Cultural assimilation

From Wikipedia, the free encyclopedia
https://en.wikipedia.org/wiki/Cultural_assimilation

Cultural assimilation is the process in which a minority group or culture comes to resemble a society's majority group or assimilates the values, behaviors, and beliefs of another group whether fully or partially.

The different types of cultural assimilation include full assimilation and forced assimilation. Full assimilation is the more prevalent of the two, as it occurs spontaneously. When used as a political ideology, assimilationism refers to governmental policies of deliberately assimilating ethnic groups into the national culture.

During cultural assimilation, minority groups are expected to adapt to the everyday practices of the dominant culture through language and appearance as well as via more significant socioeconomic factors such as absorption into the local cultural and employment communities.

Some types of cultural assimilation resemble acculturation in which a minority group or culture completely assimilates into the dominant culture in which defining characteristics of the minority culture are less obverse or outright disappear; while in other types of cultural assimilation such as cultural integration mostly found in multicultural communities, a minority group within a given society adopts aspects of the dominant culture through either cultural diffusion or for practical reason like adapting to another society's social norms while retaining their original culture. A conceptualization describes cultural assimilation as similar to acculturation while another merely considers the former as one of the latter's phases. Throughout history there have been different forms of cultural assimilation. Examples of types of acculturation include voluntary and involuntary assimilation.

Assimilation could also involve the so-called additive acculturation wherein, instead of replacing the ancestral culture, an individual expands their existing cultural repertoire.

Overview

Cultural assimilation may involve either a quick or a gradual change depending on the circumstances of the group. Full assimilation occurs when members of a society become indistinguishable from those of the dominant group in society.

Whether a given group should assimilate is often disputed by both members of the group and others in society. Cultural assimilation does not guarantee social alikeness. Geographical and other natural barriers between cultures, even if created by the predominant culture, may be culturally different. Cultural assimilation can happen either spontaneously or forcibly, the latter when more dominant cultures use various means aimed at forced assimilation.

Various types of assimilation, including forced cultural assimilation, are particularly relevant regarding Indigenous groups during colonialism taking place between the 18th, 19th, and 20th centuries. This type of assimilation included religious conversion, separation of families, changes of gender roles, division of property among foreign power, elimination of local economies, and lack of sustainable food supply. Whether via colonialism or within one nation, methods of forced assimilation are often unsustainable, leading to revolts and collapses of power to maintain control over cultural norms. Often, cultures that are forced into different cultural practices through forced cultural assimilation revert to their native practices and religions that differ from the forced cultural values of other dominant powers. In addition throughout history, voluntary assimilation is often in response to pressure from a more predominant culture, and conformity is a solution for people to remain in safety. An example of voluntary cultural assimilation would be during the Spanish Inquisition, when Jews and Muslims accepted the Roman Catholic Church as their religion, but meanwhile, many people still privately practised their traditional religions. That type of assimilation is used to convince a dominant power that a culture has peacefully assimilated yet often voluntary assimilation does not mean the group fully conforms to the accepted cultural beliefs.

The term "assimilation" is often used about not only indigenous groups but also immigrants settled in a new land. A new culture and new attitudes toward the original culture are obtained through contact and communication. Assimilation assumes that a relatively-tenuous culture gets to be united into one unified culture. That process happens through contact and accommodation between each culture. The current definition of assimilation is usually used to refer to immigrants, but in multiculturalism, cultural assimilation can happen all over the world and within varying social contexts and is not limited to specific areas.

Immigrant assimilation

Social scientists rely on four primary benchmarks to assess immigrant assimilation: socioeconomic status, geographic distribution, second language attainment, and intermarriage. William A.V. Clark defines immigrant assimilation in the United States as "a way of understanding the social dynamics of American society and that it is the process that occurs spontaneously and often unintended in the course of interaction between majority and minority groups."

Studies have also noted the positive effects of immigrant assimilation. A study by Bleakley and Chin (2010) found that people who arrived in the US at or before the age of nine from non-English speaking countries tend to speak English at a similar level as those from English speaking countries. Conversely, those who arrived after nine from non–English speaking countries have much lower speaking proficiency and this increases linearly with age at arrival. The study also noted sociocultural impacts such as those with better English skills are less likely to be currently married, more likely to divorce, have fewer children, and have spouses closer to their age. Learning to speak English well is estimated to improve income by over 33 percent. A 2014 study done by Verkuyten found that immigrant children who adapt through integration or assimilation are received more positively by their peers than those who adapt through marginalization or separation.

Perspective of dominant culture

Main article: Dominant culture

There has been little to no existing research or evidence that demonstrates whether and how immigrant's mobility gains—assimilating to a dominant country such as language ability, socioeconomic status etc.— causes changes in the perception of those who were born in the dominant country. This essential type of research provides information on how immigrants are accepted into dominant countries. In an article by Ariela Schachter, titled "From "different" to "similar": an experimental approach to understanding assimilation", a survey was taken of white American citizens to view their perception of immigrants who now resided in the United States. The survey indicated the whites tolerated immigrants in their home country. White natives are open to having "structural" relation with the immigrants-origin individuals, for instance, friends and neighbors; however, this was with the exception of black immigrants and natives and undocumented immigrants. However, at the same time, white Americans viewed all non-white Americans, regardless of legal status, as dissimilar.

A similar journal by Jens Hainmueller and Daniel J. Hopkins titled "The Hidden American Immigration Consensus: A Conjoint Analysis of Attitudes toward Immigrants" confirmed similar attitudes towards immigrants. The researchers used an experiment to reach their goal which was to test nine theoretical relevant attributes of hypothetical immigrants. Asking a population-based sample of U.S. citizens to decide between pairs of immigrants applying for admission to the United States, the U.S. citizen would see an application with information for two immigrants including notes about their education status, country, origin, and other attributes. The results showed Americans viewed educated immigrants in high-status jobs favourably, whereas they view the following groups unfavourably: those who lack plans to work, those who entered without authorization, those who are not fluent in English and those of Iraqi descent.

