Statistics is a word that embraces countless meanings and each one reflects historical cognitive instances to what is now recognized as a unified intellectual discipline. The majority of these instances, sometimes timeworn and sometimes oversimplified by necessity, are still today attributable to quantitative methodology and positivism’s view of science. Few other movements in thought have had the same shapeless impact as positivism had on scientific progress: the adherence to an empiricist view of nature and the rejection of non-scientific or pre-scientific approaches have led to a scientific knowledge tied to the realm of the observable (Keat 1979). This meant that human intellect has reached the full maturity of its development because phenomena is not explained anymore by fictional supernatural entities, as in the theological stage, nor by personified abstractions, as in the metaphysical state. What the history has just experienced is for Comte an inevitable manifestation of a Law that “consists in the fact that each of our principal conceptions, each branch of our knowledge, passes in succession through three different theoretical states: the theological or fictitious state, the metaphysical or abstract state, and the scientific or positive state” (Comte 1855, p.1, New York, 82 Nassau Street published by calvin blanchard). Although, according to Comte and generally accepted by the intellectual community of the nineteenth century, not all the sciences have reached the third stage of human knowledge and statistics’ development was incorporated in social science. In fact, “exact sciences”, whose objective procedures “left no room for disagreement or doubt about the meaning of a concept, or what might fall under it” (DiSalle 2002; p. 207) such as mathematics, physics and astronomy, are provided with “scientific method”, whereas other soft sciences were provided with “statistical methods”. These considerations help to understand why statistics is very often defined only as a method by researchers and why most of the criticism to quantitative methodologies are focused on statistical methods. In the twentieth century, with the advancement of knowledge and technologies, statistics has achieved its own dignity of a unified intellectual discipline and now has become the primary approach of quantitative thinking for a considerable set of scientific problems (Efron 2004).
Once the process of defining reality as quantifiable, objective and ontologically restricted to the senses was branching out, it took the right statistical techniques before investigating the nature of the relations between the social constructs. Income, wealth and education are key information to quantify a theoretical concept such as social class into more readily observable data, but how is it possible to show the relationship between income and education? And which one affects the other? The answers to these questions have engaged philosophy and statistics for more than two centuries. Hume, who has proved extremely influential for the Western positivist approach, identified three fundamental criterions for a causation relation (Beauchamp et al 1981): 1) spatial-temporal contiguity, 2) temporal succession, 3) constant conjunction. So, a generical fact A causes B if:1) A and B are contiguous both in space and time, 2) A precedes B, 3) A and B always happen together. Hume’s concept of causality has some conceptual gaps, such as misreading correlation for causality, and a theoretical limitation resulting from the deterministic need to have a cause for any event (Holland, 1986). A more convincing definition was provided late in the ‘70s by Suppes, who defined causality in probabilistic terms. A generical event A is said to be prima facie cause of B when: 1) A precedes B, 2) If A occurs then probabilities of B occurring increase, 3) A is said to be a genuine cause of B when there is not any third event C, that precedes both A and B and that “eliminates” A’s ability to make B more likely to occur (Suppes 1970). Hume’s heritage however committed positivist intellectuals in seeking for the techniques to identify causality, even if correlation seldom indicates that a change in a variable implicates a variation in the other one. The main deficiency in the traditional approach is represented by the ambitious willingness to explain directly the causes, rather than to examine effects resulting from the causes. The contemporary approach specialized more in defining accurately what are the effects of having a low income on education, instead of striving to show which one causes the other (Pellegrini, 2014).
The failure of statistics to explain directly the causes represents an epistemological shortcoming derived from the positivist ill-advised approach in defining causality and what to measure about it. It is crucial to discuss further this point because it has represented for long the source of epistemological and ontological criticism to quantitative methodologies and it is also the cornerstone of this analysis. Given its interdisciplinarity “…it is a mistake to see statistical theory as a field of knowledge developing simply by its own internal logic and giving rise to necessarily value-free techniques. Rather, statistical theory… is a social, historical and ideological product and not merely a collection of neutral techniques.” (Mackenzie 1979). Statistics does not have a proper subject of study, like rivers, stars or viruses, (Lindsay et al 2004) and when applied to another science (that is to say most of the time) its validity depends on the level of knowledge and literature about that particular domain. Statistics does not tell what is rain, but only if it rains and the explanatory variables are a matter of study of atmosphere sciences. If there is an unobserved factor that is influencing the probability to rain, but has not been considered in the model, then analytical statistics will only reflect a limitation of the general knowledge about that phenomenon (and anyway the analysis will contribute to the process of transforming an unknown unknown in a known unknown, explained in the terms of psychologists Luft (1916–2014) and Harrington(1916-1995)). However, the critics argue that the context of discovery cannot be separable from the context of justification because of the strong social constructionist approach of statistics (Barnes 1997) while critical realism concluded that process of observation necessarily interacts with the results, especially when working with inferential statistics, where much of the data is gathered from external organizations that often collected the information for different purposes to those of the actual study (Minger 2003). Critical realists seem to be unaware of the fundamental problems of this critique because, according to Olsen and Morgan (2005), what is at risk is the practice and the attitude of the professional or the researcher who is using analytical statistics, misreading ontology as ideology.
This scenario suggests why the interference of the observer in the results represents an evergreen controversy when it comes to critically analyse quantitative methodologies and statistics, although this issue can be extended to all sciences. The debate becomes more argumentative if considering the historical marriage between statistics and the world of action. Given that not everything can be measured, the choice about what to count can have political connotations.