Conservative activists such as David Horowitz have argued that there is a bias against Christians and conservatives in academia. Barry Ames et al., John Lee and Henry Giroux have argued that these claims are based upon anecdotal evidence that would not reliably indicate systematic bias, and that the divide is due to self-selection due to conservatives simply being less likely to pursue an academic career.Russell Jacoby has argued that claims of academic bias have been used to push measures that infringe on academic freedom.
One study of academic philosophers found that while half of
respondents believed that ideological discrimination was wrong, a
significant minority believed discrimination against individuals with
opposing ideologies was justified. A 2017 paper argued that left-wing ideologies had taken over
criminology in the 1960s and 1970s, observing a massive increase in
research around fields such as radical, Marxist and feminist
criminology. The paper's authors argued this resulted in bias, as the
ideology of scientists within the field influenced both the acceptance
of certain theories and the rejection of others; criminologists of this
period came to regard criminology as being about criticising the social
structure of society and those who supported the status quo. The authors
also argue that even in the modern day, much of the writing in
criminology remains primarily political in both origin and purpose. A 2018 study argued that since groups seen as deviant from the norm are
frequently seen as in need of explanation, if bias against
conservatives existed, then conservatives and conservatism should be
seen as more in need of explanation than liberals and liberalism, as a
liberal-biased science would see them as deviant and that they would be
described more negatively. This was confirmed by the results of the
study. Other researchers also argue that political bias
manifests in scientific research, influencing how ideological groups
are described, what measurements are used, the interpretation of results
and which results are published.
A 2018 study found bias amongst criminal law students, with
students engaging in motivated reasoning favourable to their political
in-group and demonstrating bias towards their political in-group. Mark Horowitz also argues that researchers' political views can bias their research.
A 2005 paper argued that, controlling for student ability,
there was no evidence of any disciplines being biased against
conservative students in grading. In contrast, the researchers did find
some disciplines, such as economics and business, where conservative
students achieved higher grades than would be expected by student
ability. The authors concluded that this was unlikely to be due to any
explicit or implicit bias in these disciplines, instead arguing that it
was likely due to differences in student interest in subject matter, as
well as possibly due to differences in discipline teaching methodology
interacting with student personalities and values.
Justin Tetrault argues that research into hate groups
relied too much upon stereotypes rather than rigorous analysis, likely
because said stereotypes appealed to researchers' own beliefs.
It has been argued that apparent evidence of a "prejudice
gap" between right-wingers and left-wingers—the idea that right-wingers
are more prejudiced than left-wingers—was caused by researchers having
not measured groups that left-wingers would be prejudiced towards. It
has been suggested that this was because this was not regarded as
prejudice or was not seen as worthy of investigation. Christine Reyna argues that ideological bias can affect how scales are constructed and interpreted in multiple ways. Lee Jussim argues that right-wing individuals were classified as
"cognitively rigid", however he argues this label is misleading because
what studies indicate is that right-wing individuals were less willing
to change their beliefs and to be open to new experiences relative to
left-wing individuals but this did not make them "rigid" in any absolute
sense and that absent any absolute measure as to how cognitively
flexible a person should be, labels such as "rigid" were meaningless. A 2019 study by the researchers measuring "actively open-minded
thinking" noted that the researchers' original scale was biased against
religious individuals due to test items, skewing correlations, and that
the team had not realised this error for almost two decades, requiring a
new scale.
Some scholars, such as J. F. Zipp, have said that studies
on the political orientations of professors are faulty, having focused
on unrepresentative institutions and fields; when taken as a whole, they
say that academia has become more moderate over time.
A 2019 study of European universities argued that while
university professors were more left-wing and liberal than other
professions, professors did not display a higher level of homogeneity in
political views (aside from views on immigration) than other
professions such as CEOs did, suggesting European universities are not
exclusionary compared to other institutions.
The American Council of Trustees and Alumni, a conservative group, argues that course curriculums betray a progressive bias. However, John Lee argues that this research is not based on a
probability sample and uses a research design that cannot rule out
explanations other than political bias. Furthermore, research suggests little or no leftward movement among college students while they are in college.
Academic bias has also been argued as a problem due to
discrimination against conservative students. Research has indicated
that conservative Christians may experience discrimination on colleges
and universities, but these studies are anecdotal and rely on
self-reported perceptions of discrimination. For example, the Hyers'
study includes "Belief Conflicts" and "Interaction Difficulties" as
discriminatory events. However, other work suggests that very few students experience discrimination based on political ideology.
Phillip Gray argues that ideological bias in political
science risks creating "blind spots", whereby certain ideas and
assumptions are just accepted as normal and not challenged. Gray argues
that this could mean that issues that concern the ideology of the
dominant majority could receive a lot of focus, while issues that
concern less prominent ideologies could be seen as less worthy of
investigation and thus be consequently understudied. This risks
resulting in a fairly ideologically homogenous field whereby certain
"givens" are just accepted and thus not examined. In addition, Gray
argues that this means that certain studies are not given adequate
examination if they confirm the dominant group's ideological priors,
even if the studies are flawed. Gray further argues that ideological
bias in academia risks portraying other political groups not as another
group of actors with their own beliefs but rather as a threat (too
ignorant or prejudiced to know what is good) or menace (inherently
inclined towards destructive acts and policies). This results in these
groups being portrayed as dysfunctional and requiring diagnosis rather
than understanding; while Gray does not believe political science
blatantly "otherizes" its ideological outgroups, he does argue that
there is an implicit "diagnostic" attitude towards groups that disagree
with the majority's view.
Cofnas et al. argue that activism within social science can undermine trust in scientists. Brandt et al. argue that bias can limit what topics are researched and
thus limit scientific knowledge as a whole. In addition, political bias
in social science can risk creating a perception amongst the general
public that the scientific field is producing politically biased
findings and thus not worthy of receiving public funds.
Surveys show that a college education tends to have a
"regression to the mean" effect whereby both left-wing students and
right-wing students moderate their views. Students also become more
supportive of dissent and free speech during their education.
An early audit study published in 1986 suggested that entrance into an American clinical psychology graduate program was negatively affected by whether the applicant was a fundamentalist Christian. One study examined the comments made by members of an American medical
school admission committee towards 21 Christian applicants. It concluded
that applicants were more likely to be criticised when responding to a
question on abortion with an anti-abortion response. George Yancey
says that academics are less likely to hire a colleague if they find
out that the colleague is either religiously or politically
conservative, and discrimination exists against fundamentalists,
evangelicals and to a lesser extent Republicans, though only within
certain cultural contexts.
Brent D. Slife and Jeffrey S. Reber assert that an
implicit bias against theism limits possible insights in the field of
psychology.
Jeff Colgan argues that, amongst international relations
data, there can be interpretive biases by researchers depending on their
nationality, with bias towards the United States being common due to a
large number of scholars being from the US. In this context, it has been proposed that implicit bias based on the
region from which an Academic comes (e.g. it has been argued that when
scholarly manuscripts are reviewed by peers the return address
influences perceptions of Academic quality) can be counteracted by
improved intercontinental Academic collaboration.