Adaptation to new country

As the number of international students entering the US has increased, so has the number of international students in US colleges and universities. The adaptation of these newcomers is important in cross-cultural research. In the study "Cross-Cultural Adaptation of International College Student in the United States" by Yikang Wang, the goal was to examine how the psychological and socio-cultural adaptation of international college students varied over time. The survey contained a sample of 169 international students attending a coeducational public university. The two subtypes of adaptation: psychological and socio-cultural were examined. Psychological adaptation refers to "feelings of well-being or satisfaction during cross-cultural transitions;" while socio-cultural refers to the ability to fit into the new culture. The results for both graduate and undergraduate students show both satisfaction and socio-cultural skills changed over time. Psychological adaptation had the most significant change for a student who has resided in the US for at least 24 months while socio-cultural adaptation steadily increased over time. It can be concluded that eventually over time, the minority group will shed some of their culture's characteristic when in a new country and incorporate new culture qualities. Also, it was confirmed that more time spent in a new country would result in becoming more accustomed to the dominant countries' characteristics.

Figure 2 demonstrates as the length of time resided in the United States increase—the dominant country, the life satisfaction and socio-cultural skill increase as well—positive correlation.

In turn, research by Caligiuri's group, published in 2020, shows that one semester of classroom experiential activities designed to foster international and domestic student social interaction serve to foster international students’ sense of belonging and social support.

In a study by Viola Angelini, "Life Satisfaction of Immigrant: Does cultural assimilation matter?", the theory of assimilation as having benefits for well-being. The goal of this study was to assess the difference between cultural assimilation and the subjective well-being of immigrants. The journal included a study that examined a "direct measure of assimilation with a host culture and immigrants' subjective well-being." Using data from the German Socio-Economic Panel, it was concluded that there was a positive correlation between cultural assimilation and an immigrant's life's satisfaction/wellbeing even after discarding factors such as employment status, wages, etc. "Life Satisfaction of Immigrant: Does cultural assimilation matter?" also confirms "association with life satisfaction is stronger for established immigrants than for recent ones." It was found that the more immigrants that identified with the German culture and who spoke the fluent national language—dominant country language, the more they reported to be satisfied with their lives. Life satisfaction rates were higher for those who had assimilated to the dominant country than those who had not assimilated since those who did incorporate the dominant language, religion, psychological aspects, etc.

Willingness to assimilate and cultural shock

Further information: Culture shock

In the study "Examination of cultural shock, intercultural sensitivity and willingness to adopt" by Clare D’Souza, the study uses a diary method to analyze the data collected. The study involved students undergoing a study abroad tour. The results show negative intercultural sensitivity is much greater in participants who experience "culture shock." Those who experience culture shock have emotional expression and responses of hostility, anger, negativity, anxiety frustration, isolation, and regression. Also, for one who has traveled to the country before permanently moving, they would have predetermined beliefs about the culture and their status within the country. The emotional expression for this individual includes excitement, happiness, eagerness, and euphoria.

Another article titled "International Students from Melbourne Describing Their Cross-Cultural Transitions Experiences: Culture Shock, Social Interaction, and Friendship Development" by Nish Belford focuses on cultural shock. Belford interviewed international students to explore their experience after living and studying in Melbourne, Australia. The data collected were narratives from the students that focused on variables such as "cultural similarity, intercultural communication competence, intercultural friendship, and relational identity to influence their experiences."

United States

Further information: Americanization (immigration)

Between 1880 and 1920, the United States took in roughly 24 million immigrants. This increase in immigration can be attributed to many historical changes. The beginning of the 21st century has also marked a massive era of immigration, and sociologists are once again trying to make sense of the impacts that immigration has on society and on the immigrants themselves.

Assimilation had various meanings in American sociology. Henry Pratt Fairchild associates American assimilation with Americanization or the "melting pot" theory. Some scholars also believed that assimilation and acculturation were synonymous. According to a common point of view, assimilation is a "process of interpretation and fusion" from another group or person. That may include memories, behaviors, and sentiments. By sharing their experiences and histories, they blend into the common cultural life. A related theory is structural pluralism proposed by American sociologist Milton Gordon. It describes the American situation wherein despite the cultural assimilation of ethnic groups to mainstream American society, they maintained structural separation. Gordon maintained that there is limited integration of the immigrants into American social institutions such as educational, occupational, political, and social cliques.

During The Colonial Period from 1607 to 1776, individuals immigrated to the British colonies on two very different paths—voluntary and forced migration. Those who migrated to the colonies on their own volition were drawn by the allure of cheap land, high wages, and the freedom of conscience in British North America. On the latter half, the largest population of forced migrants to the colonies was African slaves. Slavery was different from the other forced migrations as, unlike in the case of convicts, there was no possibility of earning freedom, although some slaves were manumitted in the centuries before the American Civil War. The long history of immigration in the established gateways means that the place of immigrants in terms of class, racial, and ethnic hierarchies in the traditional gateways is more structured or established, but on the other hand, the new gateways do not have much immigration history and so the place of immigrants in terms of class, racial, and ethnic hierarchies are less defined, and immigrants may have more influence to define their position. Secondly, the size of the new gateways may influence immigrant assimilation. Having a smaller gateway may influence the level of racial segregation among immigrants and native-born people. Thirdly, the difference in institutional arrangements may influence immigrant assimilation. Traditional gateways, unlike new gateways, have many institutions set up to help immigrants such as legal aid, bureaus, and social organizations. Finally, Waters and Jimenez have only speculated that those differences may influence immigrant assimilation and the way researchers that should assess immigrant assimilation.

Furthermore, the advancement and integration of immigrants into the United States has accounted for 29% of U.S. population growth since 2000. Recent arrival of immigrants to the United States has been examined closely over the last two decades. The results show the driving factors for immigration including citizenship, homeownership, English language proficiency, job status, and earning a better income.

Canada

Canada's multicultural history dates back to the period European colonization from the 16th to 19th centuries, with waves of ethnic European emigration to the region. In the 20th century, Indian, Chinese and Japanese were the largest immigrant groups.

