Nielsen Audio (formerly Arbitron ) is a consumer research company in the United States that collects listener data on radio broadcasting audiences. It was founded as the American Research Bureau by Jim Seiler in 1949 and became national by merging with Los Angeles –based Coffin, Cooper, and Clay in the early 1950s. The company's initial business was the collection of broadcast television ratings .
126-575: The company changed its name to Arbitron in the mid‑1960s, the namesake of the Arbitron System, a centralized statistical computer with leased lines to viewers' homes to monitor their activity. Deployed in New York City , it gave instant ratings data on what people were watching. A reporting board lit up to indicate which homes were listening to which broadcasts. For years, Arbitron was a part of Control Data Corporation (CDC) and in 1992, it became
252-469: 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. Consider independent identically distributed (IID) random variables with
378-415: 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 . When census data cannot be collected, statisticians collect data by developing specific experiment designs and survey samples . Representative sampling assures that inferences and conclusions can reasonably extend from
504-612: A decade between Irish immigrants and Black people for work. Rioters burned the Colored Orphan Asylum to the ground. At least 120 people were killed. Eleven Black men were lynched over five days, and the riots forced hundreds of Blacks to flee. The Black population in Manhattan fell below 10,000 by 1865. The White working class had established dominance. It was one of the worst incidents of civil unrest in American history . In 1886,
630-418: A decade earlier in 1795. 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
756-458: A given probability distribution : standard statistical inference and estimation theory defines a random sample as the random vector given by the column vector of these IID variables. The population being examined is described by a probability distribution that may have unknown parameters. 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
882-467: A given 15‑minute period), time spent listening (TSL), and market breakdowns by age, gender, and race/ethnicity. The "cume" only counts a listener once, whereas the AQH is a product of "cume" and time spent listening. For example, if you looked into a room and saw Fred and Jane, then 15 minutes later saw Fred with Sara. The "cume" would be 3 (Fred, Jane, Sara) and the AQH would be 2 (an average of two people in
1008-484: 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 lower or upper bound for a parameter (left-sided interval or right sided interval), but it can also be asymmetrical because
1134-471: 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 . 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 best illustration for
1260-548: 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
1386-1028: 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
SECTION 10
#17328769125481512-499: A novice is the predicament encountered by a criminal trial. The null hypothesis, H 0 , asserts that the defendant is innocent, whereas the alternative hypothesis, H 1 , asserts that the defendant is guilty. The indictment comes because of suspicion of the guilt. The H 0 (status quo) stands in opposition to H 1 and is maintained unless H 1 is supported by evidence "beyond a reasonable doubt". However, "failure to reject H 0 " in this case does not imply innocence, but merely that
1638-494: A part of Ceridian Corporation before the company was split in 2001. The then-current Arbitron was formed from the renaming of the old Ceridian Corporation while the spin-off firm took the Ceridian Corporation name and acted as accounting successor. On December 18, 2012, The Nielsen Company announced that it would acquire Arbitron, its only competitor, for US$ 1.26 billion. The acquisition closed on September 30, 2013, and
1764-510: A part of the colony of New York . It became a center of slavery , with 42% of households enslaving Africans by 1730. Most were domestic slaves ; others were hired out as labor. Slavery became integrally tied to New York's economy through the labor of slaves throughout the port, and the banking and shipping industries trading with the American South . During construction in Foley Square in
1890-404: 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
2016-412: A problem, it is common practice to start with a population or process to be studied. Populations can be diverse topics, such as "all people living in a country" or "every atom composing a crystal". Ideally, statisticians compile data about the entire population (an operation called a census ). This may be organized by governmental statistical institutes. Descriptive statistics can be used to summarize
2142-510: A reputation as a despotic leader. He instituted regulations on liquor sales, attempted to assert control over the Dutch Reformed Church , and blocked other religious groups from establishing houses of worship. In 1664, unable to summon any significant resistance, Stuyvesant surrendered New Amsterdam to English troops, led by Colonel Richard Nicolls , without bloodshed. The terms of the surrender permitted Dutch residents to remain in
2268-524: A result of Sandy, and the economic losses in New York City were estimated to be roughly $ 19 billion. The disaster spawned long-term efforts towards infrastructural projects to counter climate change and rising seas, with $ 15 billion in federal funding received through 2022 towards those resiliency efforts. In March 2020, the first case of COVID-19 in the city was confirmed. With its population density and its extensive exposure to global travelers,
