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129-589: 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

258-469: 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

387-535: A C grade, and improving from the 46th to 54th most polluted by ozone smog. According to daily ozone air quality data provided by the EPA, from 2021 to 2024, Pittsburgh had good or moderate air quality most of the time. Then-Allegheny County executive Rich Fitzgerald said in December 2023 that they’d seen an "80 % drop in hazardous air pollutants" and that they made EPA attainment at all eight county air monitors for

516-415: 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

645-418: 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

774-547: A decrease in city population, even as the metropolitan area population increased again. During the late 2000s recession , Pittsburgh was economically strong, adding jobs when most cities were losing them. It was one of the few cities in the United States to see housing property values rise. Between 2006 and 2011, the Pittsburgh metropolitan statistical area (MSA) experienced over 10% appreciation in housing prices,

903-613: A free state after the Revolution, enslaved African Americans sought freedom here through escape as refugees from the South, or occasionally fleeing from travelers they were serving who stayed in the city. There were active stations of the Underground Railroad in the city, and numerous refugees were documented as getting help from station agents and African-American workers in city hotels. The Drennen Slave Girl walked out of

1032-458: 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

1161-470: 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

1290-484: 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

1419-471: 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

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1548-685: A growing residential segment. Most significantly, the Pittsburgh Cultural Trust is embarking on RiverParc, a four-block mixed-use "green" community, featuring 700 residential units and multiple towers of between 20 and 30 stories. The Firstside portion of Downtown borders the Monongahela River, the historic Mon Wharf and hosts the distinctive PPG Place Gothic-style glass skyscraper complex. New condo towers have been constructed and historic office towers are converted to residential use, increasing 24-hour residents. Downtown

1677-555: 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

1806-1033: 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

1935-499: 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

2064-503: 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

2193-404: 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

2322-412: 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

2451-539: A quarter of neighborhood names make reference to "hills," "heights," or similar features. The steps of Pittsburgh consist of 800 sets of outdoor public stairways with 44,645 treads and 24,090 vertical feet. They include hundreds of streets composed entirely of stairs, and many other steep streets with stairs for sidewalks. Many provide vistas of the Pittsburgh area while attracting hikers and fitness walkers. Bike and walking trails have been built to border many of

2580-497: 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

2709-465: 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

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2838-637: 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

2967-399: 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

3096-419: 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

3225-578: Is 39.61 inches (1,006 mm) and precipitation is greatest in May while least in October; annual precipitation has historically ranged from 22.65 in (575 mm) in 1930 to 57.83 in (1,469 mm) in 2018. On average, December and January have the greatest number of precipitation days. Snowfall averages 44.1 inches (112 cm) per season, but has historically ranged from 8.8 in (22 cm) in 1918–19 to 80 in (200 cm) in 1950–51. There

3354-604: Is a city in and the county seat of Allegheny County, Pennsylvania , United States. It is the second-most populous city in Pennsylvania , after Philadelphia , and the 68th-most populous city in the U.S., with a population of 302,971 as of the 2020 census . The city is located in southwestern Pennsylvania at the confluence of the Allegheny River and the Monongahela River , which combine to form

3483-404: Is additionally where Jehovah's Witnesses traces its earliest origins, and was the host of the 2009 G20 Pittsburgh summit . Pittsburgh was named in 1758, by General John Forbes , in honor of British statesman William Pitt, 1st Earl of Chatham . As Forbes was a Scotsman , he probably pronounced the name / ˈ p ɪ t s b ər ə / PITS -bər-ə (similar to Edinburgh ). Pittsburgh

3612-486: Is an average of 59 clear days and 103 partly cloudy days per year, while 203 days are cloudy. In terms of annual percent-average possible sunshine received, Pittsburgh (45%) is similar to Seattle (49%). The American Lung Association's (ALA) 2023 "State of the Air" report (which included data from 2019 to 2021) showed air quality in Pittsburgh improving. The city received a passing grade for ozone pollution, going from an F to

