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110-609: Demographic features of the population of Zambia include population density , ethnicity , education level , health of the populace, economic status , religious affiliations and others aspects of the population . Zambia is one of the most highly urbanised countries in sub-Saharan Africa with 44% of the population concentrated in a few urban areas along the major transport corridors, while rural areas are sparsely populated. Zambia 's population comprises more than 72 Bantu -speaking ethnic groups. Some ethnic groups are small, and only two have enough people to constitute at least 10% of

220-469: 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

330-468: A significant comparison, numbers must be altered for the size of the population that is under study. For example, the fertility rate is calculated as the ratio of the number of births to women of childbearing age to the total number of women in this age range. If these adjustments were not made, we would not know if a nation with a higher rate of births or deaths has a population with more women of childbearing age or more births per eligible woman. Within

440-401: A country (or other entity) contains Population t persons at time t . What is the size of the population at time t + 1 ? Natural increase from time t to t + 1: Net migration from time t to t + 1: These basic equations can also be applied to subpopulations. For example, the population size of ethnic groups or nationalities within a given society or country is subject to

550-418: 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

660-458: 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

770-484: 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

880-471: 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

990-555: 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

1100-1033: 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

1210-460: A new product, and to analyze certain dynamics of a company's workforce. Choosing a new location for a branch of a bank, choosing the area in which to start a new supermarket, consulting a bank loan officer that a particular location would be a beneficial site to start a car wash, and determining what shopping area would be best to buy and be redeveloped in metropolis area are types of problems in which demographers can be called upon. Standardization

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1320-499: 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

1430-498: A period of transition where in demography emerged from statistics as a separate field of interest. This period included a panoply of international 'great demographers' like Adolphe Quetelet (1796–1874), William Farr (1807–1883), Louis-Adolphe Bertillon (1821–1883) and his son Jacques (1851–1922), Joseph Körösi (1844–1906), Anders Nicolas Kaier (1838–1919), Richard Böckh (1824–1907), Émile Durkheim (1858–1917), Wilhelm Lexis (1837–1914), and Luigi Bodio (1840–1920) contributed to

1540-404: 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

1650-412: 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

1760-497: 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

1870-467: A sign of prestige and recognizing that not all of their children will live to adulthood. definition: age 15 and over can read and write Demography Demography (from Ancient Greek δῆμος ( dêmos )  'people, society' and -γραφία ( -graphía )  'writing, drawing, description') is the statistical study of human populations : their size, composition (e.g., ethnic group, age), and how they change through

1980-557: A small but economically important Asian population, most of whom are Indians or Chinese . Source: According to the 2022 revision of the World Population Prospects the total population of Zambia is 19,473,125 in 2021, compared to only 2,340,000 in 1950. The proportion of children below the age of 15 in 2010 was 46.4%, 50.6% was between 15 and 65 years of age, while 3.1% was 65 years or older. Population Estimates by Sex and Age Group (01.VII.2020) (Data based on

2090-426: A standardized mortality rate (SMR) or standardized incidence rate (SIR). Population change is analyzed by measuring the change between one population size to another. Global population continues to rise, which makes population change an essential component to demographics. This is calculated by taking one population size minus the population size in an earlier census . The best way of measuring population change

2200-465: 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

2310-637: 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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2420-399: 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

2530-419: 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

2640-405: A variety of areas where researchers want to know how populations of social actors can change across time through processes of birth, death, and migration . In the context of human biological populations, demographic analysis uses administrative records to develop an independent estimate of the population. Demographic analysis estimates are often considered a reliable standard for judging

2750-499: A variety of demographic methods for modelling population processes. They include models of mortality (including the life table , Gompertz models , hazards models , Cox proportional hazards models , multiple decrement life tables , Brass relational logits), fertility (Hermes model, Coale -Trussell models, parity progression ratios ), marriage (Singulate Mean at Marriage, Page model), disability ( Sullivan's method , multistate life tables), population projections ( Lee-Carter model ,

2860-643: Is a useful demographic technique used in the analysis of a business. It can be used as an interpretive and analytic tool for the comparison of different markets. These organizations have interests about the number and characteristics of their clients so they can maximize the sale of their products, their outlook on their influence, or the ends of their power, services, and beneficial works. Statistics 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

2970-575: 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

3080-465: 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

3190-417: Is because developed countries have proportionally more older people, who are more likely to die in a given year, so that the overall mortality rate can be higher even if the mortality rate at any given age is lower. A more complete picture of mortality is given by a life table , which summarizes mortality separately at each age. A life table is necessary to give a good estimate of life expectancy. Suppose that

