**hypothesis**- In statistical hypothesis testing, the p-value or probability value is the probability for a given statistical model that, when the null hypothesis is true, the statistical summary (such as the sample mean difference between two compared groups) would be the same as or of greater magnitude than the actual observed results. (wikipedia.org)
- The p-value is used in the context of null hypothesis testing in order to quantify the idea of statistical significance of evidence. (wikipedia.org)
- X),} the probability of the hypothesis given the data, or Pr ( H ) , {\displaystyle \Pr(H),} the probability of the hypothesis being true, or Pr ( X ) , {\displaystyle \Pr(X),} the probability of observing the given data. (wikipedia.org)
- This is the inference framework in which the well-established methodologies of statistical hypothesis testing and confidence intervals are based. (wikipedia.org)
- A hypothesis is proposed for the statistical relationship between the two data sets, and this is compared as an alternative to an idealized null hypothesis of no relationship between two data sets. (wikipedia.org)
- 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. (wikipedia.org)
- Given a hypothesis about a population, for which we wish to draw inferences, statistical inference consists of (first) selecting a statistical model of the process that generates the data and (second) deducing propositions from the model. (wikipedia.org)
- The principle is akin to Occam's razor, which states that-all else being equal-the simplest hypothesis that explains the data should be selected. (wikipedia.org)
- Among the issues considered in statistical inference are the question of Bayesian inference versus frequentist inference, the distinction between Fisher's "significance testing" and Neyman-Pearson "hypothesis testing", and whether the likelihood principle should be followed. (wikipedia.org)

**Inference**- Frequentist inference is a type of statistical inference that draws conclusions from sample data by emphasizing the frequency or proportion of the data. (wikipedia.org)
- Other than frequentistic inference, the main alternative approach to statistical inference is Bayesian inference, while another is fiducial inference. (wikipedia.org)
- Frequentist inference has been associated with the frequentist interpretation of probability, specifically that any given experiment can be considered as one of an infinite sequence of possible repetitions of the same experiment, each capable of producing statistically independent results. (wikipedia.org)
- In this view, the frequentist inference approach to drawing conclusions from data is effectively to require that the correct conclusion should be drawn with a given (high) probability, among this notional set of repetitions. (wikipedia.org)
- Similarly, Bayesian inference has often been thought of as almost equivalent to the Bayesian interpretation of probability and thus that the essential difference between frequentist inference and Bayesian inference is the same as the difference between the two interpretations of what a "probability" means. (wikipedia.org)
- However, where appropriate, Bayesian inference (meaning in this case an application of Bayes' theorem) is used by those employing a frequentist interpretation of probabilities. (wikipedia.org)
- In contrast, a Bayesian approach to inference does allow probabilities to be associated with unknown parameters, where these probabilities can sometimes have a frequency probability interpretation as well as a Bayesian one. (wikipedia.org)
- Statistical inference is the process of deducing properties of an underlying probability distribution by analysis of data. (wikipedia.org)
- Statistical inference makes propositions about a population, using data drawn from the population with some form of sampling. (wikipedia.org)
- The conclusion of a statistical inference is a statistical proposition. (wikipedia.org)
- Any statistical inference requires some assumptions. (wikipedia.org)
- Descriptions of statistical models usually emphasize the role of population quantities of interest, about which we wish to draw inference. (wikipedia.org)
- Incorrect assumptions of 'simple' random sampling can invalidate statistical inference. (wikipedia.org)
- The Foundations of statistics concerns the epistemological debate in statistics over how one should conduct inductive inference from data. (wikipedia.org)

