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Topic: Statistical assumptions

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	Thomson - Introduction to Probability & Statistics 12e (Site not responding. Last check: 2007-09-11)
		Introduction to Probability and Statistics 12e, by William Mendenhall, Robert J. Beaver, and Barbara M. Beaver, has been used by hundreds of thousands of students since its first edition.
		The authors integrate modern technology, including computational software and interactive visual tools, to facilitate statistical reasoning as well as the understanding and interpretation of statistical results.
		In addition to showing how to apply statistical concepts, the authors explain how to analyze data, how to evaluate the validity of the assumptions behind statistical tests, and what to do when statistical assumptions have been violated.
	www.thomson.com /content/learning/brand_overviews/pf_intro_probability (358 words)

	Glossary
		Statistical methods such as regression require the data to satisfy various conditions, for example that the data follow a normal distribution and are independent.
		In a statistical hypothesis test, the P value is the probability of observing a test statistic at least as extreme as the value actually observed, assuming that the null hypothesis is true.
		Statistics that are used to estimate unknown parameters are called estimators: for example, the mean of a sample is a statistic that is commonly used as an estimator of the population mean.
	www.ilir.uiuc.edu /courses/lir593/493_glossary.htm (4141 words)

	Pitfalls of Data Analysis. ERIC/AE Digest.
		Statistical methodology assists researchers in making inferences about a large group (a population) based on observations of a smaller subset of that group (a sample).
		While assumption of normality implies that the scores in each treatment group are distributed in a way that corresponds to the so-called "normal" (or Gaussian) distribution, the assumption of independence indicates that each of the subject's scores are uninfluenced by the scores of anyone else who was tested.
		Statistical power refers to the probability of avoiding a Type II error and depends on the ability of one's statistical test to detect true differences of a particular size.
	www.ericdigests.org /1998-1/data.htm (1664 words)

	Methods for Investigating Goal-Oriented Psi
		Normal statistical methods are based on the assumption that the aggregation of data from multiple or repeated measurements of an effect will lead to increased reliability or accuracy of estimation.
		This assumption leads directly to the expectation that the z score (which is the square root of chi-square) is linearly related to the square root of sample size.
		This assumption requires that more information is transmitted or utilized for cases with small a priori probabilities of a hit, and, as noted in the previous sections, does not appear consistent with available data in other contexts.
	jeksite.org /psi/jp95.htm (5577 words)

	PROPHET StatGuide: Glossary
		The null hypothesis for a statistical test is the assumption that the test uses for calculating the probability of observing a result at least as extreme as the one that occurs in the data at hand.
		The chi-square test statistic is basically the sum of the squares of the differences between the observed and expected frequencies, with each squared difference divided by the corresponding expected frequency.
		It provides a t statistic that asymptotically (that is, as the sample sizes become large) approaches a t distribution, allowing for an approximate t test to be calculated when the population variances are not equal.
	www.basic.northwestern.edu /statguidefiles/sg_glos.html (7880 words)

	Statistics Solutions: Testing of Assumptions
		Parametric statistics are those which assume a certain distribution of the data (usually the normal distribution), assume an interval level of measurement, and assume homogeneity of variances when two or more samples are being compared.
		It is good practice to run descriptive statistics on one's data so that one is confident that data are generally as expected in terms of means and standard deviations, and there are no out-of-bounds entries beyond the expected range.
		That is, a significant W statistic causes the researcher to reject the assumption that the distribution is normal.
	www.statisticssolutions.com /Testing-Of-Assumptions.htm (5321 words)

	Personal Privacy in an Information Society: The Report of the Privacy Protection Study Commission
		The variety of research and statistical studies that require the collection of information in individually identifiable form is limited only by the interests and concerns of society for human wants and needs, and by the assumptions of researchers and statisticians as to the topics that merit exploration.
		Research and statistical activities are becoming more dependent on information originally collected or maintained for administrative purposes, a dependence that attenuates the relationship between researcher and data subject and weakens the individual's ability to control the way information about him is collected and used.
		Statistical methods can be descriptive, that is, any treatment designed to summarize or describe important features of data, or inferential, that is, techniques for arriving at generalizations that go beyond the sample being analyzed.
	www.epic.org /privacy/ppsc1977report/c15.htm (14988 words)

