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Thursday, April 28, 2022

Ecological fallacy

From Wikipedia, the free encyclopedia
 
An ecological fallacy (also ecological inference fallacy or population fallacy) is a formal fallacy in the interpretation of statistical data that occurs when inferences about the nature of individuals are deduced from inferences about the group to which those individuals belong. 'Ecological fallacy' is a term that is sometimes used to describe the fallacy of division, which is not a statistical fallacy. The four common statistical ecological fallacies are: confusion between ecological correlations and individual correlations, confusion between group average and total average, Simpson's paradox, and confusion between higher average and higher likelihood.

Examples

Mean and median

An example of ecological fallacy is the assumption that a population mean has a simple interpretation when considering likelihoods for an individual.

For instance, if the mean score of a group is larger than zero, this does not imply that a random individual of that group is more likely to have a positive score than a negative one (as long as there are more negative scores than positive scores an individual is more likely to have a negative score). Similarly, if a particular group of people is measured to have a lower mean IQ than the general population, it is an error to conclude that a randomly-selected member of the group is more likely than not to have a lower IQ than the mean IQ of the general population; it is also not necessarily the case that a randomly selected member of the group is more likely than not to have a lower IQ than a randomly-selected member of the general population. Mathematically, this comes from the fact that a distribution can have a positive mean but a negative median. This property is linked to the skewness of the distribution.

Consider the following numerical example:

  • Group A: 80% of people got 40 points and 20% of them got 95 points. The mean score is 51 points.
  • Group B: 50% of people got 45 points and 50% got 55 points. The mean score is 50 points.
  • If we pick two people at random from A and B, there are 4 possible outcomes:
    • A – 40, B – 45 (B wins, 40% probability – 0.8 × 0.5)
    • A – 40, B – 55 (B wins, 40% probability – 0.8 × 0.5)
    • A – 95, B – 45 (A wins, 10% probability – 0.2 × 0.5)
    • A – 95, B – 55 (A wins, 10% probability – 0.2 × 0.5)
  • Although Group A has a higher mean score, 80% of the time a random individual of A will score lower than a random individual of B.

Individual and aggregate correlations

Research dating back to Émile Durkheim suggests that predominantly Protestant localities have higher suicide rates than predominantly Catholic localities. According to Freedman, the idea that Durkheim's findings link, at an individual level, a person's religion to his or her suicide risk is an example of the ecological fallacy. A group-level relationship does not automatically characterize the relationship at the level of the individual.

Similarly, even if at the individual level, wealth is positively correlated to tendency to vote Republican, we observe that wealthier states tend to vote Democratic. For example, in 2004, the Republican candidate, George W. Bush, won the fifteen poorest states, and the Democratic candidate, John Kerry, won 9 of the 11 wealthiest states. Yet 62% of voters with annual incomes over $200,000 voted for Bush, but only 36% of voters with annual incomes of $15,000 or less voted for Bush. Aggregate-level correlation will differ from individual-level correlation if voting preferences are affected by the total wealth of the state even after controlling for individual wealth. It could be that the true driving factor in voting preference is self-perceived relative wealth; perhaps those who see themselves as better off than their neighbours are more likely to vote Republican. In this case, an individual would be more likely to vote Republican if she became wealthier, but she would be more likely to vote for a Democrat if her neighbor's wealth increased (resulting in a wealthier state).

However, the observed difference in voting habits based on state-level and individual-level wealth could also be explained by the common confusion between higher averages and higher likelihoods as discussed above. States may not be wealthier because they contain more wealthy people (i.e. more people with annual incomes over $200,000), but rather because they contain a small number of super-rich individuals; the ecological fallacy then results from incorrectly assuming that individuals in wealthier states are more likely to be wealthy.

Many examples of ecological fallacies can be found in studies of social networks, which often combine analysis and implications from different levels. This has been illustrated in an academic paper on networks of farmers in Sumatra.