2394-497: 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
2520-476: A speech denying the request, which was paraphrased on the front page of the New York Daily News as "FORD TO CITY: DROP DEAD." The Municipal Assistance Corporation was formed and granted oversight authority over the city's finances. While a resurgence in the financial industry greatly improved the city's economic health in the 1980s, New York's crime rate continued to increase through that decade and into
2646-460: 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 . The basic steps of a statistical experiment are: Experiments on human behavior have special concerns. The famous Hawthorne study examined changes to the working environment at the Hawthorne plant of
SECTION 20
#17328769125482772-637: 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. 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
2898-399: 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
3024-419: A value accurately rejecting the null hypothesis (sometimes referred to as the p-value ). 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
3150-476: Is a global center of finance and commerce , culture , technology , entertainment and media , academics and scientific output , the arts and fashion , and, as home to the headquarters of the United Nations , international diplomacy . With an estimated population in 2023 of 8,258,035 distributed over 300.46 square miles (778.2 km ), the city is the most densely populated major city in
3276-467: Is an established safe haven for global investors. As of 2023 , New York City is the most expensive city in the world for expatriates and has by a wide margin the highest U.S. city residential rents; and Fifth Avenue is the most expensive shopping street in the world. New York City is home by a significant margin to the highest number of billionaires , individuals of ultra-high net worth (greater than US$ 30 million), and millionaires of any city in
3402-575: 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
3528-465: 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 which are not invariant under some transformations. Whether or not
3654-834: 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. Most studies only sample part of
3780-428: 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
3906-418: 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
Nielsen Audio - Misplaced Pages Continue
4032-451: 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
4158-408: 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 in regards to
4284-598: Is the most populous city in the United States , located at the southern tip of New York State on one of the world's largest natural harbors . The city comprises five boroughs , each coextensive with a respective county . The city is the geographical and demographic center of both the Northeast megalopolis and the New York metropolitan area , the largest metropolitan area in the U.S. by both population and urban area . New York
4410-402: 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
4536-449: Is widely employed in government, business, and natural and social sciences. 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
4662-837: The Atlantic port to the agricultural markets and commodities of the North American interior via the Hudson River and the Great Lakes . Local politics became dominated by Tammany Hall , a political machine supported by Irish and German immigrants . In 1831, New York University was founded. Several prominent American literary figures lived in New York during the 1830s and 1840s, including William Cullen Bryant , Washington Irving , Herman Melville , Rufus Wilmot Griswold , John Keese , Nathaniel Parker Willis , and Edgar Allan Poe . Members of
4788-760: 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 or not it
4914-876: The Crown , with as many as 10,000 escaped slaves crowded into the city during the British occupation, the largest such community on the continent. When the British forces evacuated New York at the close of the war in 1783, they transported thousands of freedmen for resettlement in Nova Scotia , England, and the Caribbean . The attempt at a peaceful solution to the war took place at the Conference House on Staten Island between American delegates, including Benjamin Franklin , and British general Lord Howe on September 11, 1776. Shortly after
5040-699: The New York City Fire Department and 71 law enforcement officers. The area was rebuilt with a new World Trade Center , the National September 11 Memorial and Museum , and other new buildings and infrastructure, including the World Trade Center Transportation Hub , the city's third-largest hub. The new One World Trade Center is the tallest skyscraper in the Western Hemisphere and the seventh-tallest building in
5166-947: The Northwest Passage to the Orient for the Dutch East India Company . He sailed up what the Dutch called North River (now the Hudson River), named first by Hudson as the Mauritius after Maurice, Prince of Orange . Hudson claimed the region for the Dutch East India Company. In 1614, the area between Cape Cod and Delaware Bay was claimed by the Netherlands and called Nieuw-Nederland (' New Netherland '). The first non–Native American inhabitant of what became New York City
Nielsen Audio - Misplaced Pages Continue
