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Censoring Nearly every sample contains some cases that do not experience an event. If the dependent variable is the time of the event, what do you do with these censored cases. Time-dependent covariate Many explanatory variables like income or blood pressure change in value over time. How do you put such variables in a regression analysis. Makeshift solutions to these questions can lead to severe biases. Survival methods are explicitly designed to deal with censoring and time-dependent covariates in a statistically correct way.

Originally developed by biostatisticians, these methods have become popular in sociology, demography, psychology, economics, political science, and marketing. In Short, survival Analysis is a group of statistical methods for analysis and interpretation of survival data. Even though survival analysis can be used in a wide variety of applications e. insurance, engineering, and sociologythe main application is for analyzing clinical trials data.

Survival and hazard functions, the methods of estimating parameters and testing hypotheses that are the main part of analyses of survival data. Main topics relevant to survival data analysis are Survival and hazard functions, Types of censoring, Estimation of survival and hazard functions the Kaplan-Meier and life table estimators, Simple life tables, Peto s Logrank with trend test and hazard ratios and Wilcoxon test, can be stratifiedWei-Lachin, Comparison of survival functions The logrank and Mantel-Haenszel tests, The proportional hazards model time independent and time dependent covariates, The logistic regression model, and Methods for determining sample sizes.

In the last few years the survival analysis software available in several of the standard statistical packages has experienced a major increment in functionality, and is no longer limited to the triad of Kaplan-Meier curves, logrank tests, and simple Cox models. Further Readings Hosmer D. Lemeshow, Applied Survival Analysis Regression Modeling of Time to Event DataWiley, 1999. Swanepoel, and N.

Veraverbeke, The modified bootstrap error process for Kaplan-Meier quantiles, Statistics Probability Letters58, 31-39, 2002.Survival Analysis A Self-Learning TextSpringer-Verlag, New York, 1996.Statistical Methods for Survival Data AnalysisWiley, 1992. Grambsch, Modeling Survival Data Extending the Cox ModelSpringer 2000. This book provides thorough discussion on Cox PH model. Since the first author is also the author of the survival package in S-PLUS R, the book can be used closely with the packages in addition to SAS.

Association Among Nominal Variables. Spearman s Correlation, and Kendall s tau Application. Two measures are Spearman s rank order correlation, and Kendall s tau. Further Readings For more details see, e. Is Var1 ordered the same as Var2.Fundamental Statistics for the Behavioral Sciencesby David C. Howell, Duxbury Pr. Repeated Measures and Longitudinal Data. For those items yielding a score on a iq option wallpaper, the conventional t-test for correlated samples would be appropriate, or the Wilcoxon signed-ranks test.

What Is a Systematic Review. There are few important questions in health care which can be informed by consulting the result of a single empirical study. Systematic reviews attempt to provide answers to such problems by identifying and appraising all available studies within the relevant focus and synthesizing their results, all according to explicit methodologies. The review process places special emphasis on assessing and maximizing the value of data, both in issues of reducing bias and minimizing random error.

The systematic review method is most suitably applied to questions of patient treatment and management, although it has also been applied to answer questions regarding the value of diagnostic test results, likely prognoses and the cost-effectiveness of health care. Information Theory. Shannon defined a measure of entropy as. that, when applied to an information source, could determine the capacity of the channel required to transmit the source as encoded binary digits.

Shannon s measure of entropy is taken as a measure of the information contained in a message. This is unlike to the portion of the message that is strictly determined hence predictable by inherent structures. Entropy as defined by Shannon is closely related to entropy as defined by physicists in statistical thermodynamics. This work was the inspiration for adopting the term entropy in information theory. Other useful measures of information include mutual information which is a measure of the correlation between two event sets.

Mutual information is defined for two events X and Y as. M X, Y H X, Y - H X - H Y. where H X, Y is the join entropy defined as. H X, Y - S p x iy i log p x iy i. Mutual information is closely related to the log-likelihood ratio test for multinomial distribution, and to Pearson s Chi-square test. The field of Information Science has since expanded to cover the full range of techniques and abstract descriptions for the storage, retrieval and transmittal of information.

Incidence and Prevalence Rates. Prevalence rate PR measures the number of cases that are present at a specified period of time. It is defined as Number of cases present at a specified period of time divides by Number of persons at risk at that specified time. These two measures are related when considering the average duration D. That is, PR IR. Note that, for example, county-specific disease incidence rates can be unstable due to small populations or low rates.

In epidemiology one can say that IR reflects probability to Become thick at given age, while the PR reflects probability to Be iq option wallpaper at given age. Other topics in clinical epidemiology include the use of receiver operator curves, and the sensitivity, specificity, predictive value of a test. Further Readings Kleinbaum D. Kupper, and K. Muller, Applied Regression Analysis and Other Multivariable MethodsWadsworth Publishing Company, 1988.