3741-575: 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

3870-465: 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

3999-834: 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

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4128-428: 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

4257-460: Is home to large medical providers, including the University of Pittsburgh Medical Center , Allegheny Health Network , and 68 colleges and universities , including research and development leaders Carnegie Mellon University and the University of Pittsburgh . The area has served as the federal agency headquarters for cyber defense , software engineering , robotics , energy research , and

4386-413: Is home to the University of Pittsburgh , Carnegie Mellon University , Carlow University , Chatham University , The Carnegie Institute's Museums of Art and Natural History , Phipps Conservatory , and Soldiers and Sailors Memorial Hall . It is also home to many parks and public spaces including Mellon Park , Westinghouse Park , Schenley Park , Frick Park , The Frick Pittsburgh , Bakery Square , and

4515-635: Is known as "the Steel City" for its dominant role in the history of the U.S. steel industry . It developed as a vital link of the Atlantic coast and Midwest , as the mineral-rich Allegheny Mountains led to the region being contested by the French and British Empires, Virginians , Whiskey Rebels , and Civil War raiders . For part of the 20th century, Pittsburgh was behind only New York City and Chicago in corporate headquarters employment; it had

4644-574: Is now known as Washington's Landing, formerly Herr's Island , in what is now the Lawrenceville neighborhood. The first known European to enter the region was the French explorer Robert de La Salle from Quebec during his 1669 expedition down the Ohio River . European pioneers, primarily Dutch, followed in the early 18th century. Michael Bezallion was the first to describe the forks of

4773-418: 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

4902-679: Is primarily composed of residential neighborhoods and is noteworthy for its well-constructed and architecturally interesting homes. Many buildings date from the 19th century and are constructed of brick or stone and adorned with decorative woodwork, ceramic tile, slate roofs and stained glass. The North Side is also home to attractions such as Acrisure Stadium , PNC Park , Kamin Science Center , National Aviary , Andy Warhol Museum , Mattress Factory art museum, Children's Museum of Pittsburgh , Randyland , Penn Brewery , Allegheny Observatory , and Allegheny General Hospital . The South Side

5031-451: 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

5160-573: Is referred to as "the Point." The city extends east to include the Oakland and Shadyside sections, which are home to the University of Pittsburgh , Carnegie Mellon University , Chatham University , Carnegie Museum and Library , and many other educational, medical, and cultural institutions. The southern, western, and northern areas of the city are primarily residential. Many Pittsburgh neighborhoods are steeply sloped with two-lane roads. More than

5289-408: 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

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5418-513: Is served by the Port Authority 's light rail system and multiple bridges leading north and south. It is also home to Point Park University and Duquesne University which borders Uptown . The North Side is home to various neighborhoods in transition. The area was once known as Allegheny City and operated as its own independent city until 1907, when it was merged with Pittsburgh despite great protest from its citizens. The North Side

5547-402: 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

5676-623: Is water. The 80th meridian west passes directly through the city's downtown. The city is on the Allegheny Plateau , within the ecoregion of the Western Allegheny Plateau . The Downtown area (also known as the Golden Triangle) sits where the Allegheny River flows from the northeast and the Monongahela River from the southeast to form the Ohio River . The convergence is at Point State Park and

5805-449: 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

5934-582: The Allegheny Mountains . The Great Fire of Pittsburgh destroyed over a thousand buildings in 1845. The city rebuilt with the aid of Irish immigrants who came to escape the Great Famine . By 1857, Pittsburgh's 1,000 factories were consuming 22 million coal bushels yearly. Coal mining and iron manufacturing attracted waves of European immigrants to the area, with the most coming from Germany . Because Pennsylvania had been established as

6063-765: 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

6192-786: The Edgar Thomson Steel Works in North Braddock, Pennsylvania , which evolved into the Carnegie Steel Company . He adopted the Bessemer process to increase production. Manufacturing was key to growth of Pittsburgh and the surrounding region. Railroad lines were built into the city along both rivers, increasing transportation access to important markets. In 1901, J. P. Morgan and attorney Elbert H. Gary merged Carnegie Steel Company and several other companies into U.S. Steel . By 1910, Pittsburgh

