Fullerton Union High School is a public high school located in the Orange County, California city of Fullerton , operated by the Fullerton Joint Union High School District .
117-556: In 1893 a special election was held to create Fullerton Union High School. The school's first classroom, a rented room on the second floor of the Fullerton Elementary School building, was adequate to house the eight pupils, which constituted the first year's enrollment and the 32 books which made up the library. The high school was the second in Orange County . In 1908, FUHS's enrollment was increasing at
234-437: A Condorcet method ; these methods are also gaining popularity for lesser elections in some countries where more important elections still use more traditional counting methods. While openness and accountability are usually considered cornerstones of a democratic system, the act of casting a vote and the content of a voter's ballot are usually an important exception. The secret ballot is a relatively modern development, but it
351-572: A direct democracy , one type of non-partisan democracy , any eligible person can be nominated. Although elections were used in ancient Athens, in Rome, and in the selection of popes and Holy Roman emperors, the origins of elections in the contemporary world lie in the gradual emergence of representative government in Europe and North America beginning in the 17th century. In some systems no nominations take place at all, with voters free to choose any person at
468-461: A motion of no-confidence ). This calculation depends on a number of variables, such as its performance in opinion polls and the size of its majority. Rolling elections are elections in which all representatives in a body are elected, but these elections are spread over a period of time rather than all at once. Examples are the presidential primaries in the United States , Elections to
585-469: 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
702-418: 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
819-404: A first time offender failing to vote is a $ 20.00 fine, which increases to $ 50.00 if the offender refused to vote prior. Historically the size of eligible voters, the electorate, was small having the size of groups or communities of privileged men like aristocrats and men of a city ( citizens ). With the growth of the number of people with bourgeois citizen rights outside of cities, expanding
936-458: 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
1053-484: 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
1170-471: 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
1287-555: 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
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#17328015791701404-1033: 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
1521-429: A mechanism for selecting rulers. On the other hand, elections began to be seen as a way for the masses to express popular consent repeatedly, resulting in the triumph of the electoral process until the present day. This conceptual misunderstanding of elections as open and egalitarian when they are not innately so may thus be a root cause of the problems in contemporary governance . Those in favor of this view argue that
1638-499: 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
1755-404: 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
1872-412: 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
1989-472: A return to sortition-based selection mechanisms. The extent to which sortition should be the dominant mode of selecting rulers or instead be hybridised with electoral representation remains a topic of debate. 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
2106-497: 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
2223-645: A scientific, industrial, or social problem, it is conventional to begin with a statistical population or a statistical model to be studied. Populations can be diverse groups of people or objects such as "all people living in a country" or "every atom composing a crystal". Statistics deals with every aspect of data, including the planning of data collection in terms of the design of surveys and experiments . 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
2340-465: 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
2457-637: 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
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#17328015791702574-399: 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
2691-419: 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
2808-402: A variety of political, organizational, and corporate settings. Many countries hold elections to select people to serve in their governments, but other types of organizations hold elections as well. For example, many corporations hold elections among shareholders to select a board of directors , and these elections may be mandated by corporate law . In many places, an election to the government
2925-549: Is a variety of schedules, for example, presidents: the President of Ireland is elected every seven years, the President of Russia and the President of Finland every six years, the President of France every five years, President of the United States every four years. Predetermined or fixed election dates have the advantage of fairness and predictability. They tend to greatly lengthen campaigns, and make dissolving
3042-534: Is also used in many other private and business organisations, from clubs to voluntary associations and corporations . The global use of elections as a tool for selecting representatives in modern representative democracies is in contrast with the practice in the democratic archetype , ancient Athens , where the elections were considered an oligarchic institution and most political offices were filled using sortition , also known as allotment, by which officeholders were chosen by lot. Electoral reform describes