5292-594: The Portable People Meter (PPM) electronic audience measurement service 365 days a year. The term commonly used in the radio industry for these ratings is Arbitron book , a carryover from the era when ratings were published in a softcover report that was mailed to clients. More specifically, in the diary-measured markets these reports were called the "Spring book", "Summer book", "Fall book", and "Winter book". Between these "books", Arbitron releases interim monthly reports called "Arbitrends", which contain data from
5418-561: The Statue of Liberty , a gift from France , was dedicated in New York Harbor. The statue welcomed 14 million immigrants as they came to the U.S. via Ellis Island by ship in the late 19th and early 20th centuries, and is a symbol of the United States and American ideals of liberty and peace. In 1898, the City of New York was formed with the consolidation of Brooklyn (until then a separate city),
5544-683: The Stonewall riots were a series of violent protests by members of the gay community against a police raid that took place in the early morning of June 28, 1969, at the Stonewall Inn in Greenwich Village . They are widely considered to be the single most important event leading to the gay liberation movement and the modern fight for LGBT rights . Wayne R. Dynes , author of the Encyclopedia of Homosexuality , wrote that drag queens were
5670-477: 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
5796-546: The forecasting , prediction , and estimation of unobserved values either in or associated with the population being studied. It can include extrapolation and interpolation of time series or spatial data , as well as data mining . Mathematical statistics is the application of mathematics to statistics. Mathematical techniques used for this include mathematical analysis , linear algebra , stochastic analysis , differential equations , and measure-theoretic probability theory . Formal discussions on inference date back to
5922-432: 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
6048-707: 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
6174-586: The steamship General Slocum caught fire in the East River , killing 1,021 people. In 1911, the Triangle Shirtwaist Factory fire , the city's worst industrial disaster, killed 146 garment workers and spurred the growth of the International Ladies' Garment Workers' Union and major improvements in factory safety standards. New York's non-White population was 36,620 in 1890. New York City
6300-535: The 1990s, the African Burying Ground was discovered; the cemetery included 10,000 to 20,000 graves of colonial-era Africans, some enslaved and some free. The 1735 trial and acquittal in Manhattan of John Peter Zenger , who had been accused of seditious libel after criticizing colonial governor William Cosby , helped to establish freedom of the press in North America . In 1754, Columbia University
6426-525: The 19th century, the city was transformed by both commercial and residential development relating to its status as a national and international trading center , as well as by European immigration, respectively. The city adopted the Commissioners' Plan of 1811 , which expanded the city street grid to encompass almost all of Manhattan. The 1825 completion of the Erie Canal through central New York connected
SECTION 50
#17328769125486552-671: The British occupation began, the Great Fire of New York destroyed nearly 500 buildings, about a quarter of the structures in the city, including Trinity Church . In January 1785, the assembly of the Congress of the Confederation made New York City the national capital. New York was the last capital of the U.S. under the Articles of Confederation and the first capital under the Constitution of
6678-518: The Bronx , and Staten Island . Anchored by Wall Street in the Financial District, Manhattan , New York City has been called both the world's premier financial and fintech center and the most economically powerful city in the world. As of 2022 , the New York metropolitan area is the largest metropolitan economy in the world , with a gross metropolitan product of over US$ 2.16 trillion. If
6804-558: The County of New York (which then included parts of the Bronx), the County of Richmond, and the western portion of the County of Queens. The opening of the New York City Subway in 1904, first built as separate private systems, helped bind the new city together. Throughout the first half of the 20th century, the city became a world center for industry, commerce, and communication. In 1904,
6930-585: The Dutch West India Company relinquished its monopoly over the fur trade, leading to growth in the production and trade of food, timber, tobacco, and slaves (particularly with the Dutch West Indies ). In 1647, Peter Stuyvesant began his tenure as the last Director-General of New Netherland. During his tenure, the population of New Netherland grew from 2,000 to 8,000. Stuyvesant has been credited with improving law and order; however, he earned
7056-529: The Dutch colonial Director-General Peter Minuit , as charged by the Dutch West India Company , purchased the island of Manhattan from the Canarsie , a small Lenape band, for "the value of 60 guilders " (about $ 900 in 2018). A frequently told but disproved legend claims that Manhattan was purchased for $ 24 worth of glass beads. Following the purchase, New Amsterdam grew slowly. To attract settlers,