3300-834: 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

3410-428: 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

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3520-431: Is likely to continue to rise. Populations can change through three processes: fertility, mortality, and migration. Fertility involves the number of children that women have and is to be contrasted with fecundity (a woman's childbearing potential). Mortality is the study of the causes, consequences, and measurement of processes affecting death to members of the population. Demographers most commonly study mortality using

3630-418: 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

3740-451: 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

3850-408: 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

3960-550: Is seen as the intellectual father of ideas of overpopulation and the limits to growth. Later, more sophisticated and realistic models were presented by Benjamin Gompertz and Verhulst . In 1855, a Belgian scholar Achille Guillard defined demography as the natural and social history of human species or the mathematical knowledge of populations, of their general changes, and of their physical, civil, intellectual, and moral condition. The period 1860–1910 can be characterized as

4070-554: Is the case in much of the developing world, and most of historical demography . One of these techniques in contemporary demography is the sister method, where survey researchers ask women how many of their sisters have died or had children and at what age. With these surveys, researchers can then indirectly estimate birth or death rates for the entire population. Other indirect methods in contemporary demography include asking people about siblings, parents, and children. Other indirect methods are necessary in historical demography. There are

4180-432: Is today widely taught in many universities across the world, attracting students with initial training in social sciences, statistics or health studies. Being at the crossroads of several disciplines such as sociology , economics , epidemiology , geography , anthropology and history , demography offers tools to approach a large range of population issues by combining a more technical quantitative approach that represents

4290-402: 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

4400-510: Is used in a wide variety of contexts. For example, it is often used in business plans, to describe the population connected to the geographic location of the business. Demographic analysis is usually abbreviated as DA. For the 2010 U.S. Census, The U.S. Census Bureau has expanded its DA categories. Also as part of the 2010 U.S. Census, DA now also includes comparative analysis between independent housing estimates, and census address lists at different key time points. Patient demographics form

4510-421: Is using the intercensal percentage change. The intercensal percentage change is the absolute change in population between the censuses divided by the population size in the earlier census. Next, multiply this a hundredfold to receive a percentage . When this statistic is achieved, the population growth between two or more nations that differ in size, can be accurately measured and examined. For there to be

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4620-449: 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

4730-765: 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

4840-807: The International Union for the Scientific Study of Population , or a national association such as the Population Association of America in the United States, or affiliates of the Federation of Canadian Demographers in Canada . Population composition is the description of population defined by characteristics such as age, race , sex or marital status . These descriptions can be necessary for understanding

4950-666: The Leslie Matrix ), and population momentum ( Keyfitz ). The United Kingdom has a series of four national birth cohort studies, the first three spaced apart by 12 years: the 1946 National Survey of Health and Development , the 1958 National Child Development Study , the 1970 British Cohort Study , and the Millennium Cohort Study , begun much more recently in 2000. These have followed the lives of samples of people (typically beginning with around 17,000 in each study) for many years, and are still continuing. As

5060-516: The Middle Ages , Christian thinkers devoted much time in refuting the Classical ideas on demography. Important contributors to the field were William of Conches , Bartholomew of Lucca , William of Auvergne , William of Pagula , and Muslim sociologists like Ibn Khaldun . One of the earliest demographic studies in the modern period was Natural and Political Observations Made upon

5170-572: The United States and much of Europe ), registry statistics are the best method for estimating the number of births and deaths. A census is the other common direct method of collecting demographic data. A census is usually conducted by a national government and attempts to enumerate every person in a country. In contrast to vital statistics data, which are typically collected continuously and summarized on an annual basis, censuses typically occur only every 10 years or so, and thus are not usually

5280-487: 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

5390-546: 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

5500-666: The life table , a statistical device that provides information about the mortality conditions (most notably the life expectancy) in the population. Migration refers to the movement of persons from a locality of origin to a destination place across some predefined, political boundary. Migration researchers do not designate movements 'migrations' unless they are somewhat permanent. Thus, demographers do not consider tourists and travellers to be migrating. While demographers who study migration typically do so through census data on place of residence, indirect sources of data including tax forms and labour force surveys are also important. Demography

5610-432: 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

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5720-719: 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

5830-433: The social dynamics from historical and comparative research. This data is often compared using a population pyramid . Population composition is also a very important part of historical research. Information ranging back hundreds of years is not always worthwhile, because the numbers of people for which data are available may not provide the information that is important (such as population size ). Lack of information on

5940-739: The 2010 Population Census.): Registration of vital events is in Zambia not complete. The website Our World in Data prepared the following estimates based on statistics from the Population Department of the United Nations . Total Fertility Rate (TFR) (Wanted TFR) and Crude Birth Rate (CBR) : Fertility data as of 2013–2014 (DHS Program): At national level, the TFR was highest among women with no religious affiliation at 6.5. Among

