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Data Manipulation
Statistics, when used in a misleading fashion, can trick the casual observer into believing something other than what the data shows. That is, a misuse of statistics occurs when a statistical argument asserts a falsehood. In some cases, the misuse may be accidental. In others, it is purposeful and for the gain of the perpetrator. When the statistical reason involved is false or misapplied, this constitutes a statistical fallacy. The false statistics trap can be quite damaging for the quest for knowledge. For example, in medical science, correcting a falsehood may take decades and cost lives. Misuses can be easy to fall into. Professional scientists, even mathematicians and professional statisticians, can be fooled by even some simple methods, even if they are careful to check everything. Scientists have been known to fool themselves with statistics due to lack of knowledge of probability theory and lack of standardization of their tests. Definition, limitations and context One ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Statistics
Statistics (from German: '' Statistik'', "description of a state, a country") is the discipline that concerns the collection, organization, analysis, interpretation, and presentation of data. In applying statistics to a scientific, industrial, or social problem, it is conventional to begin with a statistical population or a statistical model to be studied. Populations can be diverse groups of people or objects such as "all people living in 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.Dodge, Y. (2006) ''The Oxford Dictionary of Statistical Terms'', Oxford University Press. 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 the sample to the population as a whole. An ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Lady Tasting Tea
In the design of experiments in statistics, the lady tasting tea is a randomized experiment devised by Ronald Fisher and reported in his book ''The Design of Experiments'' (1935). The experiment is the original exposition of Fisher's notion of a null hypothesis, which is "never proved or established, but is possibly disproved, in the course of experimentation".OED quote: 1935 R. A. Fisher, ''The Design of Experiments'' ii. 19, "We may speak of this hypothesis as the 'null hypothesis' ..the null hypothesis is never proved or established, but is possibly disproved, in the course of experimentation." The lady in question ( Muriel Bristol) claimed to be able to tell whether the tea or the milk was added first to a cup. Fisher proposed to give her eight cups, four of each variety, in random order. One could then ask what the probability was for her getting the specific number of cups she identified correct, but just by chance. Fisher's description is less than 10 pages in length ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Sampling Error
In statistics, sampling errors are incurred when the statistical characteristics of a population are estimated from a subset, or sample, of that population. Since the sample does not include all members of the population, statistics of the sample (often known as estimators), such as means and quartiles, generally differ from the statistics of the entire population (known as parameters). The difference between the sample statistic and population parameter is considered the sampling error.Sarndal, Swenson, and Wretman (1992), Model Assisted Survey Sampling, Springer-Verlag, For example, if one measures the height of a thousand individuals from a population of one million, the average height of the thousand is typically not the same as the average height of all one million people in the country. Since sampling is almost always done to estimate population parameters that are unknown, by definition exact measurement of the sampling errors will not be possible; however they can often be ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Central Limit Theorem
In probability theory, the central limit theorem (CLT) establishes that, in many situations, when independent random variables are summed up, their properly normalized sum tends toward a normal distribution even if the original variables themselves are not normally distributed. The theorem is a key concept in probability theory because it implies that probabilistic and statistical methods that work for normal distributions can be applicable to many problems involving other types of distributions. This theorem has seen many changes during the formal development of probability theory. Previous versions of the theorem date back to 1811, but in its modern general form, this fundamental result in probability theory was precisely stated as late as 1920, thereby serving as a bridge between classical and modern probability theory. If X_1, X_2, \dots, X_n, \dots are random samples drawn from a population with overall mean \mu and finite variance and if \bar_n is the sample mean of ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Design Of Experiments
The design of experiments (DOE, DOX, or experimental design) is the design of any task that aims to describe and explain the variation of information under conditions that are hypothesized to reflect the variation. The term is generally associated with experiments in which the design introduces conditions that directly affect the variation, but may also refer to the design of quasi-experiments, in which natural conditions that influence the variation are selected for observation. In its simplest form, an experiment aims at predicting the outcome by introducing a change of the preconditions, which is represented by one or more independent variables, also referred to as "input variables" or "predictor variables." The change in one or more independent variables is generally hypothesized to result in a change in one or more dependent variables, also referred to as "output variables" or "response variables." The experimental design may also identify control variables that must b ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Experiment