7182-597: The Dutch instituted the patroon system in 1628, whereby wealthy Dutchmen ( patroons , or patrons) who brought 50 colonists to New Netherland would be awarded land, local political autonomy, and rights to participate in the lucrative fur trade. This program had little success. Since 1621, the Dutch West India Company had operated as a monopoly in New Netherland, on authority granted by the Dutch States General . In 1639–1640, in an effort to bolster economic growth,
7308-580: The Native Americans and epidemics brought on by contact with the Europeans caused sizeable population losses for the Lenape between 1660 and 1670. By 1700, the Lenape population had diminished to 200. New York experienced several yellow fever epidemics in the 18th century, losing ten percent of its population in 1702 alone. In the early 18th century, New York grew in importance as a trading port while as
7434-470: The New York metropolitan area were its own country , it would have the tenth-largest economy in the world . Despite having a 24/7 rapid transit system , New York also leads the world in urban automobile traffic congestion . The city is home to the world's two largest stock exchanges by market capitalization of their listed companies: the New York Stock Exchange and Nasdaq . New York City
7560-546: The PPM. Statistics 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
7686-699: The Revolutionary War and escaped slaves, a significant free-Black population gradually developed in Manhattan. The New York Manumission Society worked for abolition and established the African Free School to educate Black children. It was not until 1827 that slavery was completely abolished in the state . Free Blacks struggled with discrimination and interracial abolitionist activism continued. New York City's population jumped from 123,706 in 1820 (10,886 of whom were Black and of which 518 were enslaved) to 312,710 by 1840 (16,358 of whom were Black). Also in
SECTION 60
#17328769125487812-461: The United States . As the U.S. capital, New York City hosted the inauguration of the first President, George Washington , and the first Congress , at Federal Hall on Wall Street . Congress drafted the Bill of Rights there. The Supreme Court held its first organizational sessions in New York in 1790. In 1790, for the first time, New York City surpassed Philadelphia as the nation's largest city. At
7938-436: The United States . As many as 800 languages are spoken in New York City, making it the most linguistically diverse city in the world. In 2021, the city was home to nearly 3.1 million residents born outside the U.S., the largest foreign-born population of any city in the world. New York City traces its origins to Fort Amsterdam and a trading post founded on Manhattan Island by Dutch colonists around 1624. The settlement
8064-416: The United States. New York City has more than double the population of Los Angeles , the nation's second-most populous city. With more than 20.1 million people in its metropolitan statistical area and 23.5 million in its combined statistical area as of 2020, New York City is one of the world's most populous megacities . The city and its metropolitan area are the premier gateway for legal immigration to
8190-694: The area for France and named it Nouvelle Angoulême (New Angoulême ). A Spanish expedition, led by the Portuguese captain Estêvão Gomes sailing for Emperor Charles V , arrived in New York Harbor in January 1525 and charted the mouth of the Hudson River , which he named Río de San Antonio ('Saint Anthony's River'). In 1609, the English explorer Henry Hudson rediscovered New York Harbor while searching for
8316-543: The beginning of the 1990s. By the mid-1990s, crime rates started to drop dramatically due to revised police strategies, improving economic opportunities, gentrification , and new residents, both American transplants and new immigrants from Asia and Latin America. New York City's population exceeded 8 million for the first time in the 2000 United States census ; further records were set in 2010 , and 2020 U.S. censuses. Important new sectors, such as Silicon Alley , emerged in
8442-583: The business elite lobbied for the establishment of Central Park , which in 1857 became the first landscaped park in an American city. The Great Irish Famine brought a large influx of Irish immigrants, of whom more than 200,000 were living in New York by 1860, representing over a quarter of the city's population. Extensive immigration from the German provinces meant that Germans comprised another 25% of New York's population by 1860. Democratic Party candidates were consistently elected to local office, increasing
8568-557: The city from New Jersey. The East River—a tidal strait —flows from Long Island Sound and separates the Bronx and Manhattan from Long Island. The Harlem River , another tidal strait between the East and Hudson rivers, separates most of Manhattan from the Bronx. The Bronx River , which flows through the Bronx and Westchester County , is the only entirely freshwater river in the city. The city's land has been altered substantially by human intervention, with considerable land reclamation along
8694-439: The city rapidly replaced Wuhan , China as the global epicenter of the pandemic during the early phase, straining the city's healthcare infrastructure. Through March 2023, New York City recorded more than 80,000 deaths from COVID-19-related complications. New York City is situated in the northeastern United States , in southeastern New York State, approximately halfway between Washington, D.C. and Boston . Its location at