6321-744: The Iroquois Confederacy , based in New York, had maintained control of much of the Ohio Valley as hunting grounds by right of conquest after defeating other tribes. By the terms of the 1768 Treaty of Fort Stanwix , the Penns were allowed to purchase the modern region from the Iroquois . A 1769 survey referenced the future city as the "Manor of Pittsburgh". Both the Colony of Virginia and

6450-487: The Köppen climate classification , Pittsburgh falls within either a hot-summer humid continental climate ( Dfa ) if the 0 °C (32 °F) isotherm is used or a humid subtropical climate ( Cfa ) if the −3 °C (27 °F) isotherm is used. Summers are hot and winters are moderately cold with wide variations in temperature. Despite this, it has one of the most pleasant summer climates between medium and large cities in

6579-556: The Ohio River . It anchors the Pittsburgh metropolitan area , which had a population of 2.457 million residents and is the largest metro area in both the Ohio Valley and Appalachia , the second-largest in Pennsylvania , and the 26th-largest in the U.S. Pittsburgh is the principal city of the greater Pittsburgh–Weirton–Steubenville combined statistical area which includes parts of Ohio and West Virginia . Pittsburgh

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6708-746: The Pittsburgh Post-Gazette was started, and in 1787, the Pittsburgh Academy was chartered. Unrest during the Whiskey Rebellion of 1794 resulted in federal troops being sent to the area. By 1797, glass manufacture began, while the population grew to around 1,400. Settlers arrived after crossing the Appalachian Mountains or through the Great Lakes . Fort Pitt (now Pittsburgh) at the source of

6837-468: The Pittsburgh Zoo and PPG Aquarium. The neighborhoods of Shadyside and Squirrel Hill are large, wealthy neighborhoods with some apartments and condos, and pedestrian-oriented shopping/business districts. Squirrel Hill is also known as the hub of Jewish life in Pittsburgh, home to approximately 20 synagogues. Oakland , heavily populated by undergraduate and graduate students, is home to most of

6966-603: 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

7095-523: The Province of Pennsylvania claimed the region under their colonial charters until 1780, when they agreed under a federal initiative to extend the Mason–Dixon line westward, placing Pittsburgh in Pennsylvania. On March 8, 1771, Bedford County, Pennsylvania was created to govern the frontier. On April 16, 1771, the city's first civilian local government was created as Pitt Township . William Teagarden

7224-487: 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

7353-546: 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

7482-432: 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

7611-719: 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

7740-445: The nuclear navy . In the private sector, Pittsburgh-based PNC is the nation's fifth-largest bank, and the city is home to ten Fortune 500 companies and seven of the largest 300 U.S. law firms. Other corporations that have regional headquarters and offices have helped Pittsburgh become the sixth-best area for U.S. job growth. Pittsburgh is sometimes called the "City of Bridges" for its 446 bridges . Its rich industrial history left

7869-587: The 1850 Fugitive Slave Act , as it required cooperation from law enforcement even in free states and increased penalties. From 1850 to 1860, the black population in Allegheny County dropped from 3,431 to 2,725 as people headed to more safety in Canada. The American Civil War boosted the city's economy with increased iron and armament demand by the Union. Andrew Carnegie began steel production in 1875 at

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7998-454: The Central, North Side/North Hills, South Side/South Hills, East End, and West End. Downtown Pittsburgh has 30 skyscrapers, nine of which top 500 feet (150 m). The U.S. Steel Tower is the tallest, at 841 ft (256 m). The Cultural District consists of a 14-block area of downtown along the Allegheny River . This district contains many theaters and arts venues and is home to

8127-518: The Elder , while the settlement was named "Pittsborough". During Pontiac's War , a loose confederation of Native American tribes laid siege to Fort Pitt in 1763; the siege was eventually lifted after Colonel Henry Bouquet defeated a portion of the besieging force at the Battle of Bushy Run . Bouquet strengthened the defenses of Fort Pitt the next year. During this period, the powerful nations of