Robinson's paradox

A 1950 paper by William S. Robinson computed the illiteracy rate and the proportion of the population born outside the US for each state and for the District of Columbia, as of the 1930 census. He showed that these two figures were associated with a negative correlation of −0.53; in other words, the greater the proportion of immigrants in a state, the lower its average illiteracy. However, when individuals are considered, the correlation was +0.12 (immigrants were on average more illiterate than native citizens). Robinson showed that the negative correlation at the level of state populations was because immigrants tended to settle in states where the native population was more literate. He cautioned against deducing conclusions about individuals on the basis of population-level, or "ecological" data. In 2011, it was found that Robinson's calculations of the ecological correlations are based on the wrong state level data. The correlation of −0.53 mentioned above is in fact −0.46. Robinson's paper was seminal, but the term 'ecological fallacy' was not coined until 1958 by Selvin.

Formal problem

The correlation of aggregate quantities (or ecological correlation) is not equal to the correlation of individual quantities. Denote by XiYi two quantities at the individual level. The formula for the covariance of the aggregate quantities in groups of size N is

The covariance of two aggregated variables depends not only on the covariance of two variables within the same individuals but also on covariances of the variables between different individuals. In other words, correlation of aggregate variables take into account cross sectional effects which are not relevant at the individual level.

The problem for correlations entails naturally a problem for regressions on aggregate variables: the correlation fallacy is therefore an important issue for a researcher who wants to measure causal impacts. Start with a regression model where the outcome is impacted by

The regression model at the aggregate level is obtained by summing the individual equations:

Nothing prevents the regressors and the errors from being correlated at the aggregate level. Therefore, generally, running a regression on aggregate data does not estimate the same model than running a regression with individual data.

The aggregate model is correct if and only if

This means that, controlling for , does not determine .

Choosing between aggregate and individual inference

There is nothing wrong in running regressions on aggregate data if one is interested in the aggregate model. For instance, for the governor of a state, it is correct to run regressions between police force on crime rate at the state level if one is interested in the policy implication of a rise in police force. However, an ecological fallacy would happen if a city council deduces the impact of an increase in police force in the crime rate at the city level from the correlation at the state level.

Choosing to run aggregate or individual regressions to understand aggregate impacts on some policy depends on the following trade-off: aggregate regressions lose individual level data but individual regressions add strong modeling assumptions. Some researchers suggest that the ecological correlation gives a better picture of the outcome of public policy actions, thus they recommend the ecological correlation over the individual level correlation for this purpose (Lubinski & Humphreys, 1996). Other researchers disagree, especially when the relationships among the levels are not clearly modeled. To prevent ecological fallacy, researchers with no individual data can model first what is occurring at the individual level, then model how the individual and group levels are related, and finally examine whether anything occurring at the group level adds to the understanding of the relationship. For instance, in evaluating the impact of state policies, it is helpful to know that policy impacts vary less among the states than do the policies themselves, suggesting that the policy differences are not well translated into results, despite high ecological correlations (Rose, 1973).

Group and total averages

Ecological fallacy can also refer to the following fallacy: the average for a group is approximated by the average in the total population divided by the group size. Suppose one knows the number of Protestants and the suicide rate in the USA, but one does not have data linking religion and suicide at the individual level. If one is interested in the suicide rate of Protestants, it is a mistake to estimate it by the total suicide rate divided by the number of Protestants. Formally, denote the mean of the group, we generally have:

However, the law of total probability gives

As we know that is between 0 and 1, this equation gives a bound for .

Simpson's paradox

A striking ecological fallacy is Simpson's paradox: the fact that when comparing two populations divided into groups, the average of some variable in the first population can be higher in every group and yet lower in the total population. Formally, when each value of Z refers to a different group and X refers to some treatment, it can happen that

When does not depend on , the Simpson's paradox is exactly the omitted variable bias for the regression of Y on X where the regressor is a dummy variable and the omitted variable is a categorical variable defining groups for each value it takes. The application is striking because the bias is high enough that parameters have opposite signs.