**analysis**- Most commonly used statistical procedures, for analysis and interpretation of statistical data, rest on assumptions about the behaviour of the data. (springer.com)
- The discussion focuses on the statistical interpretation of data rather than on the statistical procedures used in the data analysis. (springer.com)
- For an extensive discussion of the statistical analysis of biological data, the reader may refer to a multitude of books and articles. (springer.com)
- 1972. Statistical analysis of survival experiments. (springer.com)
- 1979. Log-linear models in the analysis of disease prevalence data from survival/sacrifice experiments. (springer.com)
- 1978. Exploratory analysis of disease prevalence data from survival/sacrifice experiments. (springer.com)
- The incumbent will report to the Chief of Administration and will conduct analysis of the division's case management systems performance using system documentation, and system generated data and metrics. (jobaps.com)
- Procedures-design phase: Decide on the specific procedures to be used in the gathering and statistical analysis of the data. (slideshare.net)
- Data-analysis phase: Analyze the data collected above using appropriate statistical procedures. (slideshare.net)
- Topics will include the formation of testable hypotheses, the selection and implementation of appropriate procedures, the statistical description and analysis of experimental data, and the interpretation of results. (amherst.edu)
- A one-hour weekly lab will be devoted to data analysis using statistical software.Requisite: PSYC 100 or consent of the instructor. (amherst.edu)
- The course will take a hands-on approach to research design, data collection, and data analysis. (amherst.edu)
- Time in class will be split between lectures, small group exercises and design of research projects, and data analysis using SPSS.Requisite: PSYC 122. (amherst.edu)
- For data statistical analysis and interpretation of results, software program "SPSS version 13" was used. (biomedsearch.com)
- The data type is a fundamental component of the semantic content of the variable, and controls which sorts of probability distributions can logically be used to describe the variable, the permissible operations on the variable, the type of regression analysis used to predict the variable, etc. (wikipedia.org)
- It uses techniques from spatial analysis, but also encompasses geographical activities such as the defining and naming of geographical regions for statistical purposes. (wikipedia.org)
- wherever data are collected and summarized or wherever any numerical information is analyzed or research is conducted, statistics are needed for sound analysis and interpretation of results. (wikipedia.org)
- There are several potential difficulties associated with the analysis of spatial data, among these are boundary delineation, modifiable areal units, and the level of spatial aggregation or scale. (wikipedia.org)
- For this type of data, analysts must use the same county or municipal boundaries delineated in the collected data for their subsequent analysis. (wikipedia.org)
- Since geographers are particularly concerned with the analysis of locational data, these descriptive spatial statistics (geostatistics) are often applied to summarize point patterns and to describe the degree of spatial variability of some phenomena. (wikipedia.org)
- In addition to detailed procedures and lists of required equipment and instruments, protocols often include information on safety precautions, the calculation of results and reporting standards, including statistical analysis and rules for predefining and documenting excluded data to avoid bias. (wikipedia.org)
- Methods of statistical analysis may be included to guide interpretation of the data. (wikipedia.org)
- Two main statistical methods are used in data analysis: descriptive statistics, which summarize data from 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). (wikipedia.org)
- Some definitions are: Merriam-Webster dictionary defines statistics as "a branch of mathematics dealing with the collection, analysis, interpretation, and presentation of masses of numerical data. (wikipedia.org)
- Statistics is a mathematical body of science that pertains to the collection, analysis, interpretation or explanation, and presentation of data, or as a branch of mathematics. (wikipedia.org)
- Inferential statistical analysis infers properties about a population: this includes testing hypotheses and deriving estimates. (wikipedia.org)
- In statistics, regression validation is the process of deciding whether the numerical results quantifying hypothesized relationships between variables, obtained from regression analysis, are acceptable as descriptions of the data. (wikipedia.org)
- Logistic regression with binary data is another area in which graphical residual analysis can be difficult. (wikipedia.org)
- Cross-validation is the process of assessing how the results of a statistical analysis will generalize to an independent data set. (wikipedia.org)

**Bias**- Many protocols include provisions for avoiding bias in the interpretation of results. (wikipedia.org)

**experimental**- Many of the topics discussed in this chapter pertain to experimental data in general, but the context of their use and examples given are in the field of toxicology. (springer.com)
- 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. (wikipedia.org)
- In application, a statistic is calculated from the experimental data, a probability of exceeding that statistic is determined and the probability is compared to a threshold. (wikipedia.org)

**calculation**- In statistics, the number of degrees of freedom is the number of values in the final calculation of a statistic that are free to vary. (wikipedia.org)

**measurement**- The work covers the origin, detection, and measurement of radiation and the statistical interpretation of the data. (valorebooks.com)
- ABSTRACT - Procedures for application of additive conjoint measurement to group rather than individual data are discussed. (acrwebsite.org)
- Additive conjoint measurement has been applied primarily to individual level data in marketing research studies. (acrwebsite.org)
- The concept of data type is similar to the concept of level of measurement, but more specific: For example, count data require a different distribution (e.g. a Poisson distribution or binomial distribution) than non-negative real-valued data require, but both fall under the same level of measurement (a ratio scale). (wikipedia.org)
- The issue of whether or not it 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. (wikipedia.org)
- citation needed] Measurement processes that generate statistical data are also subject to error. (wikipedia.org)