8256-568: The Monongahela House in 1850, apparently to freedom. The Merchant's Hotel was also a place where African-American workers would advise slaves the state was free and aid them in getting to nearby stations of the Underground Railroad. Sometimes refugee slaves from the South stayed in Pittsburgh, but other times they continued North, including into Canada. Many slaves left the city and county for Canada after Congress passed

8385-522: The North American front of the Seven Years' War , began with the future Pittsburgh as its center. British General Edward Braddock was dispatched with Major George Washington as his aide to take Fort Duquesne. The British and colonial force were defeated at Braddock's Field . General John Forbes finally took the forks in 1758. He began construction on Fort Pitt , named after William Pitt

8514-728: The North Side, and the Golden Triangle are characterized by more density of housing, walking neighborhoods, and a more diverse, urban feel. Pittsburgh falls within the borders of the Northeastern United States as defined by multiple US Government agencies. Pittsburgh is the principal city of the Pittsburgh Combined Statistical Area , a combined statistical area defined by the U.S. Census Bureau . Pittsburgh falls within

8643-692: The Ohio River became the main base for settlers moving into the Northwest Territory . The federal government recognizes Pittsburgh as the starting point for the Lewis and Clark Expedition . Preparations began in Pittsburgh in 1803 when Meriwether Lewis purchased a keelboat that would later be used to ascend the Missouri River . The War of 1812 cut off the supply of British goods, stimulating American industry. By 1815, Pittsburgh

8772-565: The Ohio headwaters was long inhabited by the Shawnee and several other settled groups of Native Americans . Shannopin's Town was an 18th-century Lenape (Delaware) town located roughly from where Penn Avenue is today, below the mouth of Two Mile Run, from 30th Street to 39th Street. According to George Croghan , the town was situated on the south bank of the Allegheny, nearly opposite what

8901-507: The Ohio in a 1717 manuscript, and later that year European fur traders established area posts and settlements. In 1749, French soldiers from Quebec launched an expedition to the forks to unite Canada with French Louisiana via the rivers. During 1753–1754, the British hastily built Fort Prince George before a larger French force drove them off. The French built Fort Duquesne based on LaSalle's 1669 claims. The French and Indian War ,

9030-549: 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

9159-481: The U.S. The city lies in the USDA plant hardiness zone 6b except along the rivers where the zone is 7a. The area has four distinct seasons: winters are cold and snowy, springs and falls are mild with moderate levels of sunshine, and summers are warm. As measured by percent possible sunshine, summer is by far the sunniest season, though annual sunshine is low among major US cities at well under 50%. The warmest month of

9288-399: The air and the rivers. The "Renaissance II" project followed in 1977, focused on cultural and neighborhood development. The industrial base continued to expand through the 1970s, but beginning in the early 1980s both the area's steel and electronics industries imploded during national industrial restructuring. There were massive layoffs from mill and plant closures. In the later 20th century,

9417-425: The area shifted its economic base to education, tourism, and services, largely based on healthcare/medicine, finance, and high technology such as robotics. Although Pittsburgh successfully shifted its economy and remained viable, the city's population has never rebounded to its industrial-era highs. While 680,000 people lived in the city proper in 1950, a combination of suburbanization and economic turbulence resulted in

9546-609: The area with renowned cultural institutions, including the Carnegie Museums of Pittsburgh , Pittsburgh Parks Conservancy , Pittsburgh Zoo & Aquarium , Phipps Conservatory and Botanical Gardens , the National Aviary , and a diverse cultural district . The city's major league professional sports teams include the Pittsburgh Steelers , Pittsburgh Penguins , and Pittsburgh Pirates . Pittsburgh