6050-751: The Application of Probabilities to Life Contingencies (1838). In 1755, Benjamin Franklin published his essay Observations Concerning the Increase of Mankind, Peopling of Countries, etc. , projecting exponential growth in British colonies . His work influenced Thomas Robert Malthus , who, writing at the end of the 18th century, feared that, if unchecked, population growth would tend to outstrip growth in food production, leading to ever-increasing famine and poverty (see Malthusian catastrophe ). Malthus

6160-564: The Bills of Mortality (1662) by John Graunt , which contains a primitive form of life table . Among the study's findings were that one-third of the children in London died before their sixteenth birthday. Mathematicians, such as Edmond Halley , developed the life table as the basis for life insurance mathematics. Richard Price was credited with the first textbook on life contingencies published in 1771, followed later by Augustus De Morgan , On

6270-425: The accuracy of the census information gathered at any time. In the labor force , demographic analysis is used to estimate sizes and flows of populations of workers; in population ecology the focus is on the birth, death, migration and immigration of individuals in a population of living organisms, alternatively, in social human sciences could involve movement of firms and institutional forms. Demographic analysis

6380-467: The basic demographic equation holds true by definition, in practice the recording and counting of events (births, deaths, immigration, emigration) and the enumeration of the total population size are subject to error. So allowance needs to be made for error in the underlying statistics when any accounting of population size or change is made. The figure in this section shows the latest (2004) UN ( United Nations ) WHO projections of world population out to

6490-696: The best source of data on births and deaths. Analyses are conducted after a census to estimate how much over or undercounting took place. These compare the sex ratios from the census data to those estimated from natural values and mortality data. Censuses do more than just count people. They typically collect information about families or households in addition to individual characteristics such as age, sex, marital status, literacy/education, employment status, and occupation, and geographical location. They may also collect data on migration (or place of birth or of previous residence), language, religion, nationality (or ethnicity or race), and citizenship. In countries in which

6600-518: The category of standardization , there are two major approaches: direct standardization and indirect standardization. A stable population does not necessarily remain fixed in size. It can be expanding or shrinking. The crude death rate as defined above and applied to a whole population can give a misleading impression. For example, the number of deaths per 1,000 people can be higher in developed nations than in less-developed countries, despite standards of health being better in developed countries. This

6710-439: 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

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6820-540: 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

6930-542: 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

7040-553: The core of the data for any medical institution, such as patient and emergency contact information and patient medical record data. They allow for the identification of a patient and their categorization into categories for the purpose of statistical analysis. Patient demographics include: date of birth , gender , date of death , postal code, ethnicity, blood type , emergency contact information, family doctor, insurance provider data, allergies , major diagnoses and major medical history. Formal demography limits its object of study to

7150-498: The core of the discipline with many other methods borrowed from social or other sciences. Demographic research is conducted in universities, in research institutes, as well as in statistical departments and in several international agencies. Population institutions are part of the CICRED (International Committee for Coordination of Demographic Research) network while most individual scientists engaged in demographic research are members of

7260-425: 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

7370-528: The development of demography and to the toolkit of methods and techniques of demographic analysis. Demography is the statistical and mathematical study of the size, composition, and spatial distribution of human populations and how these features change over time. Data are obtained from a census of the population and from registries: records of events like birth , deaths , migrations, marriages, divorces , diseases, and employment . To do this, there needs to be an understanding of how they are calculated and

7480-649: The distribution and abundance of organisms. As it relates to organizations and demography, organizations go through various liabilities to their continued survival. Hospitals, like all other large and complex organizations are impacted in the environment they work. For example, a study was done on the closure of acute care hospitals in Florida between a particular time. The study examined effect size, age, and niche density of these particular hospitals. A population theory says that organizational outcomes are mostly determined by environmental factors . Among several factors of

7590-406: 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

7700-495: 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

7810-478: 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

7920-474: 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

8030-402: 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

8140-450: 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

8250-408: The family. The causes of turnover can be split into two separate factors, one linked with the culture of the organization, and the other relating to all other factors. People who do not fully accept a culture might leave voluntarily. Or, some individuals might leave because they fail to fit in and fail to change within a particular organization. A basic definition of population ecology is a study of

8360-432: 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

8470-402: 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

8580-605: 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,

8690-525: The interplay of fertility (births), mortality (deaths), and migration. Demographic analysis examines and measures the dimensions and dynamics of populations; it can cover whole societies or groups defined by criteria such as education , nationality , religion , and ethnicity . Educational institutions usually treat demography as a field of sociology , though there are a number of independent demography departments. These methods have primarily been developed to study human populations, but are extended to