Sexism in academia refers to the academic bias and discrimination by a particular sex or gender in academic institutions, particularly universities, due to the ideologies, practices, and reinforcements that privilege one sex or gender over another. Sexism
in academia is not limited to but primarily affects women who are
denied the professional achievements awarded to men in their respective
fields such as positions, tenure and awards. Sexism in academia encompasses institutionalized and cultural sexist
ideologies; it is not limited to the admission process and the
under-representation of women in the sciences but also includes the lack
of women represented in college course materials and the denial of tenure, positions and awards that are generally accorded to men.
Studies have also suggested that one reason for the
unwillingness of conservatives to pursue academic careers may be because
conservatives prefer higher paying jobs and are not as tolerant of controversial ideas as progressives. Empirical support for self-selection can be found in the work of Neil Gross. Gross conducted an audit study whereby he sent emails to directors of
graduate study programs. He varied the emails so that some of them
indicated the student supported the presidential candidacy of Senator John McCain, some of them supported the presidential candidacy of then Senator Barack Obama
and some of them were politically neutral. He found that the directors
of graduate study programs did not significantly vary in their treatment
of the senders of the letters regardless of the implied political
advocacy of that sender. His work suggests an absence of systematic
discrimination against political conservatives.
Logocentrism and phonocentrism
Academic bias can refer to several types of logocentrism or phonocentrism. or the belief that some sciences and disciplines rank higher than others.
Asle Toje argues that while academic bias does not seem to
make scholars dishonest, it does affect what questions are deemed
worthy of research and what conclusions are deemed career-advancing.
Toje also argues that the field of social science is filled with biased
terminology that a priori discredits certain perspectives while lending credence to others. Similarly, Honeycutt et al. argue that bias can affect not only what
questions get asked but how they are asked – they observe that the
debate of whether rightists were more biased than leftists or if the two
were equally biased failed to consider if leftists were more biased as a
possible debate point.
Research into the relationship between race and crime has grown rapidly in recent years. More
specifically, the research delves into the potential cause and effects
of racial disparities in crime. This includes but is not limited to,
disadvantages and inequality (racially, socially and economically),
disparities in education, employment/unemployment, poverty, social
status, and social/familial structure. Also of notable interest, is the
role of exposure in childhood to violent behavior, another potential
cause of racial disparities in crime.
Research conducted in Europe and the United States on the
matter has been widely published, particularly in relation to
discrimination by criminal justice systems. However, there is also a
wide variety of research that branches off from this topic of
discrimination by the criminal justice system. It has been argued that
evidence for discrimination by the criminal justice system (and racial
disparities occurring as a result) are potentially over interpreted and
lacking supportive evidence. Therefore, it is important to consider other potential aspects of race
as a correlate of crime and the multitude of potential causes and
effects incorporated.
Race and Crime on Women and Girls
Researcher Harmon and Boppre shed light onto the potential
causes of the rise in the racial disparity between Black and White
females by examining changes in the relative odds of Black female
imprisonment to White female imprisonment. They found that the war on crime ultimately affected all racial groups
in America, but the effects were more pronounced among African Americans
and Latinos. This was revealed in official statistics, i.e., the Uniform Crime
Report, managed by the FBI. The community puts their trust in crime
statistics by the FBI to compare safer states, cities, or towns that
display the number of crimes. However, research shows that female black
offenders are often discriminated against by the law enforcement
agencies. So although Black females are admitted to prison for drug crimes at an
83% higher rate than White females at the start of the war on drugs, by
2008 Black females' admittance rate was 338% higher, a quadrupling of
the 1983 disparity. Researchers analyze the percentage of drug crimes committed by women
and girls across different racial groups to identify issues within the
data. The data highlight that the most important factor is
victimization, Black female offenders are consistently condemned for
their offenses while their victimizations are ignored.
Victimization on Women and Girls
Acquaviva and colleagues examine the disparate treatment
and experiences that Black and Latina victims face within the criminal
legal system.Their
findings show that women involved in crime frequently encounter unfair
treatment by law enforcement—both when they are labeled as offenders and
when they attempt to seek help as victims. The research also reveals
that Black female offenders constitute the highest percentage among the
racial groups studied, and the victim survey data clearly illustrates
the discrimination they face.
Another key finding involves limitations in understanding
how victim characteristics and behavior variables affect Black and
Latina victims, due to the dichotomous way these variables were
measured. The researchers noted disparities in detention and arrest rates across
racial groups, showing that Black and Latina women were more likely to
experience mistreatment or lack of assistance from law enforcement, even
when they cooperated. The study additionally evaluated the policies of
36 police departments nationwide to determine how effectively they
address profiling, police sexual misconduct, and other gendered aspects
of policing.Researchers
highlight the need for stronger, clearer policies to prevent racial
profiling and ensure that Black female offenders are not subjected to
unjust stops, searches, or arrests without reasonable cause.
Criminal adjudication: discrimination by the criminal justice system
There is a common assumption and belief that criminal adjudication
within the criminal justice system is biased, whereupon ethnicity, race
and class not only predicts but foreshadows that criminal arrests are
skewed. More specifically, this prediction is attributed to the concern
that racial minorities (African American, Latinos, Etc.) and
impoverished or poverty-stricken defendants tend to receive harsher
judged sentences compared to White, Asian, and wealthier or more
affluent defendants. One aspect to consider when examining research
about potential biases and discrimination within the Criminal Justice
System is the researcher’s possible expectancy effects, citation bias, negativity bias and an over interpretation of statistical noise. Since this discrimination is not always detected and recorded, information provided isn't always 100% accurate.
An act titled End Racial and Religious Profiling Act,
stating that federal, state, and local law enforcement were prohibited
from targeting people based on their race, ethnicity, national origin,
or religion, was introduced in the 118th Congress by Senator Ben Cardin,
but was not filed in the House. It has not yet been reintroduced in the
119th Congress.
Discrimination by the criminal justice system in Europe
Research suggests that police practices, such as racial profiling,
over-policing in areas populated by minorities and in-group bias may
result in disproportionately high numbers of racial minorities among
crime suspects in Sweden, Italy, and England and Wales. According to the Racial Disparity Audit conducted by the United Kingdom
Prime Minister, in 2017 minorities living in Wales and England were
more than 3.5 times more likely to be arrested than whites. Likewise,
this same group was far more likely to be the victims of crime with
their white counterparts only having 15 percent likelihood. Research also suggests that there may be possible discrimination by the
judicial system, which contributes to a higher number of convictions
for racial minorities in Sweden, the Netherlands, Italy, Germany, Denmark and France.
Discrimination by the criminal justice system in the United States
Research suggests that police practices, such as racial profiling,
over-policing in areas populated by minorities and in-group bias may
result in disproportionately high numbers of racial minorities among
crime suspects. Also, there may be possible discrimination by the judicial system,
which contributes to a higher number of convictions for racial
minorities. Recent research in 2024 shows that racial inequality in the U.S.
criminal justice system is caused by more than just individual bias.
Sociologist Hedwig Lee explains that racism is built into the system
itself through patterns and policies that treat some groups as less
valued. These factors work together to keep racial gaps in policing,
courts, and prisons in place over time. On average, white offenders are less likely to be arrested for their crime than non-white offenders. Studies show that prosecutors are more likely to charge people that are
a part of marginalized groups with more severe sentences than compared
to white people.