**probability**- These steps can be specified by the scientist so that there is a high probability of reaching a correct decision where, in this case, the probability relates to a yet to occur set of random events and hence does not rely on the frequency interpretation of probability. (wikipedia.org)
- The Bayesian approach allows these probabilities to have an interpretation as representing the scientist's belief that given values of the parameter are true [see Bayesian probability - Personal probabilities and objective methods for constructing priors]. (wikipedia.org)
- The result of a frequentist approach is either a "true or false" conclusion from a significance test or a conclusion in the form that a given sample-derived confidence interval covers the true value: either of these conclusions has a given probability of being correct, where this probability has either a frequency probability interpretation or a pre-experiment interpretation. (wikipedia.org)
- Probability interpretations German tank problem Everitt, B.S. (2002) The Cambridge Dictionary of Statistics, CUP ISBN 0-521-81099-X Neyman, J. (1937) "Outline of a Theory of Statistical Estimation Based on the Classical Theory of Probability", Philosophical Transactions of the Royal Society of London A, 236, 333-380. (wikipedia.org)
- Fully parametric: The probability distributions describing the data-generation process are assumed to be fully described by a family of probability distributions involving only a finite number of unknown parameters. (wikipedia.org)
- For example, every continuous probability distribution has a median, which may be estimated using the sample median or the Hodges-Lehmann-Sen estimator, which has good properties when the data arise from simple random sampling. (wikipedia.org)
- That is, it is not guaranteed to produce the true tree with high probability, given sufficient data. (wikipedia.org)
- for data collected over time, also plots of residuals against time drift in the errors (data collected over time): run charts of the response and errors versus time independence of errors: lag plot normality of errors: histogram and normal probability plot Graphical methods have an advantage over numerical methods for model validation because they readily illustrate a broad range of complex aspects of the relationship between the model and the data. (wikipedia.org)
- This can be due to incidental systematic error or flaws in the theory that generated an assumed family of probability distributions, or it may be that some observations are far from the center of the data. (wikipedia.org)
- Statistical significance is a measure of probability not practical importance. (wikipedia.org)

**descriptive statistics**- When this data is aggregated at different scales, the resulting descriptive statistics may exhibit variations, either in a systematic, predictable way, or in a more uncertain fashion. (wikipedia.org)
- Descriptive statistics is solely concerned with properties of the observed data, and does not assume that the data came from a larger population. (wikipedia.org)

**numerical**- One common situation when numerical validation methods take precedence over graphical methods is when the number of parameters being estimated is relatively close to the size of the data set. (wikipedia.org)

**assumptions**- Quite often these assumptions can be adequately justified, and the procedures accepted as fair and reasonable. (springer.com)
- But that is not always so, and it behoves the analyst to check consistency of the data with the assumptions. (springer.com)
- The parametric assumptions required for a statistical model would be somewhat restrictive relative to the nonparametric version as it is presently known. (acrwebsite.org)
- The statistical assumptions introduced by Thurstone can be interpreted to account for error at two levels: (1) the fallibility of an individual's choice on a single trial relative to some "true" choice over many similar trials and (2) the fallibility of an individual's judgment relative to some "true" judgment of a group. (acrwebsite.org)
- A statistical model is a set of assumptions concerning the generation of the observed data and similar data. (wikipedia.org)
- Non-parametric: The assumptions made about the process generating the data are much less than in parametric statistics and may be minimal. (wikipedia.org)

**standard deviation**- The result of this aggregation is that the standard deviation of the data in question is increased due to the variability among states. (wikipedia.org)
- In the case of normally distributed data, the three sigma rule means that roughly 1 in 22 observations will differ by twice the standard deviation or more from the mean, and 1 in 370 will deviate by three times the standard deviation. (wikipedia.org)

**variability**- 75 %) presented a test or statistical measure for the variability. (biomedcentral.com)

**practice**- Ms. Kang brings over 10 years' experience to the course which includes real-world case studies, enabling students to practice with clinical data. (prweb.com)
- Statistical geography is the study and practice of collecting, analysing and presenting data that has a geographic or areal dimension, such as census or demographics data. (wikipedia.org)
- The books lacked proofs or derivations of significance test statistics (which placed statistical practice in advance of statistical theory). (wikipedia.org)

**summarize**- Geographers use statistics in numerous ways:[citation needed] To describe and summarize spatial data. (wikipedia.org)