9675-547: The borders of Appalachia as defined by the Appalachian Regional Commission , and has long been characterized as the "northern urban industrial anchor of Appalachia." In its post-industrial state, Pittsburgh has been characterized as the "Paris of Appalachia", recognizing the city's cultural, educational, healthcare, and technological resources, and is the largest city in Appalachia. Under

9804-494: The city's population. Pittsburgh also became a main destination of the African-American Great Migration from the rural South during the first half of the 20th century. Limited initially by discrimination, some 95% percent of the men became unskilled steel workers. During World War II , demand for steel increased and area mills operated 24 hours a day to produce 95 million tons of steel for

9933-542: The city's rivers and hollows. The Great Allegheny Passage and Chesapeake and Ohio Canal Towpath connect the city directly to downtown Washington, D.C. (some 335 miles [539 km] away) with a continuous bike/running trail. The city consists of the Downtown area, called the Golden Triangle, and four main areas surrounding it. These surrounding areas are subdivided into distinct neighborhoods (Pittsburgh has 90 neighborhoods). Relative to downtown, these areas are known as

10062-439: 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

10191-476: The community and various developers to create a master plan for a mixed-use development that included a riverfront park, office space, housing, health-care facilities, and indoor practice fields for the Pittsburgh Steelers and Pitt Panthers . Construction of the development began in 1998. The SouthSide Works has been open since 2005, featuring many stores, restaurants, offices, and the world headquarters for American Eagle Outfitters . The East End of Pittsburgh

10320-406: 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

10449-540: 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

10578-542: 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

10707-425: 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

10836-470: The downtown skyline, and numerous other residential neighborhoods such as Sheraden and Elliott . Many of Pittsburgh's patchwork of neighborhoods still retain ethnic characters reflecting the city's settlement history. These include: Several neighborhoods on the edges of the city are less urban, featuring tree-lined streets, yards and garages, with a more suburban character. Oakland, the South Side,

10965-406: 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

11094-462: 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

11223-495: 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

11352-478: 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

11481-474: 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

11610-402: 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

11739-450: 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

11868-432: 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

11997-402: 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

12126-605: 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,

12255-437: The highest appreciation of the largest 25 metropolitan statistical areas in the United States, with 22 of the largest 25 metropolitan statistical areas experiencing depreciations in housing values. In September 2009, the 2009 G20 Pittsburgh summit was held in Pittsburgh. Pittsburgh has an area of 58.3 square miles (151 km ), of which 55.6 square miles (144 km ) is land and 2.8 square miles (7.3 km ), or 4.75%,

12384-435: The most U.S. stockholders per capita. Deindustrialization in the late 20th century resulted in massive layoffs among blue-collar workers as steel and other heavy industries declined, coinciding with several Pittsburgh-based corporations moving out of the city. However, the city divested from steel and, since the 1990s, Pittsburgh has focused its energies on the healthcare, education, and technology industries. Pittsburgh

12513-424: 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

12642-412: 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

12771-415: 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

12900-544: 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

13029-416: 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

13158-494: 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

13287-470: 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

13416-504: The record cold daily maximum is −3 °F (−19 °C), which occurred three times, most recently the day of the all-time record low, while, conversely, the record warm daily minimum is 82 °F (28 °C) on July 1, 1901. Due to elevation and location on the windward side of the Appalachian Mountains, 100 °F (38 °C)+ readings are very rare, and were last seen on July 15, 1995. Average annual precipitation

13545-421: 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

13674-461: 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

13803-439: 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

13932-399: 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

14061-405: 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

14190-482: 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

14319-412: 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

14448-686: 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

14577-408: 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

14706-432: 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. Pittsburgh, Pennsylvania Pittsburgh ( / ˈ p ɪ t s b ɜːr ɡ / PITS -burg )