Racial disparities: relationship between inequality and crime
Racial inequality,
resulting in increased disadvantages and imbalances that not only
affect but overshadow the treatment of racial groups (such as racial
minorities), has often been theorized to be a factor in the
manifestation and explanation of crime. More specifically, the aspect that economic deprivation and economic
hardships influenced the disparity in crime rates between Whites, Blacks
and other racial minorities. Overall, a wide variety of explanations and research have focused on
the effects of inequality (socially, economically, educationally),
poverty and unemployment, structural disadvantages, inadequate economic
resources, and social segregation and isolation.
Theoretical perspectives: theories, theses and dissertations
Early research into the effects of interracial economic
inequality, economic hardships, economic deprivation and factors such as
poverty and unemployment have contributed to a variety of theories,
theses and dissertations. This includes, but is not limited to, the
deprivation thesis, macrostructural theory of intergroup relations,
interracial economic inequality thesis and the macro-social theory of
social structure. One possible suggestion for racial inequality related to crime is that
areas who had a higher population of enslaved people in the 1800s would
ultimately have lasting racial prejudice embedded within these areas,
leading to increased rates of racial profiling and biased court systems. U.S. policing and criminal justice system has historical roots in
slavery and colonization, such as slave patrols, Black Codes, and Jim
Crowe Laws that criminalized freed Black people, creating a pre-existing
bias towards African American. The following theories affects on these factors:
Majority Minority Theory: policing intensity increases in minority majority areas with socioeconomic disadvantages.
Conflict Theory of Law: policing backs dominant or majority group interests.
Minority Threat Hypothesis: as minority presence or power
increases, law enforcement responds with more control and aggressive
strategies.
Research and studies
When considering the research and studies that have been
focused on the statistical rates and notable differences between race
and crime, it is important to understand possible underlying issues,
assumptions or biases that may occur. For example, previous studies have
attempted to obtain statistical rates by disaggregating crime rates or
employing race specific crime rates. However, this was shown to result in an overrepresentation of specific
racial groups such as blacks and other racial minorities (including both
delinquents and adults). Other prior (and even current) studies have also utilized data such as victimization data, homicide data, and violent crimes. However, some of these approaches had limitations, resulting in
overrepresentation or incorrect assumptions. Possible limitations to
consider are the utilization of only one measurement of discrimination
or race-crime statistics, the omission of information or facts, and
relying on subsets and overtly broad information and data sets.
In 2020 Black Americans were 9.3 times more likely than
White Americans to be homicide victims, American Indians 4.3 times, and
Latin individuals 1.9 times, based on age-adjusted data. Since, homicide
tends to be intraracial, these numbers highlight higher rates of
offending inside the same racial groups. However, other sources present data distracting from these figures.
According to data in 2023, police shooting stats showed about four in
ten individuals shot by officers were White, while about one in five
were Black and around one in eight were Hispanic. Another report from
the same year over victims of violent crimes, was found to be mostly
White at around 62%, Black individuals represented around 12%, Hispanic
individuals 17%, and Asian, American Indian, and Alaska Native
individuals making up about 4%. More recent data on arrests for violent
offenses present that approximately 53% of people arrested were White,
25% were Black, and 14% were Hispanic. This expresses the demographic
differences between victimization and arrest rates.
In a graph published by the Office of Juvenile Justice and
Delinquency Prevention, the overall detention rate for juveniles has
gone down since the 1990s; however, the rate of detention for Black,
Hispanic, and Indigenous youth is still shown as significantly higher
compared to white youth. In an additional graph published by the OJJDP, the rate of youth arrest
rates shows similar results, with Black and Indigenous youth once again
facing higher rates than white youth.
Currently, one of the tools utilized is the NIBRS database
which has assisted with obtaining a more accurate analysis. This was due
to an increase in variety and improved measure of crime. However, conflicting research and findings have brought to light a
multitude of potential limitations to the available documentation,
records and data that is available for use in race-crime specific data.
Interpretation of these studies and research conducted have resulted in a
variety of narratives and outcomes due to mixed results, a lack of
studies for racial groups such as Asians, and even aspects such as
expectancy effects and biases (such as negativity bias).
Google Trends topic searches for "Gaslighting" began a substantial increase in 2016.
Gaslighting is the manipulation of someone into questioning their perception of reality.The term derives from the 1944 film Gaslight and became popular in the mid-2010s.
Some mental health experts have expressed concern that the term has been used too broadly. In 2022, The Washington Post described it as an example of therapy speak, arguing it had become a buzzword improperly used to describe ordinary disagreements.
The term derives from the title of the 1944 film Gaslight. The film was based on the 1938 British play Gas Light by Patrick Hamilton and was a remake of the 1940 British film adaptation, Gaslight. Set among London's elite during the Victorian era, Gas Light
and its adaptations portray a seemingly genteel husband using lies and
manipulation to isolate his heiress wife and persuade her that she is
mentally ill so that he can steal from her. The wife is perturbed when the gaslights in the house periodically dim,
as they normally would if a lamp were lit elsewhere in the house,
causing the gas pressure to drop; when she asks the servants, they tell
her that nobody else is in the house. Unknown to all of them is that the
husband is upstairs searching the rooms for jewels.
The gerund form gaslighting does not appear in the play or films. Its earliest recorded use was in 1961. In The New York Times, it was first used in a 1995 column by Maureen Dowd. According to the American Psychological Association
in 2021, gaslighting "once referred to manipulation so extreme as to
induce mental illness or to justify commitment of the gaslighted person
to a psychiatric institution". It remained obscure — The New York Times used it only nine times in the following 20 years — until the 2010s, when it seeped into the English lexicon. Merriam-Webster defines gaslighting as "psychological manipulation" to make someone question their "perception of reality" leading to "dependence on the perpetrator". The American Dialect Society named gaslight the most useful new word of 2016. Oxford University Press named it a runner-up in its list of the most popular new words of 2018.
In self-help and amateur psychology
Gaslighting is a term used in self-help and amateur psychology to describe a dynamic that can occur in personal relationships (romantic or parental) and in workplace relationships. Gaslighting involves two parties: the "gaslighter", who persistently puts forth a false narrative in order to manipulate, and the "gaslighted", who struggles to maintain their individual autonomy. Gaslighting is typically effective only when there is an unequal power
dynamic or when the gaslighted has shown respect to the gaslighter.
Gaslighting is different from genuine relationship
disagreement, which is both common and important in relationships.
Gaslighting is distinct in that:
one partner is consistently listening and considering the other partner's perspective;
one partner is consistently negating the other's
perception, insisting that they are wrong, or telling them that their
emotional reaction is irrational or dysfunctional.
The term gaslighting is more often used to refer to a
pattern of behavior over a long duration, not a one-off instance of
persuasion, but the method(s) of persuasion is the defining trait of
gaslighting behavior. Over time, the listening partner may exhibit symptoms often associated with anxiety disorders, depression, or low self-esteem. Gaslighting is distinct from genuine relationship conflict in that one party manipulates the perceptions of the other.