**methods**- Analyzes data gathered and develops solutions or alternative methods of proceeding. (jobaps.com)
- Makes recommendations for and assists in the implementation of new techniques or procedures to improve methods of operations, strengthen controls, and effectively utilize resources. (jobaps.com)
- Six months experience in designing studies which includes determining study goals and objectives, information needed, data sources, sampling and collection methods. (jobaps.com)

**outlier**- An outlier can cause serious problems in statistical analyses. (wikipedia.org)
- Outlier points can therefore indicate faulty data, erroneous procedures, or areas where a certain theory might not be valid. (wikipedia.org)

**aggregation**- 1. An aggregation procedure should retain information about the variation of subjects around a "group" rank. (acrwebsite.org)

**statisticians**- Increasingly required by pharmaceutical companies, understanding CDISC standards is becoming a critical skill to have for SAS programmers, statisticians, and clinical data managers. (prweb.com)
- When census data cannot be collected, statisticians collect data by developing specific experiment designs and survey samples. (wikipedia.org)
- Ideally, statisticians compile data about the entire population (an operation called census). (wikipedia.org)

**results**- Interpretation phase: Compare your results with the results predicted on the basis of your theory. (slideshare.net)
- In other words, an enumerative study is a statistical study in which the focus is on judgment of results, and an analytic study is one in which the focus is on improvement of the process or system which created the results being evaluated and which will continue creating results in the future. (wikipedia.org)
- The interpretation of results of a test or experiment is something else. (wikipedia.org)
- The next section details the types of plots to use to test different aspects of a model and gives the correct interpretations of different results that could be observed for each type of plot. (wikipedia.org)
- In addition to these serious methodological concerns, Alcock determined that if one were to remove the data related to one particular participant, the results of the study were no longer statistically significant. (wikipedia.org)
- Policy-relevant data about curriculum emphasis, technology use, and teacher preparation and training accompanies the TIMSS Advanced results. (wikipedia.org)

**goodness-of-**- A statistical interpretation of the model is proposed and a goodness-of-fit test examined. (acrwebsite.org)
- A statistical model would allow for error in the input judgments and yield an explicit parametric goodness-of-fit test. (acrwebsite.org)
- The validation process can involve analyzing the goodness of fit of the regression, analyzing whether the regression residuals are random, and checking whether the model's predictive performance deteriorates substantially when applied to data that were not used in model estimation. (wikipedia.org)

**parameters**- Estimates of statistical parameters can be based upon different amounts of information or data. (wikipedia.org)
- The degrees of freedom are also commonly associated with the squared lengths (or "sum of squares" of the coordinates) of such vectors, and the parameters of chi-squared and other distributions that arise in associated statistical testing problems. (wikipedia.org)
- In linear regression, the relationships are modeled using linear predictor functions whose unknown model parameters are estimated from the data. (wikipedia.org)
- This is because models which depend linearly on their unknown parameters are easier to fit than models which are non-linearly related to their parameters and because the statistical properties of the resulting estimators are easier to determine. (wikipedia.org)
- If the model has been estimated over some, but not all, of the available data, then the model using the estimated parameters can be used to predict the held-back data. (wikipedia.org)

**fits the data**- These possibilities must be searched to find a tree that best fits the data according to the optimality criterion. (wikipedia.org)
- An R2 (coefficient of determination) close to one does not guarantee that the model fits the data well, because as Anscombe's quartet shows, a high R2 can occur in the presence of misspecification of the functional form of a relationship or in the presence of outliers that distort the true relationship. (wikipedia.org)
- Therefore, if the residuals appear to behave randomly, it suggests that the model fits the data well. (wikipedia.org)
- On the other hand, if non-random structure is evident in the residuals, it is a clear sign that the model fits the data poorly. (wikipedia.org)

**describe**- 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. (wikipedia.org)

**drawn**- Training modules are designed to illustrate the procedure for recording indigenous knowledge systems using cases specifically drawn from developing country situations. (columbia.edu)
- A standard statistical procedure involves the test of the relationship between two statistical data sets, or a data set and synthetic data drawn from idealized model. (wikipedia.org)

**explanatory**- hat {\beta }}),} with yi denoting the ith response in the data set and xi the vector of explanatory variables, each set at the corresponding values found in the ith observation in the data set. (wikipedia.org)
- If the model fit to the data were correct, the residuals would approximate the random errors that make the relationship between the explanatory variables and the response variable a statistical relationship. (wikipedia.org)

