You are browsing through it may be that these lines because you just read the ticket issued in *The World*, in the book “Science & Techno” from Saturday, 9 June 2012, and that you wanted to know a little more ? Then welcome !

The format of this “card blanche” requires the concision, and little can be neither credit nor *a fortiori* to cite in sufficient detail the research and the publications on which I relied for the draft. Also, for the duration of this forum (and I’ve come to learn that she will continue to be available to me all the next year), I suggest you find it here, at the time of the publication of each of these ” white cards “, a ticket that is more long in which I’ll expand my remarks, and to bring a couple of reading suggestions : it will be a way to give back to my colleagues what I have borrowed to write these short notes.

# The French, unequal in the face of the holiday

For this last white card before the interruption of summer, I had at first imagined to take to object to the holiday, and in particular the persistence, relatively unknown, inequalities of holiday departures. I would have begun by recalling that when one wants to measure something, we must first define it, and that it is thus necessary to first agree on a definition of what it is like ” go on vacation “. If one adopts the definition of the INSEE, which borrows from the world tourism Organization, are counted as “holiday” travel at least four consecutive nights away from home, to the exclusion of business trips, study trips, stays motivated by the illness or death of a loved one and stays health in specialized institutions.

With this definition, observe-t-on ? There are a dozen of years, an article of Céline Rouquette in *Economics and statistics* pointed out the persistence of inequalities of holiday departures during the 1990s. Ten years later, the departure rate has decreased in the whole population, since today it is barely half (53%) of the French who go on holiday at least once in the year, against two-thirds in the 1990s. And most importantly, the disparities are still there : 71% of managers go on holiday at least once in the year, compared to only 41% of workers, according to a study by CREDOC.

# How to measure inequality ?

Just before the summer, I wanted to take this “pretext” and this example to explain that the sociological surveys, in contrast to the experiences of the sciences like biology or physics, produce only rarely ” discovered “, and that their results are rarely in the form of “laws” are immutable. Little discoveries, but often necessary reminders : against discourse delighted of all kinds, it was to show that the sociological work is therefore primarily intended to measure, describe, and attempt to dismantle the mechanisms of production and reproduction of inequalities that still persist in France in many areas of social life, in terms of holiday departures as we have just seen, but also of course in terms of education, jobs, wages, health, access to leisure activities, feeling of insecurity… Without the work sometimes tedious and a little frustrating, but absolutely crucial, also the Observatory of inequalities strives to make it as visible as possible, is that we would not have a tendency to forget that women’s wages remain 20% lower than those of men, the life expectancy of the frames still exceeds six years, the workers, and, therefore, that 75 years after the introduction of paid holidays, yet less than half of them go on vacation ?

But at this point, I said to myself, the question without doubt, the most interesting to deal with in this carte blanche, it was how these inequalities have evolved during the last decades, and if the French society became less unequal, or if they are dug to the contrary. The question is easy to formulate, the response is much less. How, indeed, does one measure inequality ? To stay in the news, a few days of the races on the bachelor, I wanted to take a simple example, that you can easily represent on a sheet of paper in a table with two rows and two columns : that of the evolution of the inequality to obtain the precious sesame. There are a half-century, 45% of children of managers were getting, compared to only 5% of children of workers ; today, 90% of children of managers are high school graduates, compared to 45% of the children of workers. Here is this table is very simple, that I could unfortunately not reproduce in the white card, but that helps very well, however, to visualize inequalities and their evolutions :

The inequalities have increased or decreased ? If we measure the differences between these proportions, they seem to have increased (the gap falls to 45-5=+40 points to 90-45=+45 points). But if we measure inequality by a ” report “, they seem to have declined : in 1960, the proportion of children of executives, who were high school graduates was 9 times greater (45/5) than that of the children of workers, it is now only 2-fold greater (90/45)…

Not only are these two ways of measuring inequalities contradict each other, but they are not necessarily adapted to the comparison of percentages, because they… may not exceed 100% : to maintain a graduation rate of the tray 9 times higher than that of the children of workers, children of cadres should now… be 405% to get it !

