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104-670: Carl F. Rehnborg developed his vitamin products in the 1930s. His time in China between the end of 1915 and 1927 exposed him to experiences which led him to realize the impact vitamins and nutrients have on general health. He began selling his vitamins as the California Vitamin Company. In 1939 the company was renamed Nutrilite. In 1945, Rehnborg invented the multi-level marketing selling system to distribute his vitamins. Also in 1945 Lee S. Mytinger and William S. Casselberry became exclusive national distributors and operated

208-469: 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

312-567: 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

416-461: A company to distribute the vitamins. The founders of Amway , Jay Van Andel and Richard DeVos , began as independent distributors selling Nutrilite products in 1949, at a time when the product's previous distributors (Mytinger and Casselberry, Inc.) were involved in a dispute with the U.S. Food and Drug Administration (FDA), which accused them of false advertising. Van Andel and DeVos rose rapidly, becoming top-selling distributors. Concerned about

520-418: 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

624-458: 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

728-484: 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

832-471: 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

936-594: A marketing kit and initial products, as a barrier to entry. Many MLMs emphasize the recruitment of new members over actual sales, particularly sales to individuals outside of the MLM. This focus on recruitment often pressures participants to buy and use the company's products themselves, and exploit their personal relationships for sales and recruiting. Furthermore, MLMs are often scrutinized for having complex and exaggerated compensation schemes, making it difficult for most participants to earn significant income. False claims about

1040-555: 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

1144-1033: 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

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1248-499: 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

1352-545: A plan collapses, most people—except perhaps those at the very top of the pyramid—end up empty-handed." In a 2004 Staff Advisory letter to the Direct Selling Association, the FTC states: Much has been made of the personal, or internal, consumption issue in recent years. In fact, the amount of internal consumption in any multi-level compensation business does not determine whether or not the FTC will consider

1456-404: 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

1560-412: 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

1664-497: 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

1768-465: 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

1872-637: 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

1976-399: 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

2080-405: A type of direct selling . Some sources emphasize that multi-level marketing is merely one form of direct selling, rather than being direct selling. Other terms that are sometimes used to describe multi-level marketing include "word-of-mouth marketing", "interactive distribution", and " relationship marketing ". Critics have argued that the use of these and other different terms and " buzzwords "

2184-419: 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

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2288-419: A wide range of issues, including accusations that their operations closely resemble illegal pyramid schemes . Additionally, MLM companies have been accused of engaging in price fixing and participating in collusion and racketeering , often involving secret compensation deals that favor a few participants at the expense of others. Critics also point to the high initial costs for new members, such as purchasing

2392-848: Is an effort to draw distinctions between multi-level marketing and illegal Ponzi schemes , chain letters , and consumer fraud scams—where none meaningfully exist. The Direct Selling Association (DSA), a lobbying group for the MLM industry, reported that in 1990 only 25% of DSA members used the MLM business model. By 1999, this had grown to 77.3%. By 2009, 94.2% of DSA members were using MLM, accounting for 99.6% of sellers, and 97.1% of sales. Companies such as Avon , Aerus (formerly Electrolux USA), Tupperware , and Kirby were all originally single-level marketing companies, using that traditional and uncontroversial direct selling business model (distinct from MLM) to sell their goods. However, they later introduced multi-level compensation plans, becoming MLM companies. The DSA has approximately 200 members while it

2496-575: 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

2600-465: 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

2704-540: Is banned in Saudi Arabia by imposing religious fatwa nationally, for this reason MLM companies like Amway , Mary Kay , Oriflame and Herbalife sell their products by online selling method instead of MLM. MLM businesses operate in all 50 U.S. states. Businesses may use terms such as " affiliate marketing " or "home-based business franchising". Some sources say that all MLM companies are essentially pyramid schemes, even if they are legal. Utah has been named

2808-834: 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

2912-412: Is derived from a non-salaried workforce selling the company's products or services, while the earnings of the participants are derived from a pyramid-shaped or binary compensation commission system. In multi-level marketing, the compensation plan usually pays out to participants from two potential revenue streams . The first is based on a sales commission from directly selling the product or service;

3016-428: 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

3120-543: Is estimated there are over 1,000 firms using multi-level marketing in the United States alone. The origin of multi-level marketing is often disputed, but multi-level marketing style businesses existed in the 1920s and the 1930s, such as the California Vitamin Company (later named Nutrilite ) and the California Perfume Company (renamed " Avon Products "). Several sources have commented on

3224-402: Is not the MLM company's products or services. The products or services are largely peripheral to the MLM model. Rather, the true sales pitch and emphasis is on a confidence given to participants of potential financial independence through participation in the MLM, luring with phrases like "the lifestyle you deserve" or "independent distributor". Erik German's memoir My Father's Dream documents