20th century–present: Shift from assimilation to integration

Canada remains one of the largest immigrant populations in the world. The 2016 census recorded 7.5 million documented immigrants, representing a fifth of the country's total population. Focus has shifted from a rhetoric of cultural assimilation to cultural integration. In contrast to assimilationism, integration aims to preserve the roots of a minority society while still allowing for smooth coexistence with the dominant culture.

Indigenous assimilation

Australia

Further information: Aboriginal Australians, New Deal for Aborigines, and Stolen Generations

Legislation applying the policy of "protection" over Aboriginal Australians (separating them from white society) was adopted in some states and territories of Australia when they were still colonies, before the federation of Australia: in the Victoria in 1867, Western Australia in 1886, and Queensland in 1897. After federation, New South Wales crafted their policy in 1909, South Australia and the Northern Territory (which was under the control and of South Australia at the time) in 1910–11. Mission stations missions and Government-run Aboriginal reserves were created, and Aboriginal people moved onto them. Legislation restricted their movement, prohibited alcohol use and regulated employment. The policies were reinforced in the first half of the 20th century (when it was realized that Aboriginal people would not die out or be fully absorbed in white society) such as in the provisions of the Welfare Ordinance 1953, in which Aboriginal people were made wards of the state. "Part-Aboriginal" (known as half-caste) children were forcibly removed from their parents in order to educate them in European ways; the girls were often trained to be domestic servants. The protectionist policies were discontinued, and assimilationist policies took over. These proposed that "full-blood" Indigenous Australians should be allowed to “die out”, while "half-castes" were encouraged to assimilate into the white community. Indigenous people were regarded as inferior to white people by these policies, and often experienced discrimination in the predominantly white towns after having to move to seek work.

Between 1910 and 1970, several generations of Indigenous children were removed from their parents, and have become known as the Stolen Generations. The policy has done lasting damage to individuals, family and Indigenous culture.

The New Deal for Aborigines announced in 1939 marked the end of official policies based around "biological absorption" or "elimination" of Indigenous peoples, replaced with cultural assimilation as a prerequisite for civil rights. The 1961 Native Welfare Conference in Canberra, Australian federal and state government ministers formulated an official definition of "assimilation" of Indigenous Australians for government contexts. Federal territories minister Paul Hasluck informed the House of Representatives in April 1961 that:

The policy of assimilation means in the view of all Australian governments that all aborigines and part-aborigines are expected eventually to attain the same manner of living as other Australians and to live as members of a single Australian community enjoying the same rights and privileges, accepting the same responsibilities, observing the same customs and influenced by the same beliefs, hopes and loyalties as other Australians. Thus, any special measures taken for aborigines and part-aborigines are regarded as temporary measures not based on colour but intended to meet their need for special care and assistance to protect them from any ill effects of sudden change and to assist them to make the transition from one stage to another in such a way as will be favourable to their future social, economic and political advancement.

Brazil

In January 2019, the newly elected Brazil President Jair Bolsonaro stripped the Indigenous Affairs Agency FUNAI of the responsibility to identify and demarcate Indigenous lands. He argued that those territories have very tiny isolated populations and proposed to integrate them into the larger Brazilian society. According to the Survival International, "Taking responsibility for Indigenous land demarcation away from FUNAI, the Indian affairs department, and giving it to the Agriculture Ministry is virtually a declaration of open warfare against Brazil’s tribal peoples."

Canada 1800s–1990s: Forced assimilation

During the 19th and 20th centuries, and continuing until 1996, when the last Canadian Indian residential school was closed, the Canadian government, aided by Christian Churches, began an assimilationist campaign to forcibly assimilate Indigenous peoples in Canada. The government consolidated power over Indigenous land through treaties and the use of force, eventually isolating most Indigenous peoples to reserves. Marriage practices and spiritual ceremonies were banned, and spiritual leaders were imprisoned. Additionally, the Canadian government instituted an extensive residential school system to assimilate children. Indigenous children were separated from their families and no longer permitted to express their culture at these new schools. They were not allowed to speak their language or practice their own traditions without receiving punishment. There were many cases of violence and sexual abuse committed by the Christian church. The Truth and Reconciliation Commission of Canada concluded that this effort amounted to cultural genocide. The schools actively worked to alienate children from their cultural roots. Students were prohibited from speaking their native languages, were regularly abused, and were arranged marriages by the government after their graduation. The explicit goal of the Canadian government, through the Catholic and Anglican churches, was to completely assimilate Indigenous peoples into broader Canadian society and destroy all traces of their native history.

Croatia and Transylvania

During Croatia’s personal union with Hungary, ethnic Croatians were pressured to abandon their traditional customs in favor of adopting elements of Hungarian culture, such as Catholicism and the Latin alphabet. Because of this, elements of Hungarian culture were considered part of Croatian culture, and can still be seen in modern Croatian culture.

Throughout the Kingdom of Hungary, many citizens, primarily those who belonged to minority groups, were forced to convert to Catholicism. The forced conversion policy was harshest in Croatia and Transylvania, where civilians could be sent to prison for refusing to convert. Romanian cultural anthropologist Ioan Lupaș claims that between 1002, when Transylvania became part of the Kingdom of Hungary, to 1300, approximately 200,000 non-Hungarians living in Transylvania were jailed for resisting Catholic conversion, and about 50,000 of them died in prison.

Mexico and Peru

A major contributor to cultural assimilation in South America began during exploration and colonialism that often is thought by Bartolomé de Las Casas to begin in 1492 when Europeans began to explore the Atlantic in search of "the Indies", leading to the discovery of the Americas. Europe remained dominant over the Americas' Indigenous populations as resources such as labor, natural resources i.e. lumber, copper, gold, silver, and agricultural products flooded into Europe, yet these gains were one-sided, as Indigenous groups did not benefit from trade deals with colonial powers. In addition to this, colonial metropoles such as Portugal and Spain required that colonies in South America assimilate to European customs – such as following the Holy Roman Catholic Church, acceptance of Spanish or Portuguese over Indigenous languages and accepting European-style government.