It is thus necessary to use indices that take into account the fact that on the path that leads not only to the famous “80% of an age class in the bachelor’s degree” (this was the aim at the horizon 2000, which was set in 1985 by Jean-Pierre Chevènement, the minister of education of the time), the last lengths are more difficult to navigate than the first. To account for this, there are at least two indicators competitors possible. The first is to divide the progress made by the maximum progress possible : between 1960 and today, the children of cadres have come (90-45)/(100-45) = 82% the path that separated him from the success total at the bachelor’s degree, and the children of workers only (45-5)/(100-5) = 42%% of this path. We finally have our answer ? Achievement gaps have increased ?

The problem is that the second possible indicator, the one that in reality has imposed itself among the sociologists, rather said the opposite. It is to calculate and compare instead of the *odds ratio*, or ” reports of the relative opportunities “, in other words, the relationship between the success rate and the failure rate. For example, today, a child of the frames is 90/(100-90) = 9 times more likely to get the pan as not to get it. And in the light of these reports of the relative opportunities, achievement gaps have declined : in 1960, the children of executives had [45/(100-45)]/[5/(100-5)] = 15,5 times more likely than the children of workers to get the tray, rather than not obtain it ; today, they have “only” [90/(100-90)]/[45/(100-45)] = 11 times more likely.

# “The findings of the roses” and ” conclusions black “

If the sentences it takes to speak these *odds ratio* are sometimes a little convoluted, with these “rather than” the dot, it must be recognized that they are very seductive, because they are easy to calculate (no need of complicated software, a tiny calculator is sufficient), and they seem to solve very satisfactorily to mind the problem of the non-linearity of growth rates in percentage. Yet, for some, if the *odds ratio* were imposed since the 1990s, in particular among sociologists of education, in high consumption, it would not be because they were more properly the variations in inequality, but because they were… more optimistic !

This is the very meaning of the “controversy” on the measurement of inequality, which runs through the sociology of france since the mid-1980s. I’ll give a quick overview, but here is already the bibliography, in chronological order of publication, of the main items which mark out this exciting discussion methodological :

Combessie Jean-Claude, 1984, ” The evolution of comparative inequality : statistical problems “,

French Review of sociology, 25(2), 1984, p. 233-254. Online : http://www.persee.fr/web/revues/home/prescript/article/rfsoc_0035-2969_1984_num_25_2_3793Florens Jean-Pierre, 1984, ” Inequality and addiction statistics “,

French Review of sociology, 25(2), p. 255-263. Online : http://www.persee.fr/web/revues/home/prescript/article/rfsoc_0035-2969_1984_num_25_2_3794Grémy Jean-Paul, 1984, ” On the differences between percentages and their interpretation “,

French Review of sociology, 25(3), p. 396-420. Online : http://www.persee.fr/web/revues/home/prescript/article/rfsoc_0035-2969_1984_num_25_3_3824Prevot, Jean, 1985, ” about indexes and comparisons of proportions “, French Review of sociology, 26(4), p. 601-628. Online : http://www.persee.fr/web/revues/home/prescript/article/rfsoc_0035-2969_1985_num_26_4_3987

Combessie Jean-Claude, 2004, ” Thirty years of comparison of inequality of opportunity : when the method used determines the conclusion,”

Courrier des statistiques, 112, , p. 37-54. Online : http://www.insee.fr/fr/ffc/docs_ffc/cs112e.pdfVallet, Louis-André, 2007, ” On the origin, the reasons of the use, and the fertility of the odds ratio “,

Courrier des statistiques, 121-122, p. 59-65. Online : http://www.insee.fr/fr/ffc/docs_ffc/cs121k.pdfCombessie Jean-Claude, 2007, ” Response to Louis-André Vallet “,

Courrier des statistiques, 121-122, p. 66. Online : http://www.insee.fr/fr/ffc/docs_ffc/cs121l.pdfCombessie Jean-Claude, 2011, ” a critical Analysis of a history of the statistical treatment of the inequalities of fate. The case of the evolution of chance of access to higher education,

Acts of research in social sciences, n° 188, p. 4-31.

As we can see through this bibliography, it is a case that was particularly to the heart of Jean-Claude Combessie. It is difficult for me to summarize his argument in a few lines, but reading his last article, published in 2011 in the *proceedings of the research in the social sciences*, the journal created in 1975 by Pierre Bourdieu, can provide a very good summary. Unfortunately, the article is available online but restricted access on Cairn, you can also read his article of 2004, and one published by Louis-André Vallet in 2007, in the *Courrier des statistiques*, both easy to access and mostly free. Here is what it returns : Jean-Claude Combessie reviews the various different ways of measuring inequality that we have discussed previously (difference, ratio, rate of change compared with the maximum variation, odds ratio), and submits them to the test of the extent of the evolutions of the different forms of inequality in school for the past three decades, to demonstrate that the use of the odds ratio results more often than the other measures, and in particular more often than the rate of change compared with the maximum variation, “conclusions the roses “, in other words to measures suggesting a decrease in inequality.