**distributions**- The following table classifies the various simple data types, associated distributions, permissible operations, etc. (wikipedia.org)

**Tolerance**- Tolerance to the procedure and any undesirable effects noted during these sessions were recorded. (biomedsearch.com)
- 8 , 9 Accumulating data suggest that opioids lead to harmful side effects, tolerance and possibly altered brain development. (cmaj.ca)

**complexity**- Just how consistency can be checked depends on the complexity of the data. (springer.com)

**estimates**- 1977. Uncertainty estimates for low-dose-rate extrapolations of animal carcinogenicity data. (springer.com)
- 7 reviews (13 %) presented between-study variance estimates (τ 2 ) from random effects models and 3 of these presented a prediction interval or ellipse to facilitate interpretation. (biomedcentral.com)
- The presence of missing data or censoring may result in biased estimates and specific techniques have been developed to address these problems. (wikipedia.org)

**statistics**- For example, for the purposes of statistical geography, the Australian Bureau of Statistics uses the Australian Standard Geographical Classification, a hierarchical regionalisation that divides Australia up into states and territories, then statistical divisions, statistical subdivisions, statistical local areas, and finally census collection districts. (wikipedia.org)
- In the determination of internal boundaries this is also true, as these statistics may only have valid interpretations for the area and subarea configuration over which they are calculated. (wikipedia.org)
- In applying statistics to, e.g., a scientific, industrial, or social problem, it is conventional to begin with a statistical population or a statistical model process to be studied. (wikipedia.org)
- Statistics deals with all aspects of data including the planning of data collection in terms of the design of surveys and experiments. (wikipedia.org)
- While many scientific investigations make use of data, statistics is concerned with the use of data in the context of uncertainty and decision making in the face of uncertainty. (wikipedia.org)
- Naive interpretation of statistics derived from data sets that include outliers may be misleading. (wikipedia.org)
- In the development of classical statistics in the second quarter of the 20th century two competing models of inductive statistical testing were developed. (wikipedia.org)

**processes**- Interviews agency staff, observes work processes and gathers data relating to operational and managerial practices and procedures for use in evaluating services provided and/or determining compliance to goals and objectives. (jobaps.com)

**Therefore**- Therefore, some of the participating educational systems have trend data across assessments from 1995 to 2015. (wikipedia.org)

**Study**- 5. Phases of a Research Study Observation phase: Using the procedures devised in the previous step, collect your observations from the participants in your study. (slideshare.net)
- Analytic and enumerative statistical studies are two types of scientific studies: In any statistical study the ultimate aim is to provide a rational basis for action. (wikipedia.org)
- Deming summarized the distinction between enumerative and analytic studies as follows: Enumerative study: A statistical study in which action will be taken on the material in the frame being studied. (wikipedia.org)
- Analytic study: A statistical study in which action will be taken on the process or cause-system that produced the frame being studied. (wikipedia.org)
- In a statistical study, the frame is the set from which the sample is taken. (wikipedia.org)
- A statistical study can be enumerative or analytic, but it cannot be both. (wikipedia.org)

**Theory**- Although management theory likes to propound that every type of organizational structure needs to make strategic, tactical, and operational decisions, new procedures have started to emerge that work best with teams. (wikipedia.org)
- Regardless of the logical possible values, all of these data types are generally coded using real numbers, because the theory of random variables often explicitly assumes that they hold real numbers. (wikipedia.org)
- This exchange of arguments occurred 15 years after textbooks began teaching a hybrid theory of statistical testing. (wikipedia.org)

**depends**- But the mapping of computer science data types to statistical data types depends on which categorization of the latter is being implemented. (wikipedia.org)

**different**- Use of data requires knowledge about the different sources of uncertainty. (wikipedia.org)
- However, exactly the same procedures can be developed under a subtly different formulation. (wikipedia.org)
- if it is confirmed, different modeling procedures are called for. (wikipedia.org)
- As illustrated in this case, outliers may indicate data points that belong to a different population than the rest of the sample set. (wikipedia.org)