Through forceful assimilationist policies, colonial powers such as Spain used methods of violence to assert cultural dominance over Indigenous populations. One example occurred in 1519 when the Spanish explorer Hernán Cortés reached Tenochtitlán – the original capital of the Aztec Empire in Mexico. After discovering that the Aztecs practiced human sacrifice, Cortés killed high-ranked Aztecs and held Moctezuma II, the Aztec ruler, captive. Shortly after, Cortés began creating alliances to resume power in Tenochtitlán and renamed it Mexico City. Without taking away power through murder and spread of infectious diseases the Spanish conquistadores (relatively small in number) would not have been able to take over Mexico and convert many people to Catholicism and slavery. While Spaniards influenced linguistic and religious cultural assimilation among Indigenous peoples in South America during colonialism, many Indigenous languages such as the Incan language Quechua are still used in places such as Peru to this day by at least 4 million people.

New Zealand

In the course of the colonization of New Zealand from the late-18th century onwards, assimilation of the indigenous Maori population to the culture of incoming European visitors and settlers at first occurred spontaneously. Genetic assimilation commenced early and continued – the 1961 New Zealand census classified only 62.2% of Māori as "full-blood Maoris". (Compare Pākehā Māori.) Linguistic assimilation also occurred early and ongoingly: European settler populations adopted and adapted Māori words, while European languages affected Māori vocabulary (and possibly phonology).

In the 19th century colonial governments de facto encouraged assimilationist policies; by the late-20th century, policies favored bicultural development. Māori readily and early adopted some aspects of European-borne material culture (metals, muskets, potatoes) relatively rapidly. Imported ideas – such as writing, Christianity, monarchy, sectarianism, everyday European-style clothing, or disapproval of slavery – spread more slowly. Later developments (socialism, anti-colonialist theory, New Age ideas) have proven more internationally mobile. One long-standing view presents Māori communalism as unassimilated with European-style individualism.

Omphalos hypothesis

From Wikipedia, the free encyclopedia
https://en.wikipedia.org/wiki/Omphalos_hypothesis

The Omphalos hypothesis is one attempt to reconcile the scientific evidence that the Earth is billions of years old with a literal interpretation of the Genesis creation narrative, which implies that the Earth is only a few thousand years old. It is based on the religious belief that the universe was created by a divine being, within the past six to ten thousand years (in keeping with flood geology), and that the presence of objective, verifiable evidence that the universe is older than approximately ten millennia is due to the creator introducing false evidence that makes the universe appear significantly older.

The idea was named after the title of an 1857 book, Omphalos by Philip Henry Gosse, in which Gosse argued that for the world to be "functional", God must have created the Earth with mountains and canyons, trees with growth rings, Adam and Eve with fully grown hair, fingernails, and navels (ὀμφαλός omphalos is Greek for "navel"), and all living creatures with fully formed evolutionary features, etc., and that, therefore, no empirical evidence about the age of the Earth or universe can be taken as reliable.

Various supporters of Young Earth creationism have given different explanations for their belief that the universe is filled with false evidence of the universe's age, including a belief that some things needed to be created at a certain age for the ecosystems to function, or their belief that the creator was deliberately planting deceptive evidence.

The idea was widely rejected in the 19th century, when Gosse published his aforementioned book. It saw some revival in the 20th century by some Young Earth creationists, who extended the argument to include visible light that appears to originate from far-off stars and galaxies (addressing the "starlight problem").

Development of the idea

Pre-scientific sources

Stories of the beginning of human life based on the creation story in Genesis have been published for centuries. The 4th-century theologian Ephrem the Syrian described a world in which divine creation instantly produced fully grown organisms:

Although the grasses were only a moment old at their creation, they appeared as if they were months old. Likewise, the trees, although only a day old when they sprouted forth, were nevertheless like ... years old as they were fully grown and fruits were already budding on their branches.

19th-century thinkers

By the 19th century, scientific evidence of the Earth's age had been collected, and it disagreed with a literal reading of the biblical accounts. This evidence was rejected by some writers at the time, such as François-René de Chateaubriand. Chateaubriand wrote in his 1802 book, Génie du christianisme (Part I Book IV Chapter V), that "God might have created, and doubtless did create, the world with all the marks of antiquity and completeness which it now exhibits." In modern times, Rabbi Dovid Gottlieb supported a similar position, saying that the objective scientific evidence for an old universe is strong, but wrong, and that the traditional Jewish calendar is correct.

In the middle of the 19th century, the disagreement between scientific evidence about the age of the Earth and the Western religious traditions was a significant debate among intellectuals. Gosse published Omphalos in 1857 to explain his answer to this question. He concluded that the religious tradition was correct. Gosse began with the earlier idea that the Earth contained mature organisms at the instant they were created, and that these organisms had false signs of their development, such as hair on mammals, which grows over time. He extended this idea of creating a single mature organism to creating mature systems, and concluded that fossils were an artifact of the creation process and merely part of what was necessary to make creation work. Therefore, he reasoned, fossils and other signs of the Earth's age could not be used to prove its age.

Other contemporary proposals for reconciling the stories of creation in Genesis with the scientific evidence included the interval theory or gap theory of creation, in which a large interval of time passed in between the initial creation of the universe and the beginning of the Six Days of Creation. This idea was put forward by Archbishop John Bird Sumner of Canterbury in Treatise on the Records of Creation. Another popular idea, promoted by the English theologian John Pye Smith, was that the Garden of Eden described the events of only one small location. A third proposal, by French naturalist Georges-Louis Leclerc, Comte de Buffon, held that the six "days" of the creation story were arbitrary and large ages rather than 24-hour periods.

Theologians rejected Gosse's proposal on the grounds that it seemed to make the divine creator tell lies—either lying in the scriptures, or lying in nature. Scientists rejected it on the grounds that it disagreed with uniformitarianism, an explanation of geology that was widely supported at the time, and the impossibility of testing or falsifying the idea.

Modern creationists

Some modern creationists still argue against scientific evidence in the same way. For instance, John D. Morris, president of the Institute for Creation Research wrote in 1990 about the "appearance of age", saying that: "...what [God] created was functionally complete right from the start—able to fulfill the purpose for which it was created".