Legal applications

The ecological fallacy was discussed in a court challenge to the 2004 Washington gubernatorial election in which a number of illegal voters were identified, after the election; their votes were unknown, because the vote was by secret ballot. The challengers argued that illegal votes cast in the election would have followed the voting patterns of the precincts in which they had been cast, and thus adjustments should be made accordingly. An expert witness said this approach was like trying to figure out Ichiro Suzuki's batting average by looking at the batting average of the entire Seattle Mariners team, since the illegal votes were cast by an unrepresentative sample of each precinct's voters, and might be as different from the average voter in the precinct as Ichiro was from the rest of his team. The judge determined that the challengers' argument was an ecological fallacy and rejected it.

 

Ethnic groups in Europe

From Wikipedia, the free encyclopedia

Europeans are the focus of European ethnology, the field of anthropology related to the various indigenous groups that reside in the states of Europe. Groups may be defined by common genetic ancestry, common language, or both. Pan and Pfeil (2004) count 87 distinct "peoples of Europe", of which 33 form the majority population in at least one sovereign state, while the remaining 54 constitute ethnic minorities. The total number of national minority populations in Europe is estimated at 105 million people, or 14% of 770 million Europeans. The Russians are the most populous among Europeans, with a population over 134 million. There are no universally accepted and precise definitions of the terms "ethnic group" and "nationality". In the context of European ethnography in particular, the terms ethnic group, people, nationality and ethno-linguistic group, are used as mostly synonymous, although preference may vary in usage with respect to the situation specific to the individual countries of Europe.

Overview

About 20–25 million residents (3%) are members of diasporas of non-European origin. The population of the European Union, with some 450 million residents, accounts for two thirds of the current European population.

Both Spain and the United Kingdom are special cases, in that the designation of nationality, Spanish and British, may controversially take ethnic aspects, subsuming various regional ethnic groups (see nationalisms and regionalisms of Spain and native populations of the United Kingdom). Switzerland is a similar case, but the linguistic subgroups of the Swiss are discussed in terms of both ethnicity and language affiliations.

Linguistic classifications

Distribution of major languages of Europe

Of the total population of Europe of some 740 million (as of 2010), close to 90% (or some 650 million) fall within three large branches of Indo-European languages, these being;

Three stand-alone Indo-European languages do not fall within larger sub-groups and are not closely related to those larger language families;

In addition, there are also smaller sub-groups within the Indo-European languages of Europe, including;

Besides the Indo-European languages, there are other language families on the European continent which are considered unrelated to Indo-European:

History

Prehistoric populations

Simplified model for the demographic history of Europeans during the Neolithic period and the introduction of agriculture.

The Basques have been found to descend from the population of the late Neolithic or early Bronze Age directly. By contrast, Indo-European groups of Europe (the Centum, Balto-Slavic, and Albanian groups) migrated throughout most of Europe from the Pontic steppe. They are assumed to have developed in situ through admixture of earlier Mesolithic and Neolithic populations with Bronze Age, proto-Indo-Europeans. The Finnic peoples are assumed to also be descended from Proto-Uralic populations further to the east, nearer to the Ural Mountains, that had migrated to their historical homelands in Europe by about 3,000 years ago. A more recent study in 2019 found that proto-Uralic may have originated further East in Siberia among an East Asian-related populations. The authors link the arrival of Uralic languages to the arrival of Siberian-like ancestry to the Baltic region.

Reconstructed languages of Iron Age Europe include Proto-Celtic, Proto-Italic and Proto-Germanic, all of these Indo-European languages of the centum group, and Proto-Slavic and Proto-Baltic, of the satem group. A group of Tyrrhenian languages appears to have included Etruscan, Rhaetian, Lemnian, and perhaps Camunic. A pre-Roman stage of Proto-Basque can only be reconstructed with great uncertainty.

Regarding the European Bronze Age, the only relatively likely reconstruction is that of Proto-Greek (ca. 2000 BC). A Proto-Italo-Celtic ancestor of both Italic and Celtic (assumed for the Bell beaker period), and a Proto-Balto-Slavic language (assumed for roughly the Corded Ware horizon) has been postulated with less confidence. Old European hydronymy has been taken as indicating an early (Bronze Age) Indo-European predecessor of the later centum languages.