3159-408: Is an election that is held purely for show; that is, without any significant political choice or real impact on the results of the election. Sham elections are a common event in dictatorial regimes that feel the need to feign the appearance of public legitimacy . Published results usually show nearly 100% voter turnout and high support (typically at least 80%, and close to 100% in many cases) for
3276-575: 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
3393-465: 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
3510-834: 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
3627-460: Is common for political scientists to attempt to predict elections via political forecasting methods. The most expensive election campaign included US$ 7 billion spent on the 2012 United States presidential election and is followed by the US$ 5 billion spent on the 2014 Indian general election . The nature of democracy is that elected officials are accountable to the people, and they must return to
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3744-428: 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
3861-470: Is interference from the incumbent government. Dictators may use the powers of the executive (police, martial law, censorship, physical implementation of the election mechanism, etc.) to remain in power despite popular opinion in favour of removal. Members of a particular faction in a legislature may use the power of the majority or supermajority (passing criminal laws, and defining the electoral mechanisms including eligibility and district boundaries) to prevent
3978-411: Is now considered crucial in most free and fair elections, as it limits the effectiveness of intimidation. When elections are called, politicians and their supporters attempt to influence policy by competing directly for the votes of constituents in what are called campaigns. Supporters for a campaign can be either formally organized or loosely affiliated, and frequently utilize campaign advertising . It
4095-418: 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
4212-451: 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
4329-408: 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
4446-402: 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
4563-433: Is usually a competition among people who have already won a primary election within a political party . Elections within corporations and other organizations often use procedures and rules that are similar to those of governmental elections. The question of who may vote is a central issue in elections. The electorate does not generally include the entire population; for example, many countries prohibit those who are under
4680-449: 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
4797-572: The 1995 and 2002 presidential referendums in Saddam Hussein's Iraq . In Mexico , all of the presidential elections from 1929 to 1982 are considered to be sham elections, as the Institutional Revolutionary Party (PRI) and its predecessors governed the country in a de facto single-party system without serious opposition, and they won all of the presidential elections in that period with more than 70% of
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4914-662: The 2014 Crimean status referendum , as well as the 2014 Donbass status referendums and the 2022 annexation referendum in Russian-occupied Ukraine ), the 2018 and 2024 Venezuelan presidential election , the 1928 , 1935 , 1942 , 1949 , 1951 and 1958 elections in Portugal, those in Indonesia during New Order regime, the 1991 and 2019 Kazakh presidential elections , those in North Korea ,
5031-765: 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
5148-570: The Ephors of Sparta in 754 BC, under the mixed government of the Spartan Constitution . Athenian democratic elections, where all citizens could hold public office, were not introduced for another 247 years, until the reforms of Cleisthenes . Under the earlier Solonian Constitution ( c. 574 BC ), all Athenian citizens were eligible to vote in the popular assemblies, on matters of law and policy, and as jurors, but only
5265-584: The United States . Elections were used as early in history as ancient Greece and ancient Rome , and throughout the Medieval period to select rulers such as the Holy Roman Emperor (see imperial election ) and the pope (see papal election ). The Pala King Gopala (ruled c. 750s – 770s CE) in early medieval Bengal was elected by a group of feudal chieftains. Such elections were quite common in contemporary societies of
5382-487: 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
5499-546: 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
5616-432: 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
5733-719: 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
5850-485: The 18th century, some societies in Western Europe used sortition as a means to select rulers, a method which allowed regular citizens to exercise power, in keeping with understandings of democracy at the time. The idea of what constituted a legitimate government shifted in the 18th century to include consent , especially with the rise of the enlightenment . From this point onward, sortition fell out of favor as
5967-664: The European Parliament (where, due to differing election laws in each member state, elections are held on different days of the same week) and, due to logistics, general elections in Lebanon and India . The voting procedure in the Legislative Assemblies of the Roman Republic are also a classical example. In rolling elections, voters have information about previous voters' choices. While in
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#17328015791706084-528: The FUHS Wall of Fame. Election An election is a formal group decision-making process by which a population chooses an individual or multiple individuals to hold public office . Elections have been the usual mechanism by which modern representative democracy has operated since the 17th century. Elections may fill offices in the legislature , sometimes in the executive and judiciary , and for regional and local government . This process