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3328-418: 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

3432-451: 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

3536-408: 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

3640-451: Is then advertised by the MLM company to recruit more distributors in the MLM with an unrealistic anticipation of earning margins which are in reality merely theoretical and statistically improbable. Although an MLM company holds out those few top individual participants as evidence of how participation in the MLM could lead to success, the MLM business model depends on the failure of the overwhelming majority of all other participants, through

3744-402: 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

3848-449: 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

3952-765: 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

4056-477: The Chinese economic reform of 1978. This rise in multi-level marketing's popularity coincided with economic uncertainty and a new shift towards individual consumerism . Multi-level marketing was banned on the mainland by the government in 1998, citing social, economic, and taxation issues. Further regulation "Prohibition of Chuanxiao " (where MLM is a type of Chuanxiao was enacted in 2005, clause 3 of Chapter 2 of

4160-487: 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

4264-546: 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

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4368-432: 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

4472-719: 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

4576-526: The "unofficial world capital of multi-level marketing and direct sales companies" and is home to at least 15 major MLMs, more MLMs per capita than any other state. The U.S. Federal Trade Commission (FTC) states: "Steer clear of multilevel marketing plans that pay commissions for recruiting new distributors. They're actually illegal pyramid schemes. Why is pyramiding dangerous? Because plans that pay commissions for recruiting new distributors inevitably collapse when no new distributors can be recruited. And when

4680-599: The FDA dispute, they launched a new company, the American Way, (later known as Amway), to use the multi-level marketing system for other household products. The FDA/Mytinger-Casselberry dispute, which went to the United States Supreme Court , was resolved in favor of the FDA in the 1960s. In 1972, Amway bought a controlling interest in the company. In 1994 they took over complete ownership. In 2007,

4784-406: The FDA tracked the peanut butter salmonella outbreak to a Peanut Corporation of America plant, a vendor Amway had used on occasion. Multi-level marketing Multi-level marketing ( MLM ), also called network marketing or pyramid selling , is a controversial and sometimes illegal marketing strategy for the sale of products or services in which the revenue of the MLM company

4888-517: The Ministry of Commerce ("MOFCOM"). In 2016, there are 73 companies, including domestic and foreign companies, that have obtained the direct selling license. Some multi-level marketing sellers have circumvented this ban by establishing addresses and bank accounts in Hong Kong , where the practice is legal, while selling and recruiting on the mainland. It was not until August 23, 2005, that

4992-656: The Simply Nutrilite (later renamed Nutrilite Trim Advantage Body System) line was introduced. The line includes meal replacement bars, anti-oxidant, and vitamin supplements. Nutrilite's vitamin and mineral products are distributed through a multilevel marketing structure by Amway affiliates known as Independent Business Owners (IBO) in North America and 108 other countries and territories. Nutrilite also has snacks as part of its product line.(Amway, Quixtar, and Access Group are subsidiaries of Alticor). In 1948,

5096-646: The State Council promulgated rules that dealt specifically with direct sale operation- Administration of Direct Sales (entered into effect on December 1, 2005) and the Regulations for the Prohibition of Chuanxiao (entered into effect on November 1, 2005). When direct selling is allowed, it will only be permitted under the most stringent requirements, in order to ensure the operations are not pyramid schemes, MLM, or fly-by-night operations. MLM marketing

5200-514: The U.S. Food and Drug Administration seized shipments of Nutrilite, then distributed by a California firm, Mytinger & Casselberry Inc. The FDA claimed that a booklet with the product made false claims that it would cure diseases. The distributor brought suit, claiming the seizures were unconstitutional. In 1950, the U.S. Supreme Court ruled that the seizure was constitutional. In 2009, Amway voluntarily recalled three kinds of Nutrilite energy bars due to potential contamination with salmonella after

5304-853: The United States" while another states "Multi-Level Marketing, a form of Pyramid Scheme, is not necessarily fraudulent." In October 2010 it was reported that multi-level marketing companies were being investigated by a number of state attorneys general amid allegations that salespeople were primarily paid for recruiting and that more recent recruits cannot earn anything near what early entrants do. Industry critic Robert L. FitzPatrick has called multi-level marketing "the Main Street bubble" that will eventually burst. Many Islamic jurists and religious bodies, including Permanent Committee for Scholarly Research and Ifta of Saudi Arabia , have considered MLM trade to be prohibited ( haram ). They argue that MLM trade involves deceiving others into participating, and