8820-613: The city's economy. The advent of Y2K was celebrated with fanfare in Times Square . New York City suffered the bulk of the economic damage and largest loss of human life in the aftermath of the September 11, 2001, attacks . Two of the four airliners hijacked that day were flown into the twin towers of the World Trade Center, resulting in the collapse of both buildings and the deaths of 2,753 people, including 343 first responders from
8946-776: The city's ties to the South and its dominant party. In 1861, Mayor Fernando Wood called on the aldermen to declare independence from Albany and the United States after the South seceded, but his proposal was not acted on. Anger at new military conscription laws during the American Civil War (1861–1865), which spared wealthier men who could afford to hire a substitute, led to the Draft Riots of 1863 , whose most visible participants were ethnic Irish working class. The draft riots deteriorated into attacks on New York's elite, followed by attacks on Black New Yorkers after fierce competition for
9072-439: The collection, analysis, interpretation or explanation, and presentation of data , or as a branch of mathematics . 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. In applying statistics to
9198-615: The colony and allowed for religious freedom. In 1667, during negotiations leading to the Treaty of Breda after the Second Anglo-Dutch War , the victorious Dutch decided to keep the nascent plantation colony of what is now Suriname , which they had gained from the English, and in return the English kept New Amsterdam. The settlement was promptly renamed "New York" after the Duke of York (the future King James II and VII). The duke gave part of
9324-604: The colony to proprietors George Carteret and John Berkeley . On August 24, 1673, during the Third Anglo-Dutch War , Anthony Colve of the Dutch navy seized New York at the behest of Cornelis Evertsen the Youngest and rechristened it "New Orange" after William III , the Prince of Orange . The Dutch soon returned the island to England under the Treaty of Westminster of November 1674. Several intertribal wars among
9450-406: The company was re-branded as Nielsen Audio. As a condition of the deal to allow a monopoly , Nielsen must license its ratings data and technology to a third party for eight years. Arbitron's syndicated radio ratings service collects data by selecting a random sample of a population throughout the United States, primarily in 294 metropolitan areas, using a paper diary service 2‑4 times a year and
9576-535: 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
9702-538: The concepts of sufficiency , ancillary statistics , Fisher's linear discriminator and Fisher information . He also coined the term null hypothesis during the Lady tasting tea experiment, which "is never proved or established, but is possibly disproved, in the course of experimentation". In his 1930 book The Genetical Theory of Natural Selection , he applied statistics to various biological concepts such as Fisher's principle (which A. W. F. Edwards called "probably
9828-425: The data that 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 a mathematical body of science that pertains to
9954-417: The development of large housing tracts in eastern Queens and Nassau County , with Wall Street leading America's place as the world's dominant economic power. The United Nations headquarters was completed in 1952, solidifying New York's global geopolitical influence, and the rise of abstract expressionism in the city precipitated New York's displacement of Paris as the center of the art world. In 1969,
10080-406: 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
10206-406: The end of 1790, the national capital was moved to Philadelphia . During the 19th century, New York City's population grew from 60,000 to 3.43 million. Under New York State's gradual emancipation act of 1799, children of slave mothers were to be eventually liberated but to be held in indentured servitude until their mid-to-late twenties. Together with slaves freed by their masters after
10332-462: The end of the survey period is approximately three weeks. After collection, the data is marketed to radio broadcasters, radio networks , cable TV companies, advertisers, advertising agencies , out-of-home advertising companies, and the online radio industry. Major ratings products include cume (the cumulative number of unique listeners over a period), average quarter hour ( AQH share – the average number of people listening in
10458-495: The evidence was insufficient to convict. So the jury does not necessarily accept H 0 but fails to reject H 0 . 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 . What statisticians call an alternative hypothesis is simply a hypothesis that contradicts the null hypothesis. Working from a null hypothesis , two broad categories of error are recognized: Standard deviation refers to
10584-478: The expected value assumes on a given sample (also called prediction). Mean squared error is used for obtaining efficient estimators , a widely used class of estimators. Root mean square error is simply the square root of mean squared error. 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
10710-474: 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. An example of an observational study
10836-402: 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
10962-450: 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
11088-432: 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 second wave of the 1910s and 20s was initiated by William Sealy Gosset , and reached its culmination in the insights of Ronald Fisher , who wrote the textbooks that were to define the academic discipline in universities around