According to geneticist David Reich, based on ancient human genomes that his laboratory sequenced in 2016, Europeans descend from a mixture of four distinct ancestral components.

Historical populations

Map of the Roman Empire and barbarian tribes in 125 AD.

Iron Age (pre-Great Migrations) populations of Europe known from Greco-Roman historiography, notably Herodotus, Pliny, Ptolemy and Tacitus:

Historical immigration

Map showing the distribution of Slavic tribes between the 7th–9th centuries AD.

Ethno-linguistic groups that arrived from outside Europe during historical times are:

History of European ethnography

Europa Regina (Representation of Europe printed by Sebastian Munster (1570).
 
Ethnographic map of Europe, The Times Atlas (1896).

The earliest accounts of European ethnography date from Classical Antiquity. Herodotus described the Scythians and Thraco-Illyrians. Dicaearchus gave a description of Greece itself, besides accounts of western and northern Europe. His work survives only fragmentarily, but was received by Polybius and others.

Roman Empire period authors include Diodorus Siculus, Strabo and Tacitus. Julius Caesar gives an account of the Celtic tribes of Gaul, while Tacitus describes the Germanic tribes of Magna Germania. A number of authors like Diodorus Siculus, Pausanias and Sallust depict the ancient Sardinian and Corsican peoples.

The 4th century Tabula Peutingeriana records the names of numerous peoples and tribes. Ethnographers of Late Antiquity such as Agathias of Myrina Ammianus Marcellinus, Jordanes and Theophylact Simocatta give early accounts of the Slavs, the Franks, the Alamanni and the Goths.

Book IX of Isidore's Etymologiae (7th century) treats de linguis, gentibus, regnis, militia, civibus (concerning languages, peoples, realms, war and cities). Ahmad ibn Fadlan in the 10th century gives an account of the Bolghar and the Rus' peoples. William Rubruck, while most notable for his account of the Mongols, in his account of his journey to Asia also gives accounts of the Tatars and the Alans. Saxo Grammaticus and Adam of Bremen give an account of pre-Christian Scandinavia. The Chronicon Slavorum (12th century) gives an account of the northwestern Slavic tribes.

Gottfried Hensel in his 1741 Synopsis Universae Philologiae published one of the earliest ethno-linguistic map of Europe, showing the beginning of the pater noster in the various European languages and scripts. In the 19th century, ethnicity was discussed in terms of scientific racism, and the ethnic groups of Europe were grouped into a number of "races", Mediterranean, Alpine and Nordic, all part of a larger "Caucasian" group.

The beginnings of ethnic geography as an academic subdiscipline lie in the period following World War I, in the context of nationalism, and in the 1930s exploitation for the purposes of fascist and Nazi propaganda, so that it was only in the 1960s that ethnic geography began to thrive as a bona fide academic subdiscipline.

The origins of modern ethnography are often traced to the work of Bronisław Malinowski, who emphasized the importance of fieldwork. The emergence of population genetics further undermined the categorisation of Europeans into clearly defined racial groups. A 2007 study on the genetic history of Europe found that the most important genetic differentiation in Europe occurs on a line from the north to the south-east (northern Europe to the Balkans), with another east–west axis of differentiation across Europe, separating the indigenous Basques, Sardinians and Sami from other European populations. Despite these stratifications it noted the unusually high degree of European homogeneity: "there is low apparent diversity in Europe with the entire continent-wide samples only marginally more dispersed than single population samples elsewhere in the world."

Minorities

Gagauz people in Moldova
 
Sámi family in Lapland of Finland, 1936.

The total number of national minority populations in Europe is estimated at 105 million people, or 14% of Europeans.

The member states of the Council of Europe in 1995 signed the Framework Convention for the Protection of National Minorities. The broad aims of the Convention are to ensure that the signatory states respect the rights of national minorities, undertaking to combat discrimination, promote equality, preserve and develop the culture and identity of national minorities, guarantee certain freedoms in relation to access to the media, minority languages and education and encourage the participation of national minorities in public life. The Framework Convention for the Protection of National Minorities defines a national minority implicitly to include minorities possessing a territorial identity and a distinct cultural heritage. By 2008, 39 member states had signed and ratified the Convention, with the notable exception of France.