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5408-418: The author's father's failures through " get-rich-quick schemes " such as Amway . The memoir illustrates the multi-level marketing sales principle known as "selling the dream". Although the emphasis is always made on the potential of success and the positive life change that "might" or "could" (not "will" or "can") result, disclosure statements include disclaimers that they, as participants, should not rely on

5512-580: The belief that they can achieve large returns, while the statistical improbability of this is de-emphasized. MLM companies have been made illegal or otherwise strictly regulated in some jurisdictions as merely variations of the traditional pyramid scheme . Multi-level marketing is also known as "pyramid selling", "network marketing", and "referral marketing". Independent non-salaried participants, referred to as distributors (variously called "associates", "independent business owners", "independent agents", " affiliates ", etc.), are authorized to distribute

5616-439: 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

5720-553: The company's distribution chain as fellow salespeople so that these can become downline distributors. According to a report that studied the business models of 350 MLM companies in the United States , published on the Federal Trade Commission's website, at least 99% of people who join MLM companies lose money. Nonetheless, MLM companies function because downline participants are encouraged to hold onto

5824-453: The company's products or services. They are awarded their own immediate retail profit from customers plus commission from the company, not downlines, through a multi-level marketing compensation plan, which is based upon the volume of products sold through their own sales efforts as well as that of their downline organization. Independent distributors develop their organizations by either building an active consumer network , who buy direct from

5928-547: The company, or by recruiting a downline of independent distributors who also build a consumer network base, thereby expanding the overall organization. The combined number of recruits from these cycles is the sales force, called the salesperson's "downline". This "downline" is the pyramid in MLM's multiple-level structure of compensation. The overwhelming majority of MLM participants participate at either an insignificant or nil net profit. A study of 27 MLM schemes found that on average, 99.6% of participants lost money. Indeed,

6032-689: The company." (By comparison, skeptic Brian Dunning points out that "only 97.14% of Las Vegas gamblers lose money .... ." ) In part, this is because encouraging recruits to further "recruit people to compete with [them]" leads to "market saturation." It has also been claimed "(b)y its very nature, MLM is completely devoid of any scientific foundations." Because of the encouraging of recruits to further recruit their competitors, some people have even gone so far as to say at best modern MLM companies are nothing more than legalized pyramid schemes with one stating "Multi-level marketing companies have become an accepted and legally sanctioned form of pyramid scheme in

6136-540: 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

6240-542: 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

6344-425: 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

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6448-411: The detriment of most of the company's constituent workforce (the MLM participants). Only some of the profits are then shared with individual participants at the top of the MLM distributorship pyramid. The earnings of those top few participants are emphasized and championed at company seminars and conferences , thus creating the illusion that participants in the MLM can become financially successful. This

6552-635: The earning results of other participants in the highest levels of the MLM participant pyramid as an indication of what they should expect to earn. MLM companies rarely emphasize the extreme likelihood of failure, or the extreme likelihood of financial loss, from participation in MLM. MLM companies have been made illegal in some jurisdictions as a mere variation of the traditional pyramid scheme , including in China . In jurisdictions where MLM companies have not been made illegal, many illegal pyramid schemes attempt to present themselves as MLM businesses. Given that

6656-406: 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

6760-595: The effectiveness of products are also commonly reported. Major revenue for the company, or its leading distributors, often comes from participant-attended conventions, training sessions, and sales of promotional materials, adding another layer of financial burden on members. Some MLM organizations have also been accused of using cult-like techniques to build enthusiasm and loyalty among their members, which has raised additional ethical concerns. "Network marketing" and "multi-level marketing" (MLM) have been described by author Dominique Xardel as being synonymous, with it being

6864-495: 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

6968-478: 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

7072-474: 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

7176-402: 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

7280-450: 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

7384-432: 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

7488-402: 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

7592-605: 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,

7696-555: The income level of specific MLM companies or MLM companies in general: In 2015, the Government of Bangladesh banned all types of domestic and foreign MLM trade in Bangladesh. Multi-level marketing ( simplified Chinese : 传销 ; traditional Chinese : 傳銷 ; pinyin : chuán xiāo ; lit. 'spread selling') was first introduced to mainland China by American, Taiwanese, and Japanese companies following

7800-504: The injecting of money from their own pockets, so that it can become the revenue and profit of the MLM company, of which the MLM company shares only a small proportion with a few individuals at the top of the MLM participant pyramid. Other than the few at the top, participants provide nothing more than their own financial loss for the company's own profit and the profit of the top few individual participants. The main sales pitch of MLM companies to their participants and prospective participants