Broader use and conflation
In 2022, Merriam-Webster
named "gaslighting" its Word of the Year due to the vast increase in
channels and technologies used to mislead and the word becoming common
for the perception of deception. The word is often used incorrectly to refer to conflicts and disagreements. According to Robin Stern, PhD, co-founder of the Yale Center for
Emotional Intelligence, "Gaslighting is often used in an accusatory way
when somebody may just be insistent on something, or somebody may be
trying to influence you. That's not what gaslighting is."
Some mental health experts have expressed concern that the
broader use of the term is diluting its usefulness and may make it more
difficult to identify the specific type of abuse described in the
original definition. According to a 2022 Washington Post report, it had become a "trendy buzzword"
frequently improperly used to describe ordinary disagreements, rather
than those situations that align with the word's historical definition.
In psychiatry and psychology
The word gaslighting is occasionally used in clinical
literature, but is considered a colloquialism by the American
Psychological Association. Barton and Whitehead described three case reports of gaslighting with the goal of securing a person's involuntary commitment to a psychiatric hospital,
motivated by a desire to get rid of relatives or obtain financial gain:
a wife attempting to frame her husband as violent so she could elope
with her lover, another wife alleging that her pub-owning
husband was an alcoholic in order to leave him and take control of the
pub, and a retirement home manager who gave laxatives to a resident
before referring her to a psychiatric hospital for dementia and incontinence.
In 1977, at a time when published literature on gaslighting
was still sparse, Lund and Gardiner published a case report on an
elderly woman who was repeatedly involuntarily committed for alleged psychosis,
by staffers of her retirement home, but whose symptoms always
disappeared shortly after admittance without any treatment. After
investigation, it was discovered that her 'paranoia'
had been the result of gaslighting by staffers of the retirement home,
who knew the woman had suffered from paranoid psychosis 15 years prior.
The research paper "Gaslighting: A Marital Syndrome"
includes clinical observations of the impact on wives after their
reactions were mislabeled by their husbands and male therapists. Other experts have noted values and techniques of therapists can be
harmful as well as helpful to clients (or indirectly to other people in a
client's life).
In his 1996 book, Gaslighting, the Double Whammy, Interrogation and Other Methods of Covert Control in Psychotherapy and Analysis, Theo L. Dorpat recommends non-directive and egalitarian attitudes and methods on the part of clinicians, and "treating patients as active collaborators and equal partners".
He writes, "Therapists may contribute to the victim's distress through
mislabeling the [victim's] reactions.... The gaslighting behaviors of
the spouse provide a recipe for the so-called 'nervous breakdown' for some [victims, and] suicide in some of the worst situations." Dorpat also cautions clinicians about the unintentional abuse of
patients when using interrogation and other methods of covert control in
Psychotherapy and Analysis, as these methods can subtly coerce patients
rather than respect and genuinely help them.
Motivations
Gaslighting is a way to control the moment, stop conflict,
ease anxiety, and feel in control. It often deflects responsibility
however and tears down the other person. Some may gaslight their partners by denying events, including personal violence. A study found that those who gaslight tended to score high on manipulative personality traits.
Learned behavior
Gaslighting is a learned trait. A gaslighter is a student of social learning. They witness it, experience it themselves, or stumble upon it, and see that it works, both for self-regulation and coregulation. Studies have shown that gaslighting is more prevalent in couples where one or both partners have maladaptive personality traits (such as traits associated with short-term mental illness like depression), substance-induced illness (e.g., alcoholism), mood disorders (e.g., bipolar disorder), anxiety disorders (e.g., PTSD), personality disorder (e.g., BPD, NPD, etc.), neurodevelopmental disorder (e.g., ADHD), or combination of the above (i.e., co-occurrence) and are prone to and adept at convincing others to doubt their own perceptions.
Habilitation
It can be difficult to extricate oneself from a gaslighting power dynamic:
Those who gaslight must attain greater emotional awareness and self-regulation, or;
Those being gaslighted must learn that they do not need
others to validate their reality, and they need to gain self-reliance
and confidence in defining their own reality.
In medicine
Medical gaslighting is an informal term
that refers to patients having their real symptoms dismissed or
downplayed by medical professionals, leading to incorrect or delayed
diagnoses; women are more likely to be affected by the phenomenon.
In politics
Gaslighting is more likely to be effective when the gaslighter has a position of power.
In the 2008 book State of Confusion: Political Manipulation and the Assault on the American Mind, the authors contend that the prevalence of gaslighting in American politics began with the age of modern communications:
To say
gaslighting was started by... any extant group is not simply wrong, it
also misses an important point. Gaslighting comes directly from blending
modern communications, marketing, and advertising techniques with
long-standing methods of propaganda. They were simply waiting to be
discovered by those with sufficient ambition and psychological makeup to
use them.
The term has been used to describe the behavior of
politicians and media personalities on both the left and the right sides
of the political spectrum. Some examples include:
American journalists have used the word "gaslighting" to describe the actions of Donald Trump during the 2016 US presidential election and during both of his terms as president.
"Gaslighting" has been used to describe state-implemented psychological harassment techniques used in East Germany during the 1970s and 1980s. The techniques were used as part of the Stasi's (the state security service's) decomposition methods,
which were designed to paralyze the ability of hostile-negative
(politically incorrect or rebellious) people to operate without
unjustifiably imprisoning them, which would have resulted in
international condemnation.
In social systems
Gaslighting within social systems operates as a mechanism
to uphold entrenched power hierarchies, often through subtle and overt
forms of manipulation that compel individuals to question their
perceptions of reality. One striking manifestation is racial
gaslighting, a process deeply embedded within the political, economic,
social, and cultural scaffolding of a dominant racial hierarchy. By
pathologizing dissent and framing challenges to racial inequities as
misperceptions or even assaults on democratic fairness, racial
gaslighting coerces marginalized individuals into doubting their
experiences within racialized structures. This phenomenon extends beyond denial of systemic racism to active recharacterization, where the assertion of racial injustice is reframed as an act of reverse discrimination or irrational sensitivity.
In the workplace
In her 2024 book On Gaslighting, Indiana University philosopher Kate Abramson
offers the example of a boss who minimizes a complaint of harassment or
discrimination, possibly filed by a member of a marginalized group. In her framing, the gaslighter says "Don’t be so sensitive. You’re overreacting. You’re imagining things".
Statistics (from German: Statistik, orig. "description of a state, a country") is the discipline that concerns the collection, organization, analysis, interpretation, and presentation of data. In applying statistics to a scientific, industrial, or social problem, it is conventional to begin with a statistical population or a statistical model
to be studied. Populations can be diverse groups of people or objects
such as "all people living in a country" or "every atom composing a
crystal". Statistics deals with every aspect of data, including the
planning of data collection in terms of the design of surveys and experiments. Statistics is deeply related to subjects like physics, chemistry, geography, geopolitics, and especially mathematics.
When census data (comprising every member of the target population) cannot be collected, statisticians collect data by developing specific experiment designs and survey samples.
Random sampling assures that inferences and conclusions can reasonably
extend from the sample to the population as a whole. An experimental study
involves taking measurements of the system under study, manipulating
the system, and then taking additional measurements using the same
procedure to determine if the manipulation has modified the values of
the measurements. In contrast, an observational study does not involve experimental manipulation.