Indigenous minorities

Various European ethnic groups have lived there for millennia, however, the UN recognizes very few indigenous populations of Europe, which are confined to the far north and far east of the continent.

Notable indigenous minority populations in Europe that are recognized by the UN include the Uralic Nenets, Samoyed, and Komi peoples of northern Russia; Circassians of southern Russia and the North Caucasus; Crimean Tatars, Krymchaks and Crimean Karaites of Crimea in Ukraine; Sámi peoples of northern Norway, Sweden, and Finland and northwestern Russia (in an area also referred to as Sápmi); Basques of Basque Country, Spain and southern France; and the Sorbian people of Germany and Poland.

Non-indigenous minorities

Expulsions of Jews in Europe from 1100 to 1600

Many non-European ethnic groups and nationalities have migrated to Europe over the centuries. Some arrived centuries ago. However, the vast majority arrived more recently, mostly in the 20th and 21st centuries. Often, they come from former colonies of the British, Dutch, French, Portuguese and Spanish empires.

European identity

Historical

Personifications of Sclavinia, Germania, Gallia, and Roma, bringing offerings to Otto III; from a gospel book dated 990.

Medieval notions of a relation of the peoples of Europe are expressed in terms of genealogy of mythical founders of the individual groups. The Europeans were considered the descendants of Japheth from early times, corresponding to the division of the known world into three continents, the descendants of Shem peopling Asia and those of Ham peopling Africa. Identification of Europeans as "Japhetites" is also reflected in early suggestions for terming the Indo-European languages "Japhetic".

In this tradition, the Historia Brittonum (9th century) introduces a genealogy of the peoples of the Migration Period based on the sixth-century Frankish Table of Nations as follows,

The first man that dwelt in Europe was Alanus, with his three sons, Hisicion, Armenon, and Neugio. Hisicion had four sons, Francus, Romanus, Alamanus, and Bruttus. Armenon had five sons, Gothus, Valagothus, Cibidus, Burgundus, and Longobardus. Neugio had three sons, Vandalus, Saxo, and Boganus.
From Hisicion arose four nations—the Franks, the Latins, the Germans, and Britons; from Armenon, the Gothi, Valagothi, Cibidi, Burgundi, and Longobardi; from Neugio, the Bogari, Vandali, Saxones, and Tarincgi. The whole of Europe was subdivided into these tribes.[60]

The text goes then on to list the genealogy of Alanus, connecting him to Japheth via eighteen generations.

European culture

European culture is largely rooted in what is often referred to as its "common cultural heritage". Due to the great number of perspectives which can be taken on the subject, it is impossible to form a single, all-embracing conception of European culture. Nonetheless, there are core elements which are generally agreed upon as forming the cultural foundation of modern Europe. One list of these elements given by K. Bochmann includes:

Berting says that these points fit with "Europe's most positive realisations". The concept of European culture is generally linked to the classical definition of the Western world. In this definition, Western culture is the set of literary, scientific, political, artistic and philosophical principles which set it apart from other civilizations. Much of this set of traditions and knowledge is collected in the Western canon. The term has come to apply to countries whose history has been strongly marked by European immigration or settlement during the 18th and 19th centuries, such as the Americas, and Australasia, and is not restricted to Europe.

Religion

Eurobarometer Poll 2005 chart results

Since the High Middle Ages, most of Europe has been dominated by Christianity. There are three major denominations: Roman Catholic, Protestant and Eastern Orthodox, with Protestantism restricted mostly to Northern Europe, and Orthodoxy to East and South Slavic regions, Romania, Moldova, Greece, and Georgia. The Armenian Apostolic Church, part of the Oriental Church, is also in Europe – another branch of Christianity (world's oldest National Church). Catholicism, while typically centered in Western Europe, also has a very significant following in Central Europe (especially among the Germanic, Western Slavic and Hungarian peoples/regions) as well as in Ireland (with some in Great Britain).