An experiment is a procedure carried out to support or refute a hypothesis, or determine the efficacy or likelihood of something previously untried. Experiments provide insight into Causality, cause-and-effect by demonstrating what outcome occurs when a particular factor is manipulated. Experiments vary greatly in goal and scale but always rely on repeatable procedure and logical analysis of the results. There also exist natural experiment, natural experimental studies. A child may carry out basic experiments to understand how things fall to the ground, while teams of scientists may take years of systematic investigation to advance their understanding of a phenomenon. Experiments and other types of hands-on activities are very important to student learning in the science classroom. Experiments can raise test scores and help a student become more engaged and interested in the material they are learning, especially when used over time. Experiments can vary from personal and in ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Placebo
A placebo ( ) is a substance or treatment which is designed to have no therapeutic value. Common placebos include inert tablets (like sugar pills), inert injections (like saline), sham surgery, and other procedures. In general, placebos can affect how patients perceive their condition and encourage the body's chemical processes for relieving pain and a few other symptoms, but have no impact on the disease itself. Improvements that patients experience after being treated with a placebo can also be due to unrelated factors, such as regression to the mean (a statistical effect where an unusually high or low measurement is likely to be followed by a less extreme one). The use of placebos in clinical medicine raises ethical concerns, especially if they are disguised as an active treatment, as this introduces dishonesty into the doctor–patient relationship and bypasses informed consent. While it was once assumed that this deception was necessary for placebos to have any effect, the ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Overgeneralization
A faulty generalization is an informal fallacy wherein a conclusion is drawn about all or many instances of a phenomenon on the basis of one or a few instances of that phenomenon. It is similar to a proof by example in mathematics. It is an example of jumping to conclusions. For example, one may generalize about all people or all members of a group, based on what one knows about just one or a few people: * If one meets a rude person from a given country X, one may suspect that most people in country X are rude. * If one sees only white swans, one may suspect that all swans are white. Expressed in more precise philosophical language, a fallacy of defective induction is a conclusion that has been made on the basis of weak premises, or one which is not justified by sufficient or unbiased evidence. Unlike fallacies of relevance, in fallacies of defective induction, the premises are related to the conclusions, yet only weakly buttress the conclusions, hence a faulty generalization ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
:Category:Statistical Paradoxes ...
{{Commons Mathematical paradoxes Paradoxes A paradox is a logically self-contradictory statement or a statement that runs contrary to one's expectation. It is a statement that, despite apparently valid reasoning from true premises, leads to a seemingly self-contradictory or a logically u ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Linear Regression
In statistics, linear regression is a linear approach for modelling the relationship between a scalar response and one or more explanatory variables (also known as dependent and independent variables). The case of one explanatory variable is called '' simple linear regression''; for more than one, the process is called multiple linear regression. This term is distinct from multivariate linear regression, where multiple correlated dependent variables are predicted, rather than a single scalar variable. In linear regression, the relationships are modeled using linear predictor functions whose unknown model parameters are estimated from the data. Such models are called linear models. Most commonly, the conditional mean of the response given the values of the explanatory variables (or predictors) is assumed to be an affine function of those values; less commonly, the conditional median or some other quantile is used. Like all forms of regression analysis, linear regression focuse ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Simple Linear Regression
In statistics, simple linear regression is a linear regression model with a single explanatory variable. That is, it concerns two-dimensional sample points with one independent variable and one dependent variable (conventionally, the ''x'' and ''y'' coordinates in a Cartesian coordinate system) and finds a linear function (a non-vertical straight line) that, as accurately as possible, predicts the dependent variable values as a function of the independent variable. The adjective ''simple'' refers to the fact that the outcome variable is related to a single predictor. It is common to make the additional stipulation that the ordinary least squares (OLS) method should be used: the accuracy of each predicted value is measured by its squared '' residual'' (vertical distance between the point of the data set and the fitted line), and the goal is to make the sum of these squared deviations as small as possible. Other regression methods that can be used in place of ordinary least squar ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