Two main statistical methods are used in data analysis: descriptive statistics, which summarize data from a sample using indexes such as the mean or standard deviation, and inferential statistics, which draw conclusions from data that are subject to random variation (e.g., observational errors, sampling variation). Descriptive statistics are most often concerned with two sets of properties of a distribution (sample or population): central tendency (or location) seeks to characterize the distribution's central or typical value, while dispersion (or variability) characterizes the extent to which members of the distribution depart from its center and each other. Inferences made using mathematical statistics employ the framework of probability theory, which deals with the analysis of random phenomena.
A standard statistical procedure involves the collection of data leading to a test of the relationship
between two statistical data sets, or a data set and synthetic data
drawn from an idealized model. A hypothesis is proposed for the
statistical relationship between the two data sets, an alternative to an idealized null hypothesis
of no relationship between two data sets. Rejecting or disproving the
null hypothesis is done using statistical tests that quantify the sense
in which the null can be proven false, given the data that are used in
the test. Working from a null hypothesis, two basic forms of error are
recognized: Type I errors (null hypothesis is rejected when it is in fact true, giving a "false positive") and Type II errors
(null hypothesis fails to be rejected when it is in fact false, giving a
"false negative"). Multiple problems have come to be associated with
this framework, ranging from obtaining a sufficient sample size to
specifying an adequate null hypothesis.
Statistical measurement processes are also prone to error
with regard to the data they generate. Many of these errors are
classified as random (noise) or systematic (bias), but other types of errors (e.g., blunder, such as when an analyst reports incorrect units) can also occur. The presence of missing data or censoring may result in biased estimates, and specific techniques have been developed to address these problems.
"Statistics
is both the science of uncertainty and the technology of extracting
information from data." - featured in the International Encyclopedia of
Statistical Science.
Statistics is the discipline that deals with data,
facts and figures with which meaningful information is inferred. Data
may represent a numerical value, in form of quantitative data, or a
label, as with qualitative data. Data may be collected, presented and
summarised, in one of two methods called descriptive statistics. Two
elementary summaries of data, singularly called a statistic, are the
mean and dispersion. Whereas inferential statistics interprets data from
a population sample to induce statements and predictions about a
population.
Statistics is regarded as a body of science or a branch of mathematics. It is based on probability, a branch of mathematics that studies random
events. Statistics is considered the science of uncertainty. This
arises from the ways to cope with measurement and sampling error as well
as dealing with uncertanties in modelling. Although probability and
statistics were once paired together as a single subject, they are
conceptually distinct from one another. The former is based on deducing
answers to specific situations from a general theory of probability,
meanwhile statistics induces statements about a population based on a
data set. Statistics serves to bridge the gap between probability and
applied mathematical fields.
Some consider statistics to be a distinct mathematical science
rather than a branch of mathematics. While many scientific
investigations make use of data, statistics is generally concerned with
the use of data in the context of uncertainty and decision-making in the
face of uncertainty. Statistics is indexed at 62, a subclass of probability theory and
stochastic processes, in the Mathematics Subject Classification. Mathematical statistics is covered in the range 276-280 of subclass QA
(science > mathematics) in the Library of Congress Classification.
The word statistics ultimately comes from the Latin word
Status, meaning "situation" or "condition" in society, which in late
Latin adopted the meaning "state". Derived from this, political
scientist Gottfried Achenwall, coined the German word statistik (a
summary of how things stand). In 1770, the term entered the English
language through German and referred to the study of political
arrangements. The term gained its modern meaning in the 1790s in John
Sinclair's works. In modern German, the term statistik is synonymous with mathematical
statistics. The term statistic, in singular form, is used to describe a
function that returns its value of the same name.
Statistical data
Data collection
Sampling
When census data cannot be collected, statisticians collect sample data by developing specific experiment designs and survey samples. Statistics itself also provides tools for prediction and forecasting through statistical models.
To use a sample as a guide to an entire population, it is
important that it truly represents the overall population.
Representative sampling
ensures that inferences and conclusions can safely be extended from the
sample to the population as a whole. A major problem lies in
determining the extent to which the chosen sample is actually
representative. Statistics offers methods to estimate and correct for
any bias in the sample and data collection procedures. There are also
methods of experimental design that can lessen these issues at the
outset of a study, strengthening its ability to discern truths about the
population.
Sampling theory is part of the mathematical discipline of probability theory. Probability is used in mathematical statistics to study the sampling distributions of sample statistics and, more generally, the properties of statistical procedures.
The use of any statistical method is valid only when the system or
population under consideration satisfies the assumptions of the method.
The difference in point of view between classic probability theory and
sampling theory is, roughly, that probability theory starts with the
given parameters of a total population to deduce probabilities that pertain to samples. Statistical inference, however, moves in the opposite direction—inductively inferring from samples to the parameters of a larger or total population.
Experimental and observational studies
A common goal for a statistical research project is to investigate causality, and in particular to draw a conclusion on the effect of changes in the values of predictors or independent variables on dependent variables. There are two major types of causal statistical studies: experimental studies and observational studies.
In both types of studies, the effect of differences of an independent
variable (or variables) on the behavior of the dependent variable are
observed. The difference between the two types lies in how the study is
actually conducted. Each can be very effective. An experimental study
involves taking measurements of the system under study, manipulating the
system, and then taking additional measurements with different levels
using the same procedure to determine if the manipulation has modified
the values of the measurements. In contrast, an observational study does
not involve experimental manipulation.
Instead, data are gathered and correlations between predictors and
response are investigated. While the tools of data analysis work best on
data from randomized studies, they are also applied to other kinds of data—like natural experiments and observational studies—for which a statistician would use a modified, more structured estimation method (e.g., difference in differences estimation and instrumental variables, among many others) that produce consistent estimators.
Experiments
The basic steps of a statistical experiment are:
Planning the research, including finding the
number of replicates of the study, using the following information:
preliminary estimates regarding the size of treatment effects, alternative hypotheses, and the estimated experimental variability.
Consideration of the selection of experimental subjects and the ethics
of research is necessary. Statisticians recommend that experiments
compare (at least) one new treatment with a standard treatment or
control, to allow an unbiased estimate of the difference in treatment
effects.
Further examining the data set in secondary analyses, to suggest new hypotheses for future study.
Documenting and presenting the results of the study.
Experiments on human behavior have special concerns. The famous Hawthorne study examined changes to the working environment at the Hawthorne plant of the Western Electric Company. The researchers were interested in determining whether increased illumination would increase the productivity of the assembly line
workers. The researchers first measured the productivity in the plant,
then modified the illumination in an area of the plant and checked if
the changes in illumination affected productivity. It turned out that
productivity indeed improved (under the experimental conditions).
However, the study is heavily criticized today for errors in
experimental procedures, specifically for the lack of a control group and blindness. The Hawthorne effect
refers to finding that an outcome (in this case, worker productivity)
changed due to observation itself. Those in the Hawthorne study became
more productive not because the lighting was changed but because they
were being observed.