6201-556: The United States . At the same time the Kingdom of Great Britain had in 1780 about 214,000 eligible voters, 3% of the whole population. Naturalization can reshape the electorate of a country. A representative democracy requires a procedure to govern nomination for political office. In many cases, nomination for office is mediated through preselection processes in organized political parties. Non-partisan systems tend to be different from partisan systems as concerns nominations. In
6318-1053: The United States interfering between 1946 and 2000 in 81 elections and Russia or the Soviet Union in 36. In 2018 the most intense interventions, utilizing false information, were by China in Taiwan and by Russia in Latvia ; the next highest levels were in Bahrain, Qatar and Hungary. This can include falsifying voter instructions, violation of the secret ballot , ballot stuffing , tampering with voting machines, destruction of legitimately cast ballots, voter suppression , voter registration fraud, failure to validate voter residency, fraudulent tabulation of results, and use of physical force or verbal intimation at polling places. Other examples include persuading candidates not to run, such as through blackmailing, bribery, intimidation or physical violence. A sham election , or show election ,
6435-402: The age of majority from voting. All jurisdictions require a minimum age for voting. In Australia, Aboriginal people were not given the right to vote until 1962 (see 1967 referendum entry ) and in 2010 the federal government removed the rights of prisoners serving for three years or more to vote (a large proportion of whom were Aboriginal Australians). Suffrage is typically only for citizens of
6552-535: The auditorium for Baccalaureate was the Class of 1972). Since then the stadium, locker rooms, and the agriculture complex have been rebuilt. The latest replacement was the swimming pool and the science building. In 2009 a new building housing many new classrooms including several new computer driven classrooms was opened. Renovations of Plummer Auditorium were completed in 1993. It included new lighting, audio and dressing room upgrades. Air conditioning and an orchestra lift
6669-573: The balance of power in the body from shifting to a rival faction due to an election. Non-governmental entities can also interfere with elections, through physical force, verbal intimidation, or fraud, which can result in improper casting or counting of votes. Monitoring for and minimizing electoral fraud is also an ongoing task in countries with strong traditions of free and fair elections. Problems that prevent an election from being "free and fair" take various forms. The electorate may be poorly informed about issues or candidates due to lack of freedom of
6786-439: 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
6903-540: 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
7020-542: 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
7137-414: The costs (barriers to entry) associated with raising one's political profile. Ultimately, the result is the election of candidates who are superior (whether in actuality or as perceived within a cultural context) and objectively unlike the voters they are supposed to represent. Evidence suggests that the concept of electing representatives was originally conceived to be different from democracy . Prior to
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#17328015791707254-469: The country, though further limits may be imposed. In the European Union, one can vote in municipal elections if one lives in the municipality and is an EU citizen; the nationality of the country of residence is not required. In some countries, voting is required by law. Eligible voters may be subject to punitive measures such as a fine for not casting a vote. In Western Australia, the penalty for
7371-425: 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
7488-406: 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
7605-420: The elected delegates). Electoral systems are the detailed constitutional arrangements and voting systems that convert the vote into a political decision. The first step is for voters to cast the ballots , which may be simple single-choice ballots, but other types, such as multiple choice or ranked ballots may also be used. Then the votes are tallied, for which various vote counting systems may be used. and
7722-413: The election to prevent them from running. Ballots may contain only one "yes" option, or in the case of a simple "yes or no" question, security forces often persecute people who pick "no", thus encouraging them to pick the "yes" option. In other cases, those who vote receive stamps in their passport for doing so, while those who did not vote (and thus do not receive stamps) are persecuted as enemies of
7839-495: 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
7956-478: 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
8073-474: 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
8190-402: 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
8307-450: 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
8424-476: The first elections, there may be plenty of hopeful candidates, in the last rounds consensus on one winner is generally achieved. In today's context of rapid communication, candidates can put disproportionate resources into competing strongly in the first few stages, because those stages affect the reaction of latter stages. In many of the countries with weak rule of law , the most common reason why elections do not meet international standards of being "free and fair"
8541-432: 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
8658-402: 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
8775-605: 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,