	[No title]
		This study is important because most prior quantitative research studies in the field of entrepreneurship have utilized parametric statistical data analysis techniques without explicitly checking or fully discussing whether the assumptions underlying the theoretical development of such techniques were fully satisfied with the data utilized in such studies.
		The assumptions underlying the theoretical development of the parametric statistical data analysis techniques employed in this research require that the dependent variables have: (1) normal distributions; (2) equal variances for each of the sampled populations (3) symmetric distributions; (4) continuous distributions; and (5) independence of observations.
		By contrast, the assumptions underlying the theoretical development of the parametric statistical data analysis techniques employed in this research require that the dependent variables have: (1) measurement on at least an ordinal scale; (2) continuous distributions; and (3) independence of observations (Daniel, 1990; Gibbons, 1985).
	www.babson.edu /entrep/fer/papers97/robinson/rob2.htm (771 words)

	1.3.3.32. 4-Plot
		If the 4 underlying assumptions of a typical measurement process hold, then the above 4 plots will have a characteristic appearance (see the normal random numbers case study below); if any of the underlying assumptions fail to hold, then it will be revealed by anomalous appearance in one or more of the plots.
		the assumption of a common, normal distribution is violated as shown by the histogram in the lower left corner and the normal probability plot in the lower right corner.
		If the 4 assumptions do not hold, then we have a process which is drifting (with respect to location, variation, or distribution), is unpredictable, and is out of control.
	www.6sigma.us /handbook/eda/section3/4plot.htm (752 words)

	GENETIC EVIDENCE IN PATERNITY CASES - DNA
		The statistical assumptions made during paternity testing can cause the results of testing to be misleading and unreliable.
		While the focus of this article is on a serious error in statistical methodology frequently occurring in paternity testing, the same error may occur in criminal DNA testing with dire consequences.
		An attorney practicing criminal or family law needs to understand the statistical assumptions that may cause the results of genetic testing to be misleading and unreliable.
	www.fa-ir.org /alabama/cs/cs_dna.htm (1447 words)

	1.3.3.32. 4-Plot
		If the 4 underlying assumptions of a typical measurement process hold, then the above 4 plots will have a characteristic appearance (see the normal random numbers case study below); if any of the underlying assumptions fail to hold, then it will be revealed by an anomalous appearance in one or more of the plots.
		If the 4 assumptions do not hold, then we have a process that is drifting (with respect to location, variation, or distribution), is unpredictable, and is out of control.
		If the fixed distribution assumption holds (in particular, if the fixed normal distribution assumption holds), then the histogram will be bell-shaped and the normal probability plot will be approximatelylinear.
	www.itl.nist.gov /div898/handbook/eda/section3/4plot.htm (771 words)

	Pitfalls of Data Analysis
		We are all familiar with the disparaging quotes about statistics (including "There are three kinds of lies: lies, damned lies, and statistics", attributed to either Mark Twain or Disraeli, depending on whom you ask), and it's no secret that many people harbor a vague distrust of statistics as commonly used.
		The core value of statistical methodology is its ability to assist one in making inferences about a large group (a population) based on observations of a smaller subset of that group (a sample).
		The assumption regarding independence of observations is more troublesome, both because it underlies nearly all of the most commonly used statistical procedures, and because it is so frequently violated in practice.
	my.execpc.com /4A/B7/helberg/pitfalls (4269 words)