Observational study
An example of an observational study is one that explores
the association between smoking and lung cancer. This type of study
typically uses a survey to collect observations about the area of
interest and then performs statistical analysis. In this case, the
researchers would collect observations of both smokers and non-smokers,
perhaps through a cohort study, and then look for the number of cases of lung cancer in each group. A case-control study
is another type of observational study in which people with and without
the outcome of interest (e.g. lung cancer) are invited to participate
and their exposure histories are collected.
Various attempts have been made to produce a taxonomy of levels of measurement. The psychophysicist Stanley Smith Stevens
defined nominal, ordinal, interval, and ratio scales. Nominal
measurements do not have meaningful rank order among values, and permit
any one-to-one (injective) transformation. Ordinal measurements have
imprecise differences between consecutive values, but have a meaningful
order to those values, and permit any order-preserving transformation.
Interval measurements have meaningful distances between measurements
defined, but the zero value is arbitrary (as in the case with longitude and temperature measurements in Celsius or Fahrenheit),
and permit any linear transformation. Ratio measurements have both a
meaningful zero value and the distances between different measurements
defined, and permit any rescaling transformation.
Because variables conforming only to nominal or ordinal
measurements cannot be reasonably measured numerically, sometimes they
are grouped together as categorical variables, whereas ratio and interval measurements are grouped together as quantitative variables, which can be either discrete or continuous, due to their numerical nature. Such distinctions can often be loosely correlated with data type in computer science, in that dichotomous categorical variables may be represented with the Boolean data type, polytomous categorical variables with arbitrarily assigned integers in the integral data type, and continuous variables with the real data type involving floating-point arithmetic.
But the mapping of computer science data types to statistical data
types depends on which categorization of the latter is being
implemented.
Other categorizations have been proposed. For example, Mosteller and Tukey (1977) distinguished grades, ranks, counted fractions, counts, amounts, and balances. Nelder (1990) described continuous counts, continuous ratios, count ratios, and categorical modes of data. (See also: Chrisman (1998), van den Berg (1991).)
The issue of whether it is appropriate to apply different
kinds of statistical methods to data obtained from different kinds of
measurement procedures is complicated by issues concerning the
transformation of variables and the precise interpretation of research
questions. "The relationship between the data and what they describe
merely reflects the fact that certain kinds of statistical statements
may have truth values that are not invariant under some transformations.
Whether a transformation is sensible to contemplate depends on the
question one is trying to answer."
A descriptive statistic (in the count noun sense) is a summary statistic that quantitatively describes or summarizes features of a collection of information, while descriptive statistics in the mass noun sense is the process of using and analyzing those statistics. Descriptive statistics is distinguished from inferential statistics (or inductive statistics), in that descriptive statistics aims to summarize a sample, rather than use the data to learn about the population that the sample of data is thought to represent.
Statistical inference is the process of using data analysis to deduce properties of an underlying probability distribution. Inferential statistical analysis infers properties of a population, for example by testing hypotheses and deriving estimates. It is assumed that the observed data set is sampled from a larger population. Inferential statistics can be contrasted with descriptive statistics.
Descriptive statistics is solely concerned with properties of the
observed data, and it does not rest on the assumption that the data come
from a larger population.
A statistic is a random variable that is a function of the random sample, but not a function of unknown parameters.
The probability distribution of the statistic, though, may have unknown
parameters. Consider now a function of the unknown parameter: an estimator is a statistic used to estimate such function. Commonly used estimators include sample mean, unbiased sample variance and sample covariance.
A random variable that is a function of the random sample and of the unknown parameter, but whose probability distribution does not depend on the unknown parameter is called a pivotal quantity or pivot. Widely used pivots include the z-score, the chi square statistic and Student's t-value.
Between two estimators of a given parameter, the one with lower mean squared error is said to be more efficient. Furthermore, an estimator is said to be unbiased if its expected value is equal to the true value of the unknown parameter being estimated, and asymptotically unbiased if its expected value converges at the limit to the true value of such parameter.
Other desirable properties for estimators include: UMVUE
estimators that have the lowest variance for all possible values of the
parameter to be estimated (this is usually an easier property to verify
than efficiency) and consistent estimators which converges in probability to the true value of such parameter.
This still leaves the question of how to obtain estimators
in a given situation and carry the computation, several methods have
been proposed: the method of moments, the maximum likelihood method, the least squares method and the more recent method of estimating equations.
Null hypothesis and alternative hypothesis
Interpretation of statistical information can often involve the development of a null hypothesis which is usually (but not necessarily) that no relationship exists among variables or that no change occurred over time.The alternative hypothesis is the name of the hypothesis that contradicts the null hypothesis.
The best illustration for a novice is the predicament encountered by a criminal trial. The null hypothesis, H0, asserts that the defendant is innocent, whereas the alternative hypothesis, H1, asserts that the defendant is guilty. The indictment comes because of suspicion of the guilt. The H0 (the status quo) stands in opposition to H1 and is maintained unless H1 is supported by evidence "beyond a reasonable doubt". However, "failure to reject H0"
in this case does not imply innocence, but merely that the evidence was
insufficient to convict. So the jury does not necessarily accept H0 but fails to reject H0. While one can not "prove" a null hypothesis, one can test how close it is to being true with a power test, which tests for type II errors. The null hypothesis cannot be proven true because it is already assumed to be true when the test is being conducted.
Error
Working from a null hypothesis, two broad categories of error are recognized:
Type I errors where the null hypothesis is falsely rejected, giving a "false positive".
Type II errors
where the null hypothesis fails to be rejected and an actual difference
between populations is missed, giving a "false negative".
Standard deviation
refers to the extent to which individual observations in a sample
differ from a central value, such as the sample or population mean,
while Standard error refers to an estimate of difference between sample mean and population mean.
A statistical error is the amount by which an observation differs from its expected value. A residual
is the amount an observation differs from the value the estimator of
the expected value assumes on a given sample (also called prediction).
A least squares fit: in red the points to be fitted, in blue the fitted line.
Many statistical methods seek to minimize the residual sum of squares, and these are called "methods of least squares" in contrast to Least absolute deviations.
The latter gives equal weight to small and big errors, while the former
gives more weight to large errors. Residual sum of squares is also differentiable, which provides a handy property for doing regression. Least squares applied to linear regression is called ordinary least squares method and least squares applied to nonlinear regression is called non-linear least squares.
Also in a linear regression model the non deterministic part of the
model is called error term, disturbance or more simply noise. Both
linear regression and non-linear regression are addressed in polynomial least squares,
which also describes the variance in a prediction of the dependent
variable (y axis) as a function of the independent variable (x axis) and
the deviations (errors, noise, disturbances) from the estimated
(fitted) curve.
Measurement processes that generate statistical data are also subject to error. Many of these errors are classified as random (noise) or systematic (bias),
but other types of errors (e.g., blunder, such as when an analyst
reports incorrect units) can also be important. The presence of missing data or censoring may result in biased estimates and specific techniques have been developed to address these problems.
Confidence intervals: the red line is true value for the mean in this example, the blue lines are random confidence intervals for 100 realizations.