7904-508: The largest proportion of participants must operate at a net loss (after expenses are deducted) so that the few individuals in the uppermost level of the MLM pyramid can derive their significant earnings. Said earnings are then emphasized by the MLM company to all other participants to encourage their continued participation at a continuing financial loss. Many MLM companies generate billions of dollars in annual revenue and hundreds of millions of dollars in annual profit. However, profits accrue to

8008-451: The money you make is based primarily on the number of distributors you recruit and your sales to them, rather than on your sales to people outside the plan who intend to use the products. In re Amway Corp. (1979), the Federal Trade Commission indicated that multi-level marketing was not illegal per se in the United States. However, Amway was found guilty of price fixing (by effectively requiring "independent" distributors to sell at

8112-424: 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

8216-412: 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

8320-400: The overwhelming majority of MLM participants cannot realistically make a net profit, let alone a significant net profit, but instead overwhelmingly operate at net losses, some sources have defined all MLM companies as a type of pyramid scheme, even if they have not been made illegal like traditional pyramid schemes through legislative statutes . MLM companies are designed to make profit for

8424-457: The owners/shareholders of the company and a few individual participants at the top levels of the MLM pyramid of participants. According to the U.S. Federal Trade Commission (FTC), some MLM companies already constitute illegal pyramid schemes even by the narrower existing legislation, exploiting members of the organization. Companies that employ the MLM business model have often faced criticism and lawsuits. Legal claims against MLM companies cover

8528-465: The plan a pyramid scheme. The critical question for the FTC is whether the revenues that primarily support the commissions paid to all participants are generated from purchases of goods and services that are not simply incidental to the purchase of the right to participate in a money-making venture. The Federal Trade Commission warns Not all multilevel marketing plans are legitimate. Some are pyramid schemes. It's best not to get involved in plans where

8632-415: 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

8736-544: 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

8840-494: 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

8944-470: 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

9048-492: The questionable use of evangelical discourse to promote the business (Höpfl & Maddrell, 1996), and the exploitation of personal relationships for financial gain (Fitzpatrick & Reynolds, 1997)". In China, volunteers working to rescue people from the schemes have been physically attacked. MLM companies are also criticized for being unable to fulfill their promises for the majority of participants due to basic conflicts with Western cultural norms. There are even claims that

9152-852: The regulation states having downlines is illegal). O'Regan wrote 'With this regulation China makes clear that while Direct Sales is permitted in the mainland, Multi-Level Marketing is not'. MLM companies have been made illegal in China as a mere variation of the traditional pyramid scheme and as disruptive to social and economic order. MLM companies have been trying to find ways around China's prohibitions, or have been developing other methods, such as direct sales, to take their products to China through retail operations. The Direct Sales Regulations limit direct selling to cosmetics, health food, sanitary products, bodybuilding equipment and kitchen utensils, and they require Chinese or foreign companies ("FIEs") who intend to engage into direct sale business in mainland China to apply for and obtain direct selling license from

9256-651: The same fixed price) and making exaggerated income claims. The FTC advises that multi-level marketing organizations with greater incentives for recruitment than product sales are to be viewed skeptically. The FTC also warns that the practice of getting commissions from recruiting new members is outlawed in most states as "pyramiding". Walter J. Carl stated in a 2004 Western Journal of Communication article that "MLM organizations have been described by some as cults (Butterfield, 1985), pyramid schemes (Fitzpatrick & Reynolds, 1997), or organizations rife with misleading, deceptive, and unethical behavior (Carter, 1999), such as

9360-461: 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

9464-439: 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

9568-399: 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

9672-405: 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

9776-482: 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

9880-412: 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

9984-559: The second is paid out from commissions based upon the wholesale purchases made by other sellers whom the participant has recruited to also sell product. In the organizational hierarchy of MLM companies, recruited participants (as well as those whom the recruit recruits) are referred to as one's downline distributors. MLM salespeople are, therefore, expected to sell products directly to end-user retail consumers by means of relationship referrals and word of mouth marketing, but more importantly they are incentivized to recruit others to join

10088-408: 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

10192-445: The success rate for breaking even or even making money are far worse than other types of businesses: "The vast majority of MLM companies are recruiting MLM companies, in which participants must recruit aggressively to profit. Based on available data from the companies themselves, the loss rate for recruiting MLM companies is approximately 99.9%; i.e., 99.9% of participants lose money after subtracting all expenses, including purchases from

10296-407: The transaction bears resemblance to both riba and gharar . Statistics Statistics (from German : Statistik , orig. "description of a state , a country" ) is the discipline that concerns the collection, organization, analysis, interpretation, and presentation of data . In applying statistics to a scientific, industrial, or social problem, it is conventional to begin with

10400-420: 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

10504-416: 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

10608-485: 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

10712-640: 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

10816-468: 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

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