	The Department of Statistics: Courses
		The first semester in a two-semester course in mathematical statistics: random variables and their distributions, small and large sample theorems of hypothesis testing, point estimation, and confidence intervals; topics such as exponential families, univariate and multivariate linear models and nonparametric inference will also be discussed.
		Statistical inference and the testing of hypotheses multiple and partial correlation analysis; analysis of variance and regression.
		Statistical inference, decision theory, and simulation as applied to assist in making individual clinical decisions, policy recommendations, and as a guide to study design and research; topics include statistical decision theory, decision analysis, decision trees, markvo models and simulation, cost-effectiveness analysis, meta-analysis, and sensitivity analysis.
	cohesion.rice.edu /engineering/statistics/courses.cfm (1859 words)

	Multivariate Analysis Notes
		The type of model, or statistical test we choose to analyze our data with will depend upon the level at which the data is measured.
		For most statistical procedures the distinction between interval and ratio does not matter and it is common to use the term "interval" to refer to ratio data as well.
		In the field of statistics, model means a simplified version of reality specified in mathematical and/or graphical form in which some unknown characteristics (or parameters) of the target population are estimated.
	www.mrs.umn.edu /~sungurea/multivariatestatistics/notesmain1.html (1252 words)

	ESA journals -- Statistical guidelines
		Thus, the assumptions and (or) the model underlying unusual statistical analyses must be clearly stated and results must be sufficiently detailed.
		The purpose of statistical analysis is to increase the conciseness, clarity and objectivity with which results are presented and interpreted, and where an analysis does not serve those ends it probably is inappropriate.
		Unusual statistical procedures need to be explained in sufficient detail, including references if appropriate, for the reader to reconstruct the analysis.
	esapubs.org /esapubs/Statistics.htm (446 words)

	Information for Collaborators
		The critical issue in choosing the statistical methods to be used in the analysis plan is whether the specific aims are fulfilled and the key hypotheses tested.
		This assumption is violated for observations on the same person (or animal) and sometimes when observations are clustered, such as for utilization data from patients treated by the same physician.
		This occurs when the issues to be considered in the choice of statistical techniques leads to situations where no appropriate methods exist or as an alternative method when the assessment of statistical assumptions reveals a problem.
	www.biostat.iupui.edu /Collaborators/Biostat4.htm (1939 words)

	Structural Equation Modeling using AMOS: An Introduction (Site not responding. Last check: 2007-09-11)
		Statistical methods in general have this property, but SEM users and creators seem to have elevated specialized language to a new level.
		This statistical estimation is accomplished in much the same way that an exploratory factor analysis infers the presence of latent factors from shared variance among observed variables.
		Once you have obtained a model that fits well and that is theoretically consistent and it provides statistically significant parameter estimates, you must interpret it in the light of your research questions and then distill your results in written form for publication.
	www.utexas.edu /its/rc/tutorials/stat/amos (9978 words)

	Grade inflation
		The assumption was that grades (like all the other psychological variables that were being studied by scientific psychology at the time) should be normally distributed.
		It was hoped that by statistically adjusting the skew, the curve could be made to fit the increasingly select groups of students in higher level courses.
		While the statistical assumptions underlying curving were flawed, an even greater flaw in the logic of statistical grade adjustment had been overlooked.
	people.eku.edu /falkenbergs/grdinfla.htm (3742 words)

	t test (Site not responding. Last check: 2007-09-11)
		Statistical tests of the homogeneity assumption are provided by the spread-level tests within the explore procedure.
		The statistics in the row labeled "Equal variances not assumed" should be used whenever Levene's test is significant, that is, when the variances are not homogeneous.
		When reporting the results of any statistic the focus of description should be on the relative effects of the treatment for the participants in each group rather than on the statistic itself.
	web.uccs.edu /lbecker/SPSS/ttest.htm (4057 words)

	Purvis Lab @ IC : Statistical Assumptions and Independent Contrasts
		The model predicts that the absolute value of the standardised contrast should be independent of the estimated value of the character for the node at which the contrast was taken.
		Regression models make the assumption that the residual variation or scatter around the regression line has the same mean and variance at all points along the line.
		Note that the p-values of the assumption checks may differ slightly depending on which variable is the main predictor.
	www.bio.ic.ac.uk /evolve/software/caic/assumptions.html (1055 words)