8892-793: The history of elections. Males, the dominant cultural group in North America and Europe, often dominated the electorate and continue to do so in many countries. Early elections in countries such as the United Kingdom and the United States were dominated by landed or ruling class males. By 1920 all Western European and North American democracies had universal adult male suffrage (except Switzerland) and many countries began to consider women's suffrage . Despite legally mandated universal suffrage for adult males, political barriers were sometimes erected to prevent fair access to elections (see civil rights movement ). Elections are held in
9009-525: The legislature (parliamentary system) more problematic if the date should happen to fall at a time when dissolution is inconvenient (e.g. when war breaks out). Other states (e.g., the United Kingdom ) only set maximum time in office, and the executive decides exactly when within that limit it will actually go to the polls. In practice, this means the government remains in power for close to its full term, and chooses an election date it calculates to be in its best interests (unless something special happens, such as
9126-406: The modern system of elections was never meant to give ordinary citizens the chance to exercise power - merely privileging their right to consent to those who rule. Therefore, the representatives that modern electoral systems select for are too disconnected, unresponsive, and elite-serving. To deal with this issue, various scholars have proposed alternative models of democracy, many of which include
9243-424: 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
9360-412: 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
9477-428: The people . Sham elections can sometimes backfire against the party in power, especially if the regime believes they are popular enough to win without coercion, fraud or suppressing the opposition. The most famous example of this was the 1990 Myanmar general election , in which the government-sponsored National Unity Party suffered a landslide defeat by the opposition National League for Democracy and consequently,
9594-422: The polytechnic building and four tents that year. After the fire, the school's trustees debated the best location for rebuilding. The district owned the ground on which the polytechnic building stood, but the campus was small, and school work was disrupted by the numerous Santa Fe trains that roared by each day. In 1911, the present site was purchased one block east of Harbor (Spadra) Boulevard. A walnut orchard
9711-415: 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
9828-544: 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
9945-403: The predominance of elections in modern liberal democracies masks the fact that they are actually aristocratic selection mechanisms that deny each citizen an equal chance of holding public office. Such views were expressed as early as the time of Ancient Greece by Aristotle . According to French political scientist Bernard Manin, the inegalitarian nature of elections stems from four factors:
10062-452: The prescribed candidates or for the referendum choice that favours the political party in power. Dictatorial regimes can also organize sham elections with results simulating those that might be achieved in democratic countries. Sometimes, only one government-approved candidate is allowed to run in sham elections with no opposition candidates allowed, or opposition candidates are arrested on false charges (or even without any charges) before
10179-459: The press , lack of objectivity in the press due to state or corporate control, or lack of access to news and political media. Freedom of speech may be curtailed by the state, favouring certain viewpoints or state propaganda . Gerrymandering , exclusion of opposition candidates from eligibility for office, needlessly high restrictions on who may be a candidate, like ballot access rules, and manipulating thresholds for electoral success are some of
10296-494: 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
10413-489: The process of introducing fair electoral systems where they are not in place, or improving the fairness or effectiveness of existing systems. Psephology is the study of results and other statistics relating to elections (especially with a view to predicting future results). Election is the fact of electing, or being elected. To elect means "to select or make a decision", and so sometimes other forms of ballot such as referendums are referred to as elections, especially in
10530-470: 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
10647-410: The rate of 18 percent a year. To accommodate the growth, the school was moved to new quarters on West Commonwealth Avenue, an area now known as Amerige Park. School enrollment continued to grow and within two years a new polytechnic building was built to ease the overcrowding. But on November 17, 1910, the day before it could be occupied, the older FUHS building burned to the ground. FUHS was housed in
10764-446: The regime through suppression of the opposition, coercion of voters, vote rigging , reporting several votes received greater than the number of voters, outright lying, or some combination of these. In an extreme example, Charles D. B. King of Liberia was reported to have won by 234,000 votes in the 1927 general election , a "majority" that was over fifteen times larger than the number of eligible voters. Some scholars argue that
10881-756: The region. In the Chola Empire , around 920 CE, in Uthiramerur (in present-day Tamil Nadu ), palm leaves were used for selecting the village committee members. The leaves, with candidate names written on them, were put inside a mud pot. To select the committee members, a young boy was asked to take out as many leaves as the number of positions available. This was known as the Kudavolai system. The first recorded popular elections of officials to public office, by majority vote, where all citizens were eligible both to vote and to hold public office, date back to