He does not extend this idea to the geological record, preferring to believe that it was all created in the Flood, but others such as Gerald E. Aardsma go further, with his idea of "virtual history". This appears to suggest that events after the creation have changed the "virtual history" we now see, including the fossils:

This raises one more major point of difference, the handling of the Fall. Briefly, Creation with Appearance of Age runs into a theological snag with things like fossils of fish with other smaller fish in their stomachs: "Do you mean that God chose to paint, of all things, a facade of SUFFERING and DEATH onto the creation when He gave it this arbitrary appearance of age at the time of creation?" The virtual history paradigm recognizes simply that all creation type miracles entail a virtual history, so the Fall, with its creation type miracles (by which the nature of the creation was changed—"subjected to futility") carried with it its own (fallen) virtual history, which is the virtual history we now see. We do not see the original utopian pre-Fall creation with its (presumably utopian) virtual history.

Criticisms

Beginning of false creation

Although Gosse's original Omphalos hypothesis specifies a popular creation story, others have proposed that the idea does not preclude creation as recently as five minutes ago, including memories of times before this created in situ. This idea is sometimes called Last Thursdayism by its opponents, as in "the world might as well have been created last Thursday."

Scientifically, the concept is both unverifiable and unfalsifiable through any conceivable scientific study—in other words, it is impossible to conclude the truth of the hypothesis, since it requires the empirical data itself to have been arbitrarily created to look the way it does at every observable level of detail.

Deceptive creator

From a religious viewpoint, it can be interpreted as God having created a "fake" universe, such as illusions of light emitted from supernovae that never really happened, or volcanic mountains that were never really volcanoes in the first place and that never actually experienced erosion.

In a rebuttal of the claim that God might have implanted a false history of the age of the universe to test our faith in the truth of the Torah, Rabbi Natan Slifkin, an author whose works have been banned by several Haredi rabbis for going against the tenets of the Talmud, writes:

God essentially created two conflicting accounts of Creation: one in nature, and one in the Torah. How can it be determined which is the real story, and which is the fake designed to mislead us? One could equally propose that it is nature that presents the real story, and that the Torah was devised by God to test us with a fake history!

One has to be able to rely on God's truthfulness if religion is to function. Or, to put it another way—if God went to enormous lengths to convince us that the world is billions of years old, who are we to disagree?

Similar formulations

Five-minute hypothesis

The five-minute hypothesis is a skeptical hypothesis put forth by the philosopher Bertrand Russell, that proposes that the universe sprang into existence five minutes ago from nothing, with human memory and all other signs of history included. It is a commonly used example of how one may maintain extreme philosophical skepticism with regard to memory and trust in evidentially derived historical chronology.

Borges's Tlön, Uqbar, Orbis Tertius

Jorge Luis Borges, in his 1940 work, Tlön, Uqbar, Orbis Tertius, describes a fictional world in which some essentially follow as a religious belief a philosophy much like Russell's discussion on the logical extreme of Gosse's theory:

One of the schools of Tlön goes so far as to negate time: it reasons that the present is indefinite, that the future has no reality other than as a present hope, the past none other than present memory.

Borges had earlier written a short essay, "The Creation and P. H. Gosse" that explored the rejection of Gosse's Omphalos. Borges argued that its unpopularity stemmed from Gosse's explicit (if inadvertent) outlining of what Borges characterized as absurdities in the Genesis story.

Degrees of freedom (statistics)

From Wikipedia, the free encyclopedia

https://en.wikipedia.org/wiki/Degrees_of_freedom_(statistics)

In statistics, the number of degrees of freedom is the number of values in the final calculation of a statistic that are free to vary.stimates of statistical parameters can be based upon different amounts of information or data. The number of independent pieces of information that go into the estimate of a parameter is called the degrees of freedom. In general, the degrees of freedom of an estimate of a parameter are equal to the number of independent scores that go into the estimate minus the number of parameters used as intermediate steps in the estimation of the parameter itself. For example, if the variance is to be estimated from a random sample of $N$ independent scores, then the degrees of freedom is equal to the number of independent scores (N) minus the number of parameters estimated as intermediate steps (one, namely, the sample mean) and is therefore equal to $N-1$.

Mathematically, degrees of freedom is the number of dimensions of the domain of a random vector, or essentially the number of "free" components (how many components need to be known before the vector is fully determined).

The term is most often used in the context of linear models (linear regression, analysis of variance), where certain random vectors are constrained to lie in linear subspaces, and the number of degrees of freedom is the dimension of the subspace. The degrees of freedom are also commonly associated with the squared lengths (or "sum of squares" of the coordinates) of such vectors, and the parameters of chi-squared and other distributions that arise in associated statistical testing problems.

While introductory textbooks may introduce degrees of freedom as distribution parameters or through hypothesis testing, it is the underlying geometry that defines degrees of freedom, and is critical to a proper understanding of the concept.

History

Although the basic concept of degrees of freedom was recognized as early as 1821 in the work of German astronomer and mathematician Carl Friedrich Gauss, its modern definition and usage was first elaborated by English statistician William Sealy Gosset in his 1908 Biometrika article "The Probable Error of a Mean", published under the pen name "Student". While Gosset did not actually use the term 'degrees of freedom', he explained the concept in the course of developing what became known as Student's t-distribution. The term itself was popularized by English statistician and biologist Ronald Fisher, beginning with his 1922 work on chi squares.

Notation

In equations, the typical symbol for degrees of freedom is ν (lowercase Greek letter nu). In text and tables, the abbreviation "d.f." is commonly used. R. A. Fisher used n to symbolize degrees of freedom but modern usage typically reserves n for sample size. When reporting the results of statistical tests, the degrees of freedom are typically noted beside the test statistic as either subscript or in parentheses.