# The odds ratio, a “conservative revolution” ?

The question is then whether there is an indicator that is better than the other. For Louis-André Vallet this is the case : it is the odds ratio, that there are “good statistical reasons” to consider as the indicator, the more “natural” to account for the developments capped, as is the case for percentages. For Jean-Claude Combessie, there, on the contrary, nothing natural in there, and it should instead examine the reasons that have sociologists to give priority to this indicator, that he suspected of not always being ” statistics “. In fact, in the second part of his demonstration, Jean-Claude Combessie resumes the data analyzed in the literature of the last thirty years about the inequalities in the school (the principal articles are reported in the bibliography at the end of this post), calculates the different indicators to see if they will lead to the findings of “black” or ” pink “, and compares them with those actually used by the authors of the articles : it appears then, that more often than expected, these tend to use indicators that allow to conclude to a decrease of inequalities at school. In some cases, the same authors change can be an indicator of an article to another, to choose precisely such-and-such in the light of the findings “optimistic” that it allows to achieve.

For Jean-Claude Combessie, any indicator that is not “statistically” or “sociologically” better than another, it is thus necessary to examine the social meanings and political choices made by the sociologists of education, a question that led him to describe the success of the odds ratio as a symptom of a “conservative revolution” in the measurement of inequality, which tends to describe the areas where orthodoxy previous statistic tended to describe aggravations.

# For an eclecticism statistics

What practical conclusion should we draw ? To see more clearly, practically, one can take again the example of the evolution of inequalities for obtaining the bachelor’s degree, this time by examining a more complete set of data. It is not very easy to find, but you can use the graphic below, published in the latest edition of *the state of The school*, a publication of the Ministry of national education, to try to reconstruct :

In the table below, I have in the left column tried to reconstitute approximately the rate of obtaining a bachelor’s degree in successive generations of children of cadres and children of manual workers, and then in the right column I have measured the variations of these rates with the four indicators mentioned since the beginning of this post :

What do we see ? That, on the whole, it almost never happens to the reports and the odds ratio of making ” conclusions black “, then that is very clearly the case in particular of the relationship between the gap and the maximum gap possible. What should I do in these cases ? A position that is relatively simple is to foster the eclecticism statistics, and therefore to present the differing results reported by the various indicators. We will show by example, that between the children of cadres and children of manual workers born between 1979 and 1983, and who have therefore attained the normal age of the bachelor’s degree between 1997 and 2001, the inequality to obtain the bac had decreased if we consider the odds ratio, but increased if we consider the ratio between the observed deviation and the maximum deviation possible, without it being possible to decide that one of these two indicators is “better” than the other. On one side, we can say, for example, that the odds ratio allows a satisfactory way of reducing the gap between values whose variations are limited, as is the case for the percentages ; but on the other hand, the rate of change compared with the maximum possible variation in well aware of the subjective perceptions of inequalities remaining that may have the individuals : to the extent that their situations are improving, for example, in school, successive generations become more sensitive to variances smaller, which would have previously been considered insignificant.

# The evolution of educational differences, a complex equation

So far, I have tried to be careful to speak only of the inequalities of obtaining a bachelor’s degree between children of cadres and children of manual workers. In reality, if one wishes to judge of the evolution of the ” school inequalities in general “, then the equation becomes a little more complex, and it is no longer only a question of choice of indicators. On the one hand, in fact, to quote the title of an article published by Françoise Oeuvrard there are more than thirty years, we must not confuse “democratization” and “elimination” deferred : the possible reduction of inequalities to obtain the tray was accompanied by a decrease in the discriminatory power of the latter on the labour market, the benefit of higher levels of studies, where we do not see the same reduction in inequality. How to measure the effects of movement on the general evolution of inequality ? There are some interesting hypotheses on this subject in the article by Claude Thélot and Louis-André Vallet, on “the reduction of social inequalities in front of the school since the beginning of the century” (2000).