Christianity has been the dominant religion shaping European culture for at least the last 1700 years. Modern philosophical thought has very much been influenced by Christian philosophers such as St Thomas Aquinas and Erasmus. And throughout most of its history, Europe has been nearly equivalent to Christian culture, The Christian culture was the predominant force in western civilization, guiding the course of philosophy, art, and science. The notion of "Europe" and the "Western World" has been intimately connected with the concept of "Christianity and Christendom" many even attribute Christianity for being the link that created a unified European identity.

Christianity is still the largest religion in Europe; according to a 2011 survey, 76.2% of Europeans considered themselves Christians. Also according to a study on Religiosity in the European Union in 2012, by Eurobarometer, Christianity is the largest religion in the European Union, accounting for 72% of the EU's population. As of 2010 Catholics were the largest Christian group in Europe, accounting for more than 48% of European Christians. The second-largest Christian group in Europe were the Orthodox, who made up 32% of European Christians. About 19% of European Christians were part of the Protestant tradition. Russia is the largest Christian country in Europe by population, followed by Germany and Italy.

Islam has some tradition in the Balkans and the Caucasus due to conquest and colonization from the Ottoman Empire in the 16th to 19th centuries, as well as earlier though discontinued long-term presence in much of Iberia as well as Sicily. Muslims account for the majority of the populations in Albania, Azerbaijan, Kosovo, Northern Cyprus (controlled by Turks), and Bosnia and Herzegovina. Significant minorities are present in the rest of Europe. Russia also has one of the largest Muslim communities in Europe, including the Tatars of the Middle Volga and multiple groups in the Caucasus, including Chechens, Avars, Ingush and others. With 20th-century migrations, Muslims in Western Europe have become a noticeable minority. According to the Pew Forum, the total number of Muslims in Europe in 2010 was about 44 million (6%), while the total number of Muslims in the European Union in 2007 was about 16 million (3.2%).

Judaism has a long history in Europe, but is a small minority religion, with France (1%) the only European country with a Jewish population in excess of 0.5%. The Jewish population of Europe is composed primarily of two groups, the Ashkenazi and the Sephardi. Ancestors of Ashkenazi Jews likely migrated to Central Europe at least as early as the 8th century, while Sephardi Jews established themselves in Spain and Portugal at least one thousand years before that. Jews originated in the Levant where they resided for thousands of years until the 2nd century AD, when they spread around the Mediterranean and into Europe, although small communities were known to exist in Greece as well as the Balkans since at least the 1st century BC. Jewish history was notably affected by the Holocaust and emigration (including Aliyah, as well as emigration to America) in the 20th century. The Jewish population of Europe in 2010 was estimated to be approximately 1.4 million (0.2% of European population) or 10% of the world's Jewish population. In the 21st century, France has the largest Jewish population in Europe, followed by the United Kingdom, Germany, Russia and Ukraine.

In modern times, significant secularization since the 20th century, notably in secularist France, Estonia and the Czech Republic. Currently, distribution of theism in Europe is very heterogeneous, with more than 95% in Poland, and less than 20% in the Czech Republic and Estonia. The 2005 Eurobarometer poll found that 52% of EU citizens believe in God. According to a Pew Research Center Survey in 2012 the Religiously Unaffiliated (Atheists and Agnostics) make up about 18.2% of the European population in 2010. According to the same Survey the Religiously Unaffiliated make up the majority of the population in only two European countries: Czech Republic (76%) and Estonia (60%).

Pan-European identity

"Pan-European identity" or "Europatriotism" is an emerging sense of personal identification with Europe, or the European Union as a result of the gradual process of European integration taking place over the last quarter of the 20th century, and especially in the period after the end of the Cold War, since the 1990s. The foundation of the OSCE following the 1990s Paris Charter has facilitated this process on a political level during the 1990s and 2000s.

From the later 20th century, 'Europe' has come to be widely used as a synonym for the European Union even though there are millions of people living on the European continent in non-EU member states. The prefix pan implies that the identity applies throughout Europe, and especially in an EU context, and 'pan-European' is often contrasted with national identity.

Authorship of the Bible

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