Of random vectors

Geometrically, the degrees of freedom can be interpreted as the dimension of certain vector subspaces. As a starting point, suppose that we have a sample of independent normally distributed observations,

${\displaystyle X_1,\dots ,X_n.}$

This can be represented as an n-dimensional random vector:

${\displaystyle \left(\begin{array}{c}{X}_1\\ ⋮\\ X_n\end{array}\right).}$

Since this random vector can lie anywhere in n-dimensional space, it has n degrees of freedom.

Now, let ${\displaystyle \overline{X}}$ be the sample mean. The random vector can be decomposed as the sum of the sample mean plus a vector of residuals:

${\displaystyle \left(\begin{array}{c}{X}_1\\ ⋮\\ X_n\end{array}\right)=\overline{X}\left(\begin{array}{c}1\\ ⋮\\ 1\end{array}\right)+\left(\begin{array}{c}{X}_1-\overline{X}\\ ⋮\\ X_n-\overline{X}\end{array}\right).}$

The first vector on the right-hand side is constrained to be a multiple of the vector of 1's, and the only free quantity is ${\displaystyle \overline{X}}$. It therefore has 1 degree of freedom.

The second vector is constrained by the relation $\sum _{i=1}^n(X_i-\overline{X})=0$. The first n − 1 components of this vector can be anything. However, once you know the first n − 1 components, the constraint tells you the value of the nth component. Therefore, this vector has n − 1 degrees of freedom.

Mathematically, the first vector is the oblique projection of the data vector onto the subspace spanned by the vector of 1's. The 1 degree of freedom is the dimension of this subspace. The second residual vector is the least-squares projection onto the (n − 1)-dimensional orthogonal complement of this subspace, and has n − 1 degrees of freedom.

In statistical testing applications, often one is not directly interested in the component vectors, but rather in their squared lengths. In the example above, the residual sum-of-squares is

${\displaystyle \sum _{i=1}^n(X_i-\overline{X}{)}^2={\Vert \begin{array}{c}{X}_1-\overline{X}\\ ⋮\\ X_n-\overline{X}\end{array}\Vert }^2.}$

If the data points ${\displaystyle X_i}$ are normally distributed with mean 0 and variance ${\displaystyle {\sigma }^2}$, then the residual sum of squares has a scaled chi-squared distribution (scaled by the factor ${\displaystyle {\sigma }^2}$), with n − 1 degrees of freedom. The degrees-of-freedom, here a parameter of the distribution, can still be interpreted as the dimension of an underlying vector subspace.

Likewise, the one-sample t-test statistic,

${\displaystyle \frac{\sqrt{n}(\overline{X}-{\mu }_0)}{\sqrt{\sum _{i=1}^n(X_i-\overline{X}{)}^2/(n-1)}}}$

follows a Student's t distribution with n − 1 degrees of freedom when the hypothesized mean ${\displaystyle {\mu }_0}$ is correct. Again, the degrees-of-freedom arises from the residual vector in the denominator.

In structural equation models

When the results of structural equation models (SEM) are presented, they generally include one or more indices of overall model fit, the most common of which is a χ² statistic. This forms the basis for other indices that are commonly reported. Although it is these other statistics that are most commonly interpreted, the degrees of freedom of the χ² are essential to understanding model fit as well as the nature of the model itself.

Degrees of freedom in SEM are computed as a difference between the number of unique pieces of information that are used as input into the analysis, sometimes called knowns, and the number of parameters that are uniquely estimated, sometimes called unknowns. For example, in a one-factor confirmatory factor analysis with 4 items, there are 10 knowns (the six unique covariances among the four items and the four item variances) and 8 unknowns (4 factor loadings and 4 error variances) for 2 degrees of freedom. Degrees of freedom are important to the understanding of model fit if for no other reason than that, all else being equal, the fewer degrees of freedom, the better indices such as χ² will be.

It has been shown that degrees of freedom can be used by readers of papers that contain SEMs to determine if the authors of those papers are in fact reporting the correct model fit statistics. In the organizational sciences, for example, nearly half of papers published in top journals report degrees of freedom that are inconsistent with the models described in those papers, leaving the reader to wonder which models were actually tested.

Of residuals

Further information: Residuals (statistics)

A common way to think of degrees of freedom is as the number of independent pieces of information available to estimate another piece of information. More concretely, the number of degrees of freedom is the number of independent observations in a sample of data that are available to estimate a parameter of the population from which that sample is drawn. For example, if we have two observations, when calculating the mean we have two independent observations; however, when calculating the variance, we have only one independent observation, since the two observations are equally distant from the sample mean.

In fitting statistical models to data, the vectors of residuals are constrained to lie in a space of smaller dimension than the number of components in the vector. That smaller dimension is the number of degrees of freedom for error, also called residual degrees of freedom.

Example

Perhaps the simplest example is this. Suppose

${\displaystyle X_1,\dots ,X_n}$

are random variables each with expected value μ, and let

${\displaystyle {\overline{X}}_n=\frac{X_1+\cdots +X_n}{n}}$

be the "sample mean." Then the quantities

${\displaystyle X_i-{\overline{X}}_n}$

are residuals that may be considered estimates of the errors X_i − μ. The sum of the residuals (unlike the sum of the errors) is necessarily 0. If one knows the values of any n − 1 of the residuals, one can thus find the last one. That means they are constrained to lie in a space of dimension n − 1. One says that there are n − 1 degrees of freedom for errors.

An example which is only slightly less simple is that of least squares estimation of a and b in the model

${\displaystyle Y_i=a+b{x}_i+e_i\text{ for }i=1,\dots ,n}$

where x_i is given, but e_i and hence Y_i are random. Let ${\displaystyle \hat{a}}$ and ${\displaystyle \hat{b}}$ be the least-squares estimates of a and b. Then the residuals

${\displaystyle {\hat{e}}_i=y_i-(\hat{a}+\hat{b}{x}_i)}$

are constrained to lie within the space defined by the two equations

${\displaystyle {\hat{e}}_1+\cdots +{\hat{e}}_n=0,}$

${\displaystyle x_1{\hat{e}}_1+\cdots +x_n{\hat{e}}_n=0.}$

One says that there are n − 2 degrees of freedom for error.