8800-463: The last 30 years and still averages among the world's highest, almost 6 children per woman, largely because of the country's lack of access to family planning services, education for girls, and employment for women. Zambia also exhibits wide fertility disparities based on rural or urban location, education, and income. Poor, uneducated women from rural areas are more likely to marry young, to give birth early, and to have more children, viewing children as

8910-418: The measurement of population processes, while the broader field of social demography or population studies also analyses the relationships between economic, social, institutional, cultural, and biological processes influencing a population. Demographic thoughts traced back to antiquity, and were present in many civilisations and cultures, like Ancient Greece , Ancient Rome , China and India . Made up of

9020-424: 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

9130-413: The nation will become a nation of immigrants. This influx is projected to rise over the next century as new immigrants and their children will account for over half the U.S. population. These demographic shifts could ignite major adjustments in the economy, more specifically, in labor markets. People decide to exit organizations for many reasons, such as, better jobs, dissatisfaction, and concerns within

9240-458: The original data-collection procedures may prevent accurate evaluation of data quality. The demographic analysis of labor markets can be used to show slow population growth, population aging , and the increased importance of immigration. The U.S. Census Bureau projects that in the next 100 years, the United States will face some dramatic demographic changes. The population is expected to grow more slowly and age more rapidly than ever before and

9350-412: 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

9460-415: 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

9570-544: 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

9680-634: The population. The majority of Zambians are subsistence farmers , but the country is also fairly urbanised , with 42% of the population being city residents. The predominant religion is a blend of traditional beliefs and Christianity . Immigrants , mostly British or South African , as well as some white Zambian citizens (about 40,000), live mainly in Lusaka and in the Copperbelt in northern Zambia, where they are either employed in mines , financial and related activities or retired. Zambia also has

9790-516: The prefix demo- and the suffix -graphy , the term demography refers to the overall study of population. In ancient Greece, this can be found in the writings of Herodotus , Thucydides , Hippocrates , Epicurus , Protagoras , Polus , Plato and Aristotle . In Rome, writers and philosophers like Cicero , Seneca , Pliny the Elder , Marcus Aurelius , Epictetus , Cato , and Columella also expressed important ideas on this ground. In

9900-494: 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

10010-418: 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

10120-566: The questions they answer which are included in these four concepts: population change , standardization of population numbers, the demographic bookkeeping equation, and population composition. There are two types of data collection —direct and indirect—with several methods of each type. Direct data comes from vital statistics registries that track all births and deaths as well as certain changes in legal status such as marriage, divorce, and migration (registration of place of residence). In developed countries with good registration systems (such as

10230-461: 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

10340-417: The same sources of change. When dealing with ethnic groups, however, "net migration" might have to be subdivided into physical migration and ethnic reidentification ( assimilation ). Individuals who change their ethnic self-labels or whose ethnic classification in government statistics changes over time may be thought of as migrating or moving from one population subcategory to another. More generally, while

10450-439: 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

10560-399: 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

10670-405: 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

10780-482: 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

10890-447: The samples have been drawn in a nationally representative way, inferences can be drawn from these studies about the differences between four distinct generations of British people in terms of their health, education, attitudes, childbearing and employment patterns. Indirect standardization is used when a population is small enough that the number of events (births, deaths, etc.) are also small. In this case, methods must be used to produce

11000-412: 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

11110-408: 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

11220-404: The theory, there are four that apply to the hospital closure example: size, age, density of niches in which organizations operate, and density of niches in which organizations are established. Problems in which demographers may be called upon to assist business organizations are when determining the best prospective location in an area of a branch store or service outlet, predicting the demand for

11330-420: 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

11440-416: 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

11550-485: 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

11660-640: 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

11770-478: The vital registration system may be incomplete, the censuses are also used as a direct source of information about fertility and mortality; for example, the censuses of the People's Republic of China gather information on births and deaths that occurred in the 18 months immediately preceding the census. Indirect methods of collecting data are required in countries and periods where full data are not available, such as

11880-827: The women with religious affiliation Protestants had the highest TFR of 6.0, followed by Muslims with 5.9 and Catholics with 5.7. The following demographic statistics of Zambia in 2022 are from the World Population Review. The following demographic statistics are from the CIA World Factbook , unless otherwise indicated. (2010 est.) Zambia's youthful population consists primarily of Bantu-speaking people representing nearly 70 different ethnicities. Zambia's high fertility rate continues to drive rapid population growth, averaging almost 3 percent annually between 2000 and 2010. The country's total fertility rate has fallen by less than 1.5 children per woman during

11990-468: 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

12100-533: The year 2150 (red = high, orange = medium, green = low). The UN "medium" projection shows world population reaching an approximate equilibrium at 9 billion by 2075. Working independently, demographers at the International Institute for Applied Systems Analysis in Austria expect world population to peak at 9 billion by 2070. Throughout the 21st century, the average age of the population

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