11214-402: 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
11340-457: The founding of a Dutch fur trading settlement on Governors Island . In 1625, construction was started on a citadel and Fort Amsterdam , later called Nieuw Amsterdam (New Amsterdam), on present-day Manhattan Island. The colony of New Amsterdam extended from the southern tip of Manhattan to modern-day Wall Street , where a 12-foot (3.7 m) wooden stockade was built in 1653 to protect against Native American and English raids. In 1626,
11466-605: 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. 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,
11592-466: The ice (and its subsequent retreat) contributed to the separation of what is now Long Island and Staten Island. That action left bedrock at a relatively shallow depth, providing a solid foundation for most of Manhattan's skyscrapers. The Hudson River flows through the Hudson Valley into New York Bay . Between New York City and Troy, New York , the river is an estuary . The Hudson River separates
11718-542: The last American stronghold in Manhattan, causing George Washington and his forces to retreat across the Hudson River to New Jersey , pursued by British forces. After the battle, in which the Americans were defeated, the British made the city their military and political base of operations in North America. The city was a haven for Loyalist refugees and escaped slaves who joined the British lines for freedom promised by
11844-424: The most celebrated argument in evolutionary biology ") and Fisherian runaway , a concept in sexual selection about a positive feedback runaway effect found in evolution . 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
11970-419: The most populous urbanized area in the world in the early 1920s, overtaking London . The metropolitan area surpassed 10 million in the early 1930s, becoming the first megacity . The Great Depression saw the election of reformer Fiorello La Guardia as mayor and the fall of Tammany Hall after eighty years of political dominance. Returning World War II veterans created a post-war economic boom and
12096-544: The mouth of the Hudson River , which feeds into a naturally sheltered harbor and then into the Atlantic Ocean , has helped the city grow in significance as a trading port. Most of the city is built on the three islands of Long Island, Manhattan, and Staten Island. During the Wisconsin glaciation , 75,000 to 11,000 years ago, the New York City area was situated at the edge of a large ice sheet . The erosive forward movement of
12222-492: The only " transgender folks around" during the June 1969 Stonewall riots. The transgender community in New York City played a significant role in fighting for LGBT equality. In the 1970s, job losses due to industrial restructuring caused New York City to suffer from economic problems and rising crime rates. Growing fiscal deficits in 1975 led the city to appeal to the federal government for financial aid; President Gerald Ford gave
12348-412: 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 the drug 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
12474-415: The population data. Numerical descriptors include mean and standard deviation for continuous data (like income), while frequency and percentage are more useful in terms of describing categorical data (like education). When a census is not feasible, a chosen subset of the population called a sample is studied. Once a sample that is representative of the population is determined, data is collected for
12600-544: 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 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 from
12726-416: The previous three months known as "rolling average" reports. The two interim reports would be known, for example, as "Spring, Phase I" and "Spring, Phase II". Arbitron recruits diary survey respondents to note their listening habits in a seven-day paper diary and mail it back to Arbitron. The respondents are paid a small cash incentive for their participation. Turnaround time for release of data from
12852-494: The problem of how to analyze big data . When full 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 assures that inferences and conclusions can safely extend from
12978-466: 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
13104-421: The room in a given 15‑minute period). Responding to requests from its customers—radio broadcasters, ad agencies and advertisers—that expressed their interest in the collection of more accurate ratings data, Arbitron introduced the Portable People Meter (PPM) service in 2007. The PPM is a wearable portable device, much like a pager or mobile phone , that electronically gathers subaudible codes that identify
13230-461: 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
13356-439: The sample data to draw inferences about the population represented while accounting for randomness. These inferences may take the form of answering yes/no questions about the data ( hypothesis testing ), estimating numerical characteristics of the data ( estimation ), describing associations within the data ( correlation ), and modeling relationships within the data (for example, using regression analysis ). Inference can extend to
13482-399: The sample members in an observational or experimental setting. Again, descriptive statistics can be used to summarize the sample data. However, drawing the sample contains an element of randomness; hence, the numerical descriptors from the sample are also prone to uncertainty. To draw meaningful conclusions about the entire population, inferential statistics are needed. It uses patterns in