Notationally, the capital letter Y is used in specifying the model, while lower-case y in the definition of the residuals; that is because the former are hypothesized random variables and the latter are actual data.

We can generalise this to multiple regression involving p parameters and covariates (e.g. p − 1 predictors and one mean (=intercept in the regression)), in which case the cost in degrees of freedom of the fit is p, leaving n - p degrees of freedom for errors

In linear models

The demonstration of the t and chi-squared distributions for one-sample problems above is the simplest example where degrees-of-freedom arise. However, similar geometry and vector decompositions underlie much of the theory of linear models, including linear regression and analysis of variance. An explicit example based on comparison of three means is presented here; the geometry of linear models is discussed in more complete detail by Christensen (2002).

Suppose independent observations are made for three populations, ${\displaystyle X_1,\dots ,X_n}$, ${\displaystyle Y_1,\dots ,Y_n}$ and ${\displaystyle Z_1,\dots ,Z_n}$. The restriction to three groups and equal sample sizes simplifies notation, but the ideas are easily generalized.

The observations can be decomposed as

${\displaystyle \begin{array}{rl}{X}_i& =\overline{M}+(\overline{X}-\overline{M})+(X_i-\overline{X})\\ Y_i& =\overline{M}+(\overline{Y}-\overline{M})+(Y_i-\overline{Y})\\ Z_i& =\overline{M}+(\overline{Z}-\overline{M})+(Z_i-\overline{Z})\end{array}}$

where ${\displaystyle \overline{X},\overline{Y},\overline{Z}}$ are the means of the individual samples, and ${\displaystyle \overline{M}=(\overline{X}+\overline{Y}+\overline{Z})/3}$ is the mean of all 3n observations. In vector notation this decomposition can be written as

${\displaystyle \left(\begin{array}{c}{X}_1\\ ⋮\\ X_n\\ Y_1\\ ⋮\\ Y_n\\ Z_1\\ ⋮\\ Z_n\end{array}\right)=\overline{M}\left(\begin{array}{c}1\\ ⋮\\ 1\\ 1\\ ⋮\\ 1\\ 1\\ ⋮\\ 1\end{array}\right)+\left(\begin{array}{c}\overline{X}-\overline{M}\\ ⋮\\ \overline{X}-\overline{M}\\ \overline{Y}-\overline{M}\\ ⋮\\ \overline{Y}-\overline{M}\\ \overline{Z}-\overline{M}\\ ⋮\\ \overline{Z}-\overline{M}\end{array}\right)+\left(\begin{array}{c}{X}_1-\overline{X}\\ ⋮\\ X_n-\overline{X}\\ Y_1-\overline{Y}\\ ⋮\\ Y_n-\overline{Y}\\ Z_1-\overline{Z}\\ ⋮\\ Z_n-\overline{Z}\end{array}\right).}$

The observation vector, on the left-hand side, has 3n degrees of freedom. On the right-hand side, the first vector has one degree of freedom (or dimension) for the overall mean. The second vector depends on three random variables, ${\displaystyle \overline{X}-\overline{M}}$, ${\displaystyle \overline{Y}-\overline{M}}$ and ${\displaystyle \overline{Z}-\overline{M}}$. However, these must sum to 0 and so are constrained; the vector therefore must lie in a 2-dimensional subspace, and has 2 degrees of freedom. The remaining 3n − 3 degrees of freedom are in the residual vector (made up of n − 1 degrees of freedom within each of the populations).

In analysis of variance (ANOVA)

In statistical testing problems, one usually is not interested in the component vectors themselves, but rather in their squared lengths, or Sum of Squares. The degrees of freedom associated with a sum-of-squares is the degrees-of-freedom of the corresponding component vectors.

The three-population example above is an example of one-way Analysis of Variance. The model, or treatment, sum-of-squares is the squared length of the second vector,

${\displaystyle \text{SST}=n(\overline{X}-\overline{M}{)}^2+n(\overline{Y}-\overline{M}{)}^2+n(\overline{Z}-\overline{M}{)}^2}$

with 2 degrees of freedom. The residual, or error, sum-of-squares is

${\displaystyle \text{SSE}=\sum _{i=1}^n(X_i-\overline{X}{)}^2+\sum _{i=1}^n(Y_i-\overline{Y}{)}^2+\sum _{i=1}^n(Z_i-\overline{Z}{)}^2}$

with 3(n−1) degrees of freedom. Of course, introductory books on ANOVA usually state formulae without showing the vectors, but it is this underlying geometry that gives rise to SS formulae, and shows how to unambiguously determine the degrees of freedom in any given situation.

Under the null hypothesis of no difference between population means (and assuming that standard ANOVA regularity assumptions are satisfied) the sums of squares have scaled chi-squared distributions, with the corresponding degrees of freedom. The F-test statistic is the ratio, after scaling by the degrees of freedom. If there is no difference between population means this ratio follows an F-distribution with 2 and 3n − 3 degrees of freedom.

In some complicated settings, such as unbalanced split-plot designs, the sums-of-squares no longer have scaled chi-squared distributions. Comparison of sum-of-squares with degrees-of-freedom is no longer meaningful, and software may report certain fractional 'degrees of freedom' in these cases. Such numbers have no genuine degrees-of-freedom interpretation, but are simply providing an approximate chi-squared distribution for the corresponding sum-of-squares. The details of such approximations are beyond the scope of this page.

In probability distributions

Several commonly encountered statistical distributions (Student's t, chi-squared, F) have parameters that are commonly referred to as degrees of freedom. This terminology simply reflects that in many applications where these distributions occur, the parameter corresponds to the degrees of freedom of an underlying random vector, as in the preceding ANOVA example. Another simple example is: if ${\displaystyle X_i;i=1,\dots ,n}$ are independent normal ${\displaystyle (\mu ,{\sigma }^2)}$ random variables, the statistic

${\displaystyle \frac{\sum _{i=1}^n(X_i-\overline{X}{)}^2}{{\sigma }^2}}$

follows a chi-squared distribution with n − 1 degrees of freedom. Here, the degrees of freedom arises from the residual sum-of-squares in the numerator, and in turn the n − 1 degrees of freedom of the underlying residual vector ${\displaystyle \{X_i-\overline{X}\}}$.