	Strategic Financial Planning System - Risk Analysis (Site not responding. Last check: 2007-09-11)
		The Risk Analysis Tool creates the appropriate input screen for the assumptions and distributions you specify, and you can use the unique SFPS data entry tools to enter statistical assumptions easily.
		Statistical Distribution—A line graph showing the mean, one standard deviation below and above the mean, and 5th and 95th percentiles.
		Risk Analysis assumptions and results can be printed and result graphs can be printed or copied to the Windows Clipboard for placement in other software applications.
	www.ferox.com /sfps/risk.html (762 words)

	Chapter 8: Statistical Description of Fourier Coefficients
		Another implication is that each sample of noise is statistically independent of all of the other noise values and yet is drawn from a population which has the same statistical properties as all of the other samples.
		In statistics the standard deviation of the mean of D data values is usually called the standard error of the mean and is equal to σ/√D, where s is the standard deviation of the population from which the data are drawn.
		This is not surprising because the central limit theorem of probability theory states that the sum of a large number of independent variables tends to Gaussian regardless of the probability distributions of the individual variables.
	research.opt.indiana.edu /Library/FourierBook/ch08.html (2986 words)

	GSBS Course: Introduction to Biostatistics and Bioinformatics
		This course is a one-semester overview of statistical concepts most often used in the design and analysis of biomedical studies.
		Because this course is primarily for statistics majors, the applied methods will be related to theory whenever practical.
		Emphasis will also be given to identifying statistical assumptions and performing analyses to verify these assumptions.
	www.uth.tmc.edu /gsbs/courses/gs010033.html (151 words)

	Statistical inference - Wikipedia, the free encyclopedia
		It has been suggested that this article or section be merged with inferential statistics.
		Inferential statistics or statistical induction comprises the use of statistics to make inferences concerning some unknown aspect of a population.
		Statistical inference is inference about a population from a random sample drawn from it or, more generally, about a random process from its observed behavior during a finite period of time.
	en.wikipedia.org /wiki/Statistical_inference (159 words)

	Statistical assumptions - Wikipedia, the free encyclopedia
		Statistical assumptions are general assumptions about statistical populations.
		Statistics, like all mathematical disciplines, does not generate valid conclusions from nothing.
		In order to generate interesting conclusions about real statistical populations, it is usually required to make some background assumptions.
	en.wikipedia.org /wiki/Statistical_assumptions (121 words)

	Trader's Roundtable :: View topic - How to judge whether a statistical technique is robust?
		A robust statistical estimator is one that is not perturbed much by mistaken assumptions about the nature of the distribution.
		I have no idea specifically what he uses of course, but id think summary statistics, converted into useful metrics that do not rely on assumptions like a normal distribution, would be something of what he is talking about.
		A statistical test or procedure is robust if it maintains the significance level close to a desired significance level a for a wide variety of underlying probability distributions with good power for all the distributions.
	www.tradingblox.com /forum/viewtopic.php?p=8821 (1041 words)

	Research_Proposal_Elements Part 3
		The distribution of the ages of patients undergoing and not undergoing colonoscopy will be examined with descriptive statistics (median, mean, standard deviation) and boxplots.
		If the normality and equal variance assumptions are satisfied, the difference in mean age in the two groups will be tested using a t test.
		If the assumptions are not met, a non-parametric test will be used (Wilcoxon rank-sum test).
	www.ucalgary.ca /md/CAH/research/prop_el3.htm (891 words)

	Agroportal - Mercados Agrícolas (Site not responding. Last check: 2007-09-11)
		This publication provides a picture of the likely developments of agricultural markets up to 2009, based on a certain number of assumptions and on the statistical information available in April 2002.
		This publication provides a picture of the likely developments of agricultural markets up to 2012, based on a certain number of assumptions and on the statistical information available in May 2005.
		This publication provides a picture of the likely medium-term developments of agricultural markets, based on a certain number of assumptions and on the statistical information available at the end of November 2006.
	www.agroportal.pt /agros/mercados.htm (1104 words)

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