**model**- These individual level applications often result in important insights but if the model is to develop its full potential for practical marketing problems then changes should be made which also allow its use on aggregate data. (acrwebsite.org)
- These problems could be solved more reasonably if the additive conjoint model were statistical in nature rather than mathematical. (acrwebsite.org)
- Most applications fall into one of the following two broad categories: If the goal is prediction, or forecasting, or error reduction, linear regression can be used to fit a predictive model to an observed data set of y and X values. (wikipedia.org)
- Given a data set { y i , x i 1 , … , x i p } i = 1 n {\displaystyle \{y_{i},\,x_{i1},\ldots ,x_{ip}\}_{i=1}^{n}} of n statistical units, a linear regression model assumes that the relationship between the dependent variable yi and the p-vector of regressors xi is linear. (wikipedia.org)
- One problem with the R2 as a measure of model validity is that it can always be increased by adding more variables into the model, except in the unlikely event that the additional variables are exactly uncorrelated with the dependent variable in the data sample being used. (wikipedia.org)
- A basic, though not quantitatively precise, way to check for problems that render a model inadequate is to conduct a visual examination of the residuals (the mispredictions of the data used in quantifying the model) to look for obvious deviations from randomness. (wikipedia.org)
- Serial correlation of the residuals can indicate model misspecification, and can be checked for with the Durbin-Watson statistic. (wikipedia.org)

**implementation**- Documents findings of studies and prepares recommendations for implementation of new systems, procedures, or organizational changes. (jobaps.com)

**laboratory**- Protocols written for use by a specific laboratory may incorporate or reference standard operating procedures (SOP) governing general practices required by the laboratory. (wikipedia.org)

**dependent variable**- The decision as to which variable in a data set is modeled as the dependent variable and which are modeled as the independent variables may be based on a presumption that the value of one of the variables is caused by, or directly influenced by the other variables. (wikipedia.org)

**problems**- Use of data requires also understanding of the distinction between enumerative studies and analytic problems. (wikipedia.org)

**process**- It is prediction that a specific change in a process or procedure will be a wise choice, or that no change would be better. (wikipedia.org)
- In addition, TIMSS provides contextual data on crucial curricular, instructional, and resource-related factors that can impact the teaching and learning process. (wikipedia.org)

**subsequent**- Acute pain caused by skin-breaking procedures can lead to physiologic instability and behavioural distress, and it has downstream effects on subsequent pain processing, development and stress responsivity. (cmaj.ca)
- Achievement data from subsequent TIMSS assessment cycles were linked to these scales so that increases or decreases in average achievement may be monitored across assessments. (wikipedia.org)

**Often**- Such distinctions can often be loosely correlated with data type in computer science, in that dichotomous categorical variables may be represented with 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 computation. (wikipedia.org)
- Data that cannot be described using a single number are often shoehorned into random vectors of real-valued random variables, although there is an increasing tendency to treat them on their own. (wikipedia.org)
- In statistical testing applications, often one isn't directly interested in the component vectors, but rather in their squared lengths. (wikipedia.org)

**estimation**- until recently, it was the only widely used character-based tree estimation method used for morphological data. (wikipedia.org)

**sample**- The sample size is another important concept and can lead to biased data simply due to an unlikely event. (wikipedia.org)
- In most larger samplings of data, some data points will be further away from the sample mean than what is deemed reasonable. (wikipedia.org)

**problem**- See also: Modifiable areal unit problem In many cases the subdivision of spatial data has already been determined, this is evident in demographic datasets, as the available information will be grouped into their respective counties or municipalities. (wikipedia.org)
- However, the data themselves do not lead to a simple, arithmetic solution to the problem. (wikipedia.org)
- Along with the overall students' achievement data, TIMSS comprehensive assessments include data on student performance in various mathematics and science domains (algebra, geometry, biology, chemistry, etc.) and on performance in the problem solving challenges in each of these contexts. (wikipedia.org)

**given**- In this issue of CMAJ , 2 randomized controlled trials evaluate the efficacy of sucrose given orally and a topical coolant spray for reducing acute pain due to skin-breaking procedures. (cmaj.ca)

**differ**- The procedure in newly-diagnosed patients does not differ from previously diagnosed patients with the exception of the rate of referral to a specialist. (springer.com)
- Additionally, the pathological appearance of outliers of a certain form appears in a variety of datasets, indicating that the causative mechanism for the data might differ at the extreme end (King effect). (wikipedia.org)

**census**- Socio-economic data may be available at a variety of scales, for example: municipalities, regional districts, census tracts, enumeration districts, or at the provincial/state level. (wikipedia.org)

**mechanisms**- i.e. that the data-generating mechanisms really have been correctly specified. (wikipedia.org)