In the application of these distributions to linear models, the degrees of freedom parameters can take only integer values. The underlying families of distributions allow fractional values for the degrees-of-freedom parameters, which can arise in more sophisticated uses. One set of examples is problems where chi-squared approximations based on effective degrees of freedom are used. In other applications, such as modelling heavy-tailed data, a t or F-distribution may be used as an empirical model. In these cases, there is no particular degrees of freedom interpretation to the distribution parameters, even though the terminology may continue to be used.

In non-standard regression

Many non-standard regression methods, including regularized least squares (e.g., ridge regression), linear smoothers, smoothing splines, and semiparametric regression, are not based on ordinary least squares projections, but rather on regularized (generalized and/or penalized) least-squares, and so degrees of freedom defined in terms of dimensionality is generally not useful for these procedures. However, these procedures are still linear in the observations, and the fitted values of the regression can be expressed in the form

${\displaystyle \hat{y}=Hy,}$

where ${\displaystyle \hat{y}}$ is the vector of fitted values at each of the original covariate values from the fitted model, y is the original vector of responses, and H is the hat matrix or, more generally, smoother matrix.

For statistical inference, sums-of-squares can still be formed: the model sum-of-squares is ${\displaystyle \Vert Hy{\Vert }^2}$; the residual sum-of-squares is ${\displaystyle \Vert y-Hy{\Vert }^2}$. However, because H does not correspond to an ordinary least-squares fit (i.e. is not an orthogonal projection), these sums-of-squares no longer have (scaled, non-central) chi-squared distributions, and dimensionally defined degrees-of-freedom are not useful.

The effective degrees of freedom of the fit can be defined in various ways to implement goodness-of-fit tests, cross-validation, and other statistical inference procedures. Here one can distinguish between regression effective degrees of freedom and residual effective degrees of freedom.

Regression effective degrees of freedom

For the regression effective degrees of freedom, appropriate definitions can include the trace of the hat matrix, tr(H), the trace of the quadratic form of the hat matrix, tr(H'H), the form tr(2H – H H'), or the Satterthwaite approximation, tr(H'H)²/tr(H'HH'H). In the case of linear regression, the hat matrix H is X(X 'X)⁻¹X ', and all these definitions reduce to the usual degrees of freedom. Notice that

${\displaystyle \mathrm{tr}(H)=\sum _i{h}_{ii}=\sum _i\frac{\mathrm{\partial }{\hat{y}}_i}{\mathrm{\partial }{y}_i},}$

the regression (not residual) degrees of freedom in linear models are "the sum of the sensitivities of the fitted values with respect to the observed response values", i.e. the sum of leverage scores.

One way to help to conceptualize this is to consider a simple smoothing matrix like a Gaussian blur, used to mitigate data noise. In contrast to a simple linear or polynomial fit, computing the effective degrees of freedom of the smoothing function is not straightforward. In these cases, it is important to estimate the Degrees of Freedom permitted by the ${\displaystyle H}$ matrix so that the residual degrees of freedom can then be used to estimate statistical tests such as ${\displaystyle {\chi }^2}$.

Residual effective degrees of freedom

There are corresponding definitions of residual effective degrees-of-freedom (redf), with H replaced by I − H. For example, if the goal is to estimate error variance, the redf would be defined as tr((I − H)'(I − H)), and the unbiased estimate is (with ${\displaystyle \hat{r}=y-Hy}$),

${\displaystyle {\hat{\sigma }}^2=\frac{\Vert \hat{r}{\Vert }^2}{\mathrm{tr}\left((I-H{)}^{\prime }(I-H)\right)},}$

or:

${\displaystyle {\hat{\sigma }}^2=\frac{\Vert \hat{r}{\Vert }^2}{n-\mathrm{tr}(2H-H{H}^{\prime })}=\frac{\Vert \hat{r}{\Vert }^2}{n-2\mathrm{tr}(H)+\mathrm{tr}(H{H}^{\prime })}}$

${\displaystyle {\hat{\sigma }}^2\approx \frac{\Vert \hat{r}{\Vert }^2}{n-1.25\mathrm{tr}(H)+0.5}.}$

The last approximation above reduces the computational cost from O(n²) to only O(n). In general the numerator would be the objective function being minimized; e.g., if the hat matrix includes an observation covariance matrix, Σ, then ${\displaystyle \Vert \hat{r}{\Vert }^2}$ becomes ${\displaystyle {\hat{r}}^{\prime }{\mathrm{\Sigma }}^{-1}\hat{r}}$.

General

Note that unlike in the original case, non-integer degrees of freedom are allowed, though the value must usually still be constrained between 0 and n.

Consider, as an example, the k-nearest neighbour smoother, which is the average of the k nearest measured values to the given point. Then, at each of the n measured points, the weight of the original value on the linear combination that makes up the predicted value is just 1/k. Thus, the trace of the hat matrix is n/k. Thus the smooth costs n/k effective degrees of freedom.

As another example, consider the existence of nearly duplicated observations. Naive application of classical formula, n − p, would lead to over-estimation of the residuals degree of freedom, as if each observation were independent. More realistically, though, the hat matrix H = X(X ' Σ⁻¹ X)⁻¹X ' Σ⁻¹ would involve an observation covariance matrix Σ indicating the non-zero correlation among observations.

The more general formulation of effective degree of freedom would result in a more realistic estimate for, e.g., the error variance σ², which in its turn scales the unknown parameters' a posteriori standard deviation; the degree of freedom will also affect the expansion factor necessary to produce an error ellipse for a given confidence level.

Other formulations

Similar concepts are the equivalent degrees of freedom in non-parametric regression, the degree of freedom of signal in atmospheric studies, and the non-integer degree of freedom in geodesy.

The residual sum-of-squares ${\displaystyle \Vert y-Hy{\Vert }^2}$ has a generalized chi-squared distribution, and the theory associated with this distribution provides an alternative route to the answers provided above.