Most studies only sample part of a population, so results
do not fully represent the whole population. Any estimates obtained from
the sample only approximate the population value. Confidence intervals
allow statisticians to express how closely the sample estimate matches
the true value in the whole population. Often they are expressed as 95%
confidence intervals. Formally, a 95% confidence interval for a value is
a range where, if the sampling and analysis were repeated under the
same conditions (yielding a different dataset), the interval would
include the true (population) value in 95% of all possible cases. This
does not imply that the probability that the true value is in the confidence interval is 95%. From the frequentist perspective, such a claim does not even make sense, as the true value is not a random variable.
Either the true value is or is not within the given interval. However,
it is true that, before any data are sampled and given a plan for how
to construct the confidence interval, the probability is 95% that the
yet-to-be-calculated interval will cover the true value: at this point,
the limits of the interval are yet-to-be-observed random variables.
One approach that does yield an interval that can be interpreted as
having a given probability of containing the true value is to use a credible interval from Bayesian statistics: this approach depends on a different way of interpreting what is meant by "probability", that is as a Bayesian probability.
In principle, confidence intervals can be symmetrical or
asymmetrical. An interval can be asymmetrical because it works as a
lower or upper bound for a parameter (left-sided interval or right sided
interval), but it can also be asymmetrical if a two-sided interval is
built violating symmetry around the estimate. Sometimes the bounds of a
confidence interval are reached asymptotically, and these are used to
approximate the true bounds.
Statistics rarely give a simple Yes/No type answer to the
question under analysis. Interpretation often comes down to the level of
statistical significance applied to the numbers and often refers to the
probability of a value accurately rejecting the null hypothesis
(sometimes referred to as the p-value).
In this graph the black line is probability distribution for the test statistic, the critical region is the set of values to the right of the observed data point (observed value of the test statistic) and the p-value is represented by the green area.
The standard approach is to test a null hypothesis against an alternative hypothesis. A critical region
is the set of values of the estimator that leads to refuting the null
hypothesis. The probability of type I error is therefore the probability
that the estimator belongs to the critical region given that null
hypothesis is true (statistical significance)
and the probability of type II error is the probability that the
estimator does not belong to the critical region given that the
alternative hypothesis is true. The statistical power of a test is the probability that it correctly rejects the null hypothesis when the null hypothesis is false.
Referring to statistical significance does not necessarily
mean that the overall result is significant in real-world terms. For
example, in a large study of a drug it may be shown that the drug has a
statistically significant but very small beneficial effect, such that it
is unlikely to help the patient noticeably.
Although in principle the acceptable level of statistical significance may be subject to debate, the significance level
is the largest p-value that allows the test to reject the null
hypothesis. This test is logically equivalent to saying that the p-value
is the probability, assuming the null hypothesis is true, of observing a
result at least as extreme as the test statistic. Therefore, the smaller the significance level, the lower the probability of committing type I error.
A difference that is highly statistically
significant can still be of no practical significance, but it is
possible to properly formulate tests to account for this. One response
involves going beyond reporting only the significance level to include the p-value when reporting whether a hypothesis is rejected or accepted. The p-value, however, does not indicate the size
or importance of the observed effect and can also seem to exaggerate
the importance of minor differences in large studies. A better and
increasingly common approach is to report confidence intervals. Although these are produced from the same calculations as those of hypothesis tests or p-values, they describe both the size of the effect and the uncertainty surrounding it.
Fallacy of the transposed conditional, aka prosecutor's fallacy: criticisms arise because the hypothesis testing approach forces one hypothesis (the null hypothesis)
to be favored, since what is being evaluated is the probability of the
observed result given the null hypothesis and not probability of the
null hypothesis given the observed result. An alternative to this
approach is offered by Bayesian inference, although it requires establishing a prior probability.
Rejecting the null hypothesis does not automatically prove the alternative hypothesis.
As everything in inferential statistics it relies on sample size, and therefore under fat tails p-values may be seriously mis-computed.
Examples
Some well-known statistical tests and procedures are:
As an example, suppose that 1 in 1000 women in a
population have breast cancer. Suppose that all (100%) of those with
cancer will get a positive test result (detection of cancer), while 5%
without breast cancer will also get a positive result (falsely detecting cancer) - that is, the test has a false positive rate of 5%
Suppose a woman in this population had a positive
mammogram. By Bayes law, the chance that she actually has cancer is
given by taking the prior odds of having cancer (around 1:1000) and
multiplying by the likelihood ratio 20:1 (since a cancer patient is 20
times more likely to get a positive result than a healthy patient) to
get the posterior odds 20:1000 = 1:50, which is around 2%. Many find
this probability unintuitively small due to neglecting the low base rate of cancer.
As an example, in one study only 18% of doctors got the correct answer,
with 45% of them giving a probability of cancer of 95%, and the average
probability being 56% (overestimating by a factor of 30).
For statistical modelling purposes, Bayesian models tend to be hierarchical. For example, one could model each YouTube channel as having video views distributed as a normal distribution with channel dependent mean and variance ,
while modeling the channel means as themselves coming from a normal
distribution representing the distribution of average video view counts
per channel, and the variances as coming from another distribution.
Bayesian methods have been aided by the increase in available computing power to compute the posterior probability using numerical approximation techniques like Markov Chain Monte Carlo.
Exploratory data analysis (EDA) is an approach to analyzingdata sets to summarize their main characteristics, often with visual methods. A statistical model
can be used or not, but primarily EDA is for seeing what the data can
tell us beyond the formal modeling or hypothesis testing task.
Formal discussions on inference date back to the mathematicians and cryptographers of the Islamic Golden Age between the 8th and 13th centuries. Al-Khalil (717–786) wrote the Book of Cryptographic Messages, which contains one of the first uses of permutations and combinations, to list all possible Arabic words with and without vowels. Al-Kindi's Manuscript on Deciphering Cryptographic Messages gave a detailed description of how to use frequency analysis to decipher encrypted messages, providing an early example of statistical inference for decoding. Ibn Adlan (1187–1268) later made an important contribution on the use of sample size in frequency analysis.
Although the term statistic was introduced by the Italian scholar Girolamo Ghilini in 1589 with reference to a collection of facts and information about a state, it was the German Gottfried Achenwall in 1749 who started using the term as a collection of quantitative information, in the modern use for this science. The earliest writing containing statistics in Europe dates back to 1663, with the publication of Natural and Political Observations upon the Bills of Mortality by John Graunt.
Early applications of statistical thinking revolved around
the needs of states to base policy on demographic and economic data,
hence its stat- etymology.
The scope of the discipline of statistics broadened in the early 19th
century to include the collection and analysis of data in general.
Today, statistics is widely employed in government, business, and
natural and social sciences.
Carl Friedrich Gauss made major contributions to probabilistic methods leading to statistics.
The mathematical foundations of statistics developed from discussions concerning games of chance among mathematicians such as Gerolamo Cardano, Blaise Pascal, Pierre de Fermat, and Christiaan Huygens. Although the idea of probability was already examined in ancient and medieval law and philosophy (such as the work of Juan Caramuel), probability theory as a mathematical discipline only took shape at the very end of the 17th century, particularly in Jacob Bernoulli's posthumous work Ars Conjectandi. This was the first book where the realm of games of chance and the
realm of the probable (which concerned opinion, evidence, and argument)
were combined and submitted to mathematical analysis. The method of least squares was first described by Adrien-Marie Legendre in 1805, though Carl Friedrich Gauss presumably made use of it a decade earlier in 1795.