And on the other hand, there is at least one other phenomenon to be taken into account if one wants to measure the general evolution of school inequalities : it is not enough to measure inequalities between children of managers and workers, or more generally, between children of different social backgrounds, it is also necessary to take account of the fact that the social structure itself is changing, that the distribution of students between different social backgrounds changes, and that, for example, there are more and more children of cadres and fewer children of workers. Even in school completion rates unchanged for these two categories, these changes of structure are sufficient to change the overall level of inequality in the whole population considered. Then there must be other indicators, such as, for example, the Gini coefficient, but that is another story… This will be for a next post !

# Bibliographic references

Barbut, Marc, 2007, *The Measurement of inequality. Ambiguities and paradoxes*, Geneva, Droz

Duru-Bellat Marie, Kieffer, Annick, 2000, ” The democratization of education in France. Controversy around a topical issue “, *Population*, 55(1), p. 51-80. Online : http://www.persee.fr/web/revues/home/prescript/article/pop_0032-4663_2000_num_55_1_7097

Euriat Michel, Thélot, Claude, 1995, ” The social recruitment of the elite school in France. Evolution of inequality from 1950 to 1990 “, Revue française de sociologie, 36(3), p. 403-438. Online : http://www.persee.fr/web/revues/home/prescript/article/rfsoc_0035-2969_1995_num_36_3_5065

Florens Jean-Pierre, 1984, ” Inequality and addiction statistics “, *French Review of sociology*, 25(2), p. 255-263. Online : http://www.persee.fr/web/revues/home/prescript/article/rfsoc_0035-2969_1984_num_25_2_3794

Goux Dominique, Maurin, Eric Maurin, 1997, “Democratization of school, and persistence of inequality,” Economics and Statistics, 306, p. 27-39. Online : http://www.persee.fr/web/revues/home/prescript/article/estat_0336-1454_1997_num_306_1_2570

Grémy Jean-Paul, 1984, ” On the differences between percentages and their interpretation “, *French Review of sociology*, 25(3), p. 396-420. Online : http://www.persee.fr/web/revues/home/prescript/article/rfsoc_0035-2969_1984_num_25_3_3824

Hoibian Sandra, 2010, ” Holiday 2010 : The financial constraints foster new trade-offs “, Crédoc, survey on ” living Conditions and Aspirations of the French “. Online : http://www.credoc.fr/pdf/Sou/vacances_ete_2010.pdf

Maurin, Louis, 2008, “The Observatory of inequalities : a status report “, *Information sociales*, n° 148, p. 106-107. Online : http://www.cairn.info/revue-informations-sociales-2008-4-page-106.htm

Maurin, Louis, Savidan, Patrick (ed), 2008, *The state of inequality in France. Data and analyses*, Belin

Oeuvrard Françoise, 1979, ” “Democratisation,” or elimination deferred ? Note on the evolution of social recruitment of secondary education in France, between 1958 and 1976 “, *Acts of research in social sciences*, 30, p. 87-97. Online : http://www.persee.fr/web/revues/home/prescript/article/arss_0335-5322_1979_num_30_1_3491

Prevot, Jean, 1985, ” about indexes and comparisons of proportions “, French Review of sociology, 26(4), p. 601-628. Online : http://www.persee.fr/web/revues/home/prescript/article/rfsoc_0035-2969_1985_num_26_4_3987

Prost, Antoine, 1986, *education is democratized ?*, Paris, PUF

Rouquette Celine, 2001, ” holiday Departures: the persistence of inequality “, *Economics and Statistics*, 345, 1, pp. 33-53. Online : http://www.insee.fr/fr/ffc/docs_ffc/ES345B.pdf

Thélot, Claude, Vallet, Louis-André, 2000, ” The reduction of inequities in the school since the beginning of the century “, *Economie et Statistique*, n° 334, p. 3-32. Online : http://www.insee.fr/fr/ffc/docs_ffc/es334a.pdf

Vallet, Louis-André, 1988, ” The evolution of inequality of opportunity in education. A point of view of statistical modelling “, *French Review of sociology*, 29(3), p. 395-423. Online : http://www.persee.fr/web/revues/home/prescript/article/rfsoc_0035-2969_1988_num_29_3_2524

Vallet, Louis-André, 2007, ” On the origin, the reasons of the use, and the fertility of the odds ratio “, *Courrier des statistiques*, 121-122, p. 59-66. Online : http://www.insee.fr/fr/ffc/docs_ffc/cs121k.pdf