13608-405: The sample to the population as a whole. A major problem lies in determining the extent that the sample chosen is actually representative. Statistics offers methods to estimate and correct for any bias within 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 capability to discern truths about
13734-482: 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
13860-412: 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
13986-686: The source of a broadcast, such as a radio station . Arbitron recruits and compensates a cross-section of consumers to wear the meter for an average of one year and up to two years. The audience estimates generated from each monthly survey are used as the buy/sell currency for radio stations and advertisers/agencies. As of December 2009, the PPM was measured in 33 media markets , including Houston , Philadelphia , Pittsburgh , New York City , Atlanta , Detroit , Long Island , Middlesex - Somerset - Union , Chicago , Los Angeles , Riverside - San Bernardino , San Francisco , Jacksonville , Baltimore , and San Jose . By 2010, 48 markets are being measured using
14112-408: 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
14238-406: 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. New York City New York , often called New York City or NYC ,
14364-420: 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
14490-416: The two sided interval is built violating symmetry around the estimate. Sometimes the bounds for 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
14616-485: 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
14742-620: 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
14868-518: The world by pinnacle height, with its spire reaching a symbolic 1,776 feet (541.3 m), a reference to the year of U.S. independence . The Occupy Wall Street protests in Zuccotti Park in the Financial District of Lower Manhattan began on September 17, 2011, receiving global attention and popularizing the Occupy movement against social and economic inequality worldwide. New York City
14994-504: The world. In 1664, New York was named in honor of the Duke of York (later King James II of England ). James's elder brother, King Charles II , appointed the Duke as proprietor of the former territory of New Netherland , including the city of New Amsterdam , when the Kingdom of England seized it from Dutch control. In the pre-Columbian era , the area of present-day New York City
15120-462: The world. Fisher's most important publications were his 1918 seminal paper The Correlation between Relatives on the Supposition of Mendelian Inheritance (which was the first to use the statistical term, variance ), his classic 1925 work Statistical Methods for Research Workers and his 1935 The Design of Experiments , where he developed rigorous design of experiments models. He originated
15246-422: Was Juan Rodriguez , a merchant from Santo Domingo who arrived in Manhattan during the winter of 1613–14, trapping for pelts and trading with the local population as a representative of the Dutch colonists. A permanent European presence near New York Harbor was established in 1624, making New York the 12th-oldest continuously occupied European-established settlement in the continental United States , with
15372-552: Was heavily affected by Hurricane Sandy in late October 2012. Sandy's impacts included flooding that led to the days-long shutdown of the subway system and flooding of all East River subway tunnels and of all road tunnels entering Manhattan except the Lincoln Tunnel . The New York Stock Exchange closed for two days due to weather for the first time since the Great Blizzard of 1888 . At least 43 people died in New York City as
15498-525: Was a prime destination in the early 20th century for Blacks during the Great Migration from the American South, and by 1916, New York City had the largest urban African diaspora in North America. The Harlem Renaissance of literary and cultural life flourished during the era of Prohibition . The larger economic boom generated construction of skyscrapers competing in height. New York City became
15624-821: Was founded. The Stamp Act Congress met in New York in October 1765, as the Sons of Liberty organization emerged in the city and skirmished over the next ten years with British troops stationed there. The Battle of Long Island , the largest battle of the American Revolutionary War , was fought in August 1776 within modern-day Brooklyn. A British rout of the Continental Army at the Battle of Fort Washington in November 1776 eliminated
15750-521: Was inhabited by Algonquians , including the Lenape . Their homeland, known as Lenapehoking , included the present-day areas of Staten Island , Manhattan , the Bronx , the western portion of Long Island (including Brooklyn and Queens ), and the Lower Hudson Valley . The first documented visit into New York Harbor by a European was in 1524 by explorer Giovanni da Verrazzano . He claimed
15876-468: Was named New Amsterdam in 1626 and was chartered as a city in 1653. The city came under English control in 1664 and was temporarily renamed New York after King Charles II granted the lands to his brother, the Duke of York , before being permanently renamed New York in November 1674. New York City was the U.S. capital from 1785 until 1790. The modern city was formed by the 1898 consolidation of its five boroughs : Manhattan , Brooklyn , Queens ,
#547452