10998-1092: The results were annulled. Examples of sham elections include: the presidential and parliamentary elections of the Islamic Republic of Iran , the 1929 and 1934 elections in Fascist Italy , the 1942 general election in Imperial Japan , those in Nazi Germany , East Germany , the 1940 elections of Stalinist "People's Parliaments" to legitimise the Soviet occupation of Estonia , Latvia and Lithuania , those in Egypt under Gamal Abdel Nasser , Anwar Sadat , Hosni Mubarak , and Abdel Fattah el-Sisi , those in Bangladesh under Sheikh Hasina , those in Russia under Vladimir Putin (including
11115-461: 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
11232-439: 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
11349-399: 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
11466-405: 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
11583-482: 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
11700-412: 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
11817-408: 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
11934-532: The term citizen, the electorates grew to numbers beyond the thousands. Elections with an electorate in the hundred thousands appeared in the final decades of the Roman Republic , by extending voting rights to citizens outside of Rome with the Lex Julia of 90 BC , reaching an electorate of 910,000 and estimated voter turnout of maximum 10% in 70 BC, only again comparable in size to the first elections of
12051-577: The three highest classes of citizens could vote in elections. Nor were the lowest of the four classes of Athenian citizens (as defined by the extent of their wealth and property, rather than by birth) eligible to hold public office, through the reforms of Solon . The Spartan election of the Ephors, therefore, also predates the reforms of Solon in Athens by approximately 180 years. Questions of suffrage , especially suffrage for minority groups, have dominated
12168-431: The time of voting—with some possible exceptions such as through a minimum age requirement—in the jurisdiction. In such cases, it is not required (or even possible) that the members of the electorate be familiar with all of the eligible persons, though such systems may involve indirect elections at larger geographic levels to ensure that some first-hand familiarity among potential electees can exist at these levels (i.e., among
12285-420: 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
12402-416: 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
12519-466: The unequal treatment of candidates by voters, the distinction of candidates required by choice, the cognitive advantage conferred by salience, and the costs of disseminating information. These four factors result in the evaluation of candidates based on voters' partial standards of quality and social saliency (for example, skin colour and good looks). This leads to self-selection biases in candidate pools due to unobjective standards of treatment by voters and
12636-485: 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
12753-587: 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
12870-456: The vote. The first seriously competitive presidential election in modern Mexican history was that of 1988 , in which for the first time the PRI candidate faced two strong opposition candidates, though it is believed that the government rigged the result. The first fair election was held in 1994 , though the opposition did not win until 2000 . A predetermined conclusion is permanently established by
12987-422: The voters at prescribed intervals to seek their mandate to continue in office. For that reason, most democratic constitutions provide that elections are held at fixed regular intervals. In the United States, elections for public offices are typically held between every two and six years in most states and at the federal level, with exceptions for elected judicial positions that may have longer terms of office. There
13104-422: The voting system then determines the result on the basis of the tally. Most systems can be categorized as either proportional , majoritarian or mixed . Among the proportional systems, the most commonly used are party-list proportional representation (list PR) systems, among majoritarian are first-past-the-post electoral system (single winner plurality voting ) and different methods of majority voting (such as
13221-410: The ways the structure of an election can be changed to favour a specific faction or candidate. Scheduling frequent elections can also lead to voter fatigue . Those in power may arrest or assassinate candidates, suppress or even criminalize campaigning, close campaign headquarters, harass or beat campaign workers, or intimidate voters with violence. Foreign electoral intervention can also occur, with
13338-408: The widely used two-round system ). Mixed systems combine elements of both proportional and majoritarian methods, with some typically producing results closer to the former ( mixed-member proportional ) or the other (e.g. parallel voting ). Many countries have growing electoral reform movements, which advocate systems such as approval voting , single transferable vote , instant runoff voting or
13455-468: 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
13572-658: Was added as well. The Charles Kassler fresco "Pastoral California" was uncovered and completely restored in 1997. The school provides opportunities for students to be involved in Honors , Advanced Placement (AP), and International Baccalaureate (IB) courses. Fullerton's sports teams are known as the Indians, and are members of the California Interscholastic Federation 's Southern Section. Many of Fullerton's notable alumni are listed on
13689-471: Was removed prior to building, and the former site was sold to the City of Fullerton for use as a park. The school's facilities have changed over the years to meet educational and community needs. Plummer Auditorium was built in 1930-32 and its original ironwork, which was made by students on the campus, was kept when Plummer was refurbished and remodeled to meet earthquake standards in 1972 (the first class to use
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