Even in these qualitative studies, it appears in watermark indicators in the concepts and the relationships between variables in monographic descriptions "(2002.25). It is the case of a signified revelation made by the researcher Thomas.I of the Chicago School, who, far from displaying an anti-quantitativist attitude wrote in this regard: "It is clear that the statistical studies of the behavior of populations will have little meaning as the statistics are not supported by the lives of individuals "(in Zolesio.E 2004). Those highly significant researchers’ attitudes invite us to relativize the epistemological and methodological orientation often overly attributed to the emblematic Chicago School to empirical and qualitative trend at the expense of the quantitative approach to urban developments. To do this, we borrow the entire testimony of one of the most distinguished researchers  of Chicago School saying that “methods of statistics and case study do not conflict with each other. They are in fact interdependent. Statistical comparisons and correlations can often suggest ways for research using case studies, and documentary materials, by uncovering process, will inevitably afford more appropriate statistical indicators. However, if we want statistics and case study each making its contribution as tool of sociological research, we must guarantee them equal recognition and provide an opportunity to both methods of perfecting its own technique. Moreover, the interaction of the two methods will undoubtedly be fruitful "(in 2004 Zolesio.E 19).

 

Highlighting the benefits of the implementation of the principle of methodological pluralism necessarily leads us to ask the embarrassing question: is the implementation of the complementarity of quantitative and qualitative methods means clustering and putting the two methods at an equal level? A key issue, we’ll try an answer later. For the moment, let us confine ourselves to show what is the complementary of the two methods within the realm of methodological pragmatism.

 

In research practice, it is extremely scarce, if any happen, to see a search of qualitative or quantitative nature in a pure state. Borrowing one of two methods to the other are either in the form of verbal expressions, or data. Indeed, starting from this principle, we take advantage of Passeron's testimony in this regard. For him, "The contrast between qualitative and quantitative data analysis appears [Passeron.JC] as artificial as each of these modes of analysis used "surreptitiously" in its reasoning, elements of the other mode, so making incommensurability obsolete" (1997 Groulx.LH 49). In the wake of this statement, then we understand how interview, as a qualitative technic is used in order to generate sociological categories to be subjected afterwards subsequently by quantitative survey and sample processing. In this context, we will evoke as well, for illustrative purposes, the practice of content analysis, a qualitative technic that borrows the rudiments of quantitative reasoning when dealing with quantitative content analysis.

 

Also, a quantitative treatment of survey data can lead to a typology, which in turn may present the benefit of identifying individuals characteristics with a view to deepening the investigation within a qualitative approach of a research question.

 

Finally in an exploratory perspective, the focus group technic often serves to identify thematic categories of analysis registered after doing discourse analysis of a target group and then be poured into a survey scheme for measuring.

Conclusion:

 

Make praise or “glorify” the hybrid method based on the principle of methodological pluralism does not solve the problem of real-mode combination of two methods that the epistemological and ontological foundations separate but at the same time the need for reasoning added to the complexity of social phenomena, tends to make closer.

 

An enigma which reveals the limits of how to operate at best the principle of triangulation (need for further analysis) on one side, and that reflect the "trouble" or “inconvenience” consequently to the fact of epistemological embedding of each method on the other. From this point of view, it is illusory and unproductive to try to establish some sort of balance or fairness between the methodological approaches and the analysis of the object of study, to the extent that the use of mixed method means systematically pooling of two different pathways in the field of representation, conceptualization and construction of an object of study in the social sciences. Does this mean that any attempt to adding methods is by definition a lost cause? No, the conceptual level of research being dominant, it can only be done in the wake of a single ontological and epistemological orientation at a time. Therefore, the addition of a second method would be one extra-capture (deepening) what appears to be insufficient in the dominant method.

 

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