Karl Pearson, a founder of mathematical statistics
In the 1830s-1850s, "statistical offices" and national
"statistical societies" were founded in Europe and America, and in the
mid-19th century, the idea arose of "organized contacts between the
statisticians of different countries although informal contacts occurred
earlier". In those days, the name "statistics" referred mainly to "matters of
state", and British statisticians were often called "statists".
The modern field of statistics emerged in the late 19th and early 20th century in three stages. The first wave, at the turn of the century, was led by the work of Francis Galton and Karl Pearson,
who transformed statistics into a rigorous mathematical discipline used
for analysis, not just in science, but in industry and politics as
well. Galton's contributions included introducing the concepts of standard deviation, correlation, regression analysis
and the application of these methods to the study of the variety of
human characteristics—height, weight and eyelash length among others. Pearson developed the Pearson product-moment correlation coefficient, defined as a product-moment, the method of moments for the fitting of distributions to samples and the Pearson distribution, among many other things. Galton and Pearson founded Biometrika as the first journal of mathematical statistics and biostatistics (then called biometry), and the latter founded the world's first university statistics department at University College London.
The final wave, which mainly saw the refinement and
expansion of earlier developments, emerged from the collaborative work
between Egon Pearson and Jerzy Neyman in the 1930s. They introduced the concepts of "Type II" error, power of a test and confidence intervals.
Jerzy Neyman in 1934 showed that stratified random sampling was in
general a better method of estimation than purposive (quota) sampling.
Among the early attempts to measure national economic activity were those of William Petty in the 17th century. In the 20th century the uniform System of National Accounts was developed.
Today, statistical methods are applied in all fields that
involve decision making, for making accurate inferences from a collated
body of data and for making decisions in the face of uncertainty based
on statistical methodology. The use of modern computers
has expedited large-scale statistical computations and has also made
possible new methods that are impractical to perform manually.
Statistics continues to be an area of active research, for example on
the problem of how to analyze big data.
Applications
Applied statistics, theoretical statistics and mathematical statistics
Applied statistics, sometimes referred to as Statistical science, comprises descriptive statistics and the application of inferential statistics. Theoretical statistics concerns the logical arguments underlying justification of approaches to statistical inference, as well as encompassing mathematical statistics. Mathematical statistics includes not only the manipulation of probability distributions necessary for deriving results related to methods of estimation and inference, but also various aspects of computational statistics and the design of experiments.
Statistical consultants can help organizations and companies that do not have in-house expertise relevant to their particular questions.
Machine learning and data mining
Machine learning models are statistical and probabilistic models that capture patterns in the data through use of computational algorithms.
A typical statistics course covers descriptive statistics, probability, binomial and normal distributions, test of hypotheses and confidence intervals, linear regression, and correlation. Modern fundamental statistical courses for undergraduate students focus
on correct test selection, results interpretation, and use of free
statistics software.
The rapid and sustained increases in computing power
starting from the second half of the 20th century have had a substantial
impact on the practice of statistical science. Early statistical models
were almost always from the class of linear models, but powerful computers, coupled with suitable numerical algorithms, caused an increased interest in nonlinear models (such as neural networks) as well as the creation of new types, such as generalized linear models and multilevel models.
Increased computing power has also led to the growing popularity of computationally intensive methods based on resampling, such as permutation tests and the bootstrap, while techniques such as Gibbs sampling have made use of Bayesian models
more feasible. The computer revolution has implications for the future
of statistics with a new emphasis on "experimental" and "empirical"
statistics. A large number of both general and special purpose statistical software are now available. Examples of available software capable of complex statistical computation include programs such as Mathematica, SAS, SPSS, and R.
Statistics form a key basis tool in business and
manufacturing as well. It is used to understand measurement systems
variability, control processes (as in statistical process control or SPC), for summarizing data, and to make data-driven decisions.
Misuse of statistics
can produce subtle but serious errors in description and
interpretation—subtle in the sense that even experienced professionals
make such errors, and serious in the sense that they can lead to
devastating decision errors. For instance, social policy, medical
practice, and the reliability of structures like bridges all rely on the
proper use of statistics.
Even when statistical techniques are correctly applied,
the results can be difficult to interpret for those lacking expertise.
The statistical significance
of a trend in the data—which measures the extent to which a trend could
be caused by random variation in the sample—may or may not agree with
an intuitive sense of its significance. The set of basic statistical
skills (and skepticism) that people need to deal with information in
their everyday lives properly is referred to as statistical literacy.
There is a general perception that statistical knowledge is all-too-frequently intentionally misused by finding ways to interpret only the data that are favorable to the presenter. A mistrust and misunderstanding of statistics is associated with the quotation, "There are three kinds of lies: lies, damned lies, and statistics". Misuse of statistics can be both inadvertent and intentional, and the book How to Lie with Statistics, by Darrell Huff,
outlines a range of considerations. In an attempt to shed light on the
use and misuse of statistics, reviews of statistical techniques used in
particular fields are conducted (e.g. Warne, Lazo, Ramos, and Ritter
(2012)).
Ways to avoid misuse of statistics include using proper diagrams and avoiding bias. Misuse can occur when conclusions are overgeneralized
and claimed to be representative of more than they really are, often by
either deliberately or unconsciously overlooking sampling bias. Bar graphs are arguably the easiest diagrams to use and understand, and
they can be made either by hand or with simple computer programs. Most people do not look for bias or errors, so they are not noticed.
Thus, people may often believe that something is true even if it is not
well represented. To make data gathered from statistics believable and accurate, the sample taken must be representative of the whole. According to Huff, "The dependability of a sample can be destroyed by [bias]... allow yourself some degree of skepticism."
To assist in the understanding of statistics Huff proposed a series of questions to be asked in each case:
Who says so? (Do they have an axe to grind?)
How do they know? (Do they have the resources to know the facts?)
What's missing? (Do they give us a complete picture?)
Did someone change the subject? (Do they offer us the right answer to the wrong problem?)
Does it make sense? (Is their conclusion logical and consistent with what we already know?)
The confounding variable problem: X and Y may be correlated, not because there is causal relationship between them, but because both depend on a third variable Z. Z is called a confounding factor.
The concept of correlation
is particularly noteworthy for the potential confusion it can cause.
Statistical analysis of a data set often reveals that two variables
(properties) of the population under consideration tend to vary
together, as if they were connected. For example, a study of annual
income that also looks at age of death might find that poor people tend
to have shorter lives than affluent people. The two variables are said
to be correlated; however, they may or may not be the cause of one
another. The correlation could instead be produced by a third,
previously unconsidered factor, called a lurking variable or confounding variable. For example, higher incomes may have a tendency to allow for more
leisure time, which in turn allows for more time spent exercising. It
may be that this higher level of activity causes the longer lifespans
observed in the more affluent group. Raising income levels therefore
does not in itself cause people to live longer. Rather, a confounding
variable is responsible for the increase.
For this reason, correlation does not imply causation: a causal relationship between the two variables cannot be inferred from their correlation alone.
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