14835-420: 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

14964-416: 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

15093-862: The universities, and the Petersen Events Center . The Strip District to the west along the Allegheny River is an open-air marketplace by day and a clubbing destination by night. Bloomfield is Pittsburgh's Little Italy and is known for its Italian restaurants and grocers. Lawrenceville is a revitalizing rowhouse neighborhood popular with artists and designers. The Hill District was home to photographer Charles Harris as well as various African-American jazz clubs. Other East End neighborhoods include Point Breeze , Regent Square , Highland Park , Homewood , Lincoln-Lemington-Belmar , Larimer , East Hills , East Liberty , Polish Hill , Hazelwood , Garfield, Morningside, and Stanton Heights. The West End includes Mt. Washington , with its famous view of

15222-485: 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

15351-640: 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

15480-572: The value of homes in the South Side had increased in value by about 10% annually for the 10 years leading up to 2014. East Carson Street has developed as one of the most vibrant areas of the city, packed with diverse shopping, ethnic eateries, vibrant nightlife, and live music venues. In 1993, the Urban Redevelopment Authority of Pittsburgh purchased the South Side Works steel mill property. It collaborated with

15609-400: The war effort. This resulted in the highest levels of air pollution in the city's almost century of industry. The city's reputation as the "arsenal of democracy" was being overshadowed by James Parton 's 1868 observation of Pittsburgh being "hell with the lid off." Following World War II, the city launched a clean air and civic revitalization project known as the "Renaissance," cleaning up

15738-468: 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

15867-604: The year in Pittsburgh is July, with a 24-hour average of 73.2 °F (22.9 °C). Conditions are often humid, and combined with highs reaching 90 °F (32 °C) on an average 9.5 days a year, a considerable heat index arises. The coolest month is January, when the 24-hour average is 28.8 °F (−1.8 °C), and lows of 0 °F (−18 °C) or below can be expected on an average 2.6 nights per year. Officially, record temperatures range from −22 °F (−30 °C), on January 19, 1994 to 103 °F (39 °C), which occurred three times, most recently on July 16, 1988;

15996-486: Was federally recognized as "Pittsburg", though use of the final h was retained during this period by the city government and other local organizations. After a public campaign, the federal decision to drop the h was reversed. The Pittsburg Press continued spelling the city without an h until 1921. [REDACTED]   Kingdom of France 1690s–1763 [REDACTED]   Great Britain 1681–1781 [REDACTED]   United States 1776–present The area of

16125-545: Was incorporated as a borough on April 22, 1794, with the following Act: "Be it enacted by the Pennsylvania State Senate and Pennsylvania House of Representatives of the Commonwealth of Pennsylvania ... by the authority of the same, that the said town of Pittsburgh shall be ... erected into a borough, which shall be called the borough of Pittsburgh for ever." From 1891 to 1911, the city's name

16254-517: Was once the site of railyards and associated dense, inexpensive housing for mill and railroad workers. Starting in the late 20th century, the city undertook a Main Street program in cooperation with the National Trust for Historic Preservation , encouraging design and landscape improvements on East Carson Street, and supporting new retail. The area has become a local Pittsburgher destination, and

16383-542: Was producing significant quantities of iron, brass, tin, and glass. On March 18, 1816, the 46-year-old local government became a city. It was served by numerous river steamboats that increased trading traffic on the rivers. In the 1830s, many Welsh people from the Merthyr steelworks immigrated to the city following the aftermath of the Merthyr Rising . By the 1840s, Pittsburgh was one of the largest cities west of

16512-625: Was the nation's eighth-largest city , accounting for between one-third and one-half of national steel output. The Pittsburgh Agreement was subscribed in May 1918 between the Czech and Slovak nationalities, as envisioned by T. G. Masaryk , concerning the future foundation of Czechoslovakia . The city suffered severe flooding in March 1936. The city's population swelled to more than a half million, attracting numerous European immigrants to its industrial jobs. By 1940, non-Hispanic whites were 90.6% of

16641-584: Was the first constable, and William Troop was the first clerk. Following the American Revolution , the village of Pittsburgh continued to grow. One of its earliest industries was boat building for settlers of the Ohio Country . In 1784, Thomas Vickroy completed a town plan which was approved by the Penn family attorney. Pittsburgh became a possession of Pennsylvania in 1785. The following year,

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