Miettinen O.Theoretical EpidemiologyDelmar Publishers, 1986. Software Selection. 1 Ease of learning, 2 Amount of help incorporated for the user, 3 Level of the user, 4 Number of tests and routines involved, 5 Ease of data entry, 6 Data validation and if necessary, data locking and security7 Accuracy of the tests and routines, 8 Integrated data analysis graphs and progressive reporting on analysis in one screen9 Cost.

No one software meets everyone s needs. Determine the needs first and then ask the questions relevant to the above seven criteria. Spatial Data Analysis. Many natural phenomena involve a random distribution of points in space. Biologists who observe the locations of cells of a certain type in an organ, astronomers who plot the positions of the stars, botanists who record the positions of plants of a certain species and geologists detecting the distribution of a rare mineral in rock are all observing spatial point patterns in two or three dimensions.

Such phenomena can be modelled by spatial point processes. The spatial linear model is fundamental to a number of techniques used in image processing, for example, for locating gold ore deposits, or creating maps. There are many unresolved problems in this area such as the behavior of maximum likelihood estimators and predictors, and diagnostic tools.

There are strong connections between kriging predictors for the spatial linear model and spline methods of interpolation and smoothing. The two-dimensional version of splines kriging can be used to construct deformations of the plane, which are of key importance in shape analysis. For analysis of spatially auto-correlated data in of logistic regression for example, one may use of the Moran Coefficient which is available is some statistical packages such as Spacestat.

This statistic tends to be between -1 and 1, though are not restricted to this range. Values near 1 indicate similar values tend to cluster; values near -1 indicate dissimilar values tend to cluster; values near -1 n-1 indicate values tend to be randomly scattered. Boundary Line Analysis. The main application of this analysis is in the soil electrical conductivity EC which stems from the fact that sands have a low conductivity, silts have a medium conductivity and clays have a high conductivity.

Consequently, conductivity measured at low frequencies correlates strongly to soil grain size and texture. The boundary line analysis, therefore, is a method of analyzing yield with soil electrical conductivity data. This method isolates the top yielding points for each soil EC range and fits a non-linear line or equation to represent the top-performing yields within each soil EC range.

This method knifes through the cloud of EC Yield data and describes their relationship when other factors are removed or reduced. The upper boundary represents the maximum possible response to that limiting factor, e. ECand points below the boundary line represents conditions where other factors have limited the response variable. Therefore, one may also use boundary line analysis to compare responses among species.

Further Readings Kitchen N.K Sudduth, and S. Drummond, Soil Electrical Conductivity as a Crop Productivity Measure for Claypan Soils, Journal of Production Agriculture12 4607-617, 1999. Geostatistics Modeling. Further Readings Christakos G.Modern Spatiotemporal GeostatisticsOxford University Press, 2000. Box-Cox Power Transformation. Among others the Box-Cox power transformation is often used for this purpose.

trying different values of p between -3 and 3 is usually sufficient but there are MLE methods for estimating the best p. A good source on this and other transformation methods is Madansky A.Prescriptions for working StatisticiansSpringer-Verlag, 1988. For percentages or proportions such as for binomial proportionsArcsine transformations would work better. The original idea of Arcsin p Ѕ is to establish variances as equal for all groups.

The arcsin transform is derived analytically to be the variance-stabilizing and normalizing transformation. The same limit theorem also leads to the square root transform for Poisson variables such as counts and to the arc hyperbolic tangent i.Fisher s Z transform for correlation. The Arcsin Test yields a z and the 2x2 contingency test yields a chi-sq. But z 2 chi-sq, for large sample size.

A good source is Rao C.Linear Statistical Inference and Its ApplicationsWiley, 1973. How to normalize a set of data consisting of negative and positive values, and make them positive between the range 0. Define XNew X-min max-min. Box Cox power transformation is also very effective for a wide variety of nonnormality. y transformed y l. where l ranges in practice from -3. As such it includes, inverse, square root, logarithm, etc. Note that as l approaches 0, one gets a log transformation.

Multiple Comparison Tests. Multiple comparison procedures include topics such as Control of the family-Wise Error rate, The closure Principle, Hierarchical Families of Hypotheses, Single-Step and Stepwise Procedures, and P-value Adjustments. Areas of applications include multiple comparisons among treatment means, multiple endpoints in clinical trials, multiple sub-group comparisons, etc. Nemenyi s multiple comparison test is analogous to Tukey s test, using rank sums in place of means and using n 2 k nk 1 12 Ѕ as the estimate of standard error SEwhere n is the size of each sample and k is the number of samples means.

Similarly to the Tukey test, you compare rank sum A - rank sum B SE to the studentized range for k. It is also equivalent to the Dunn Miller test which uses mean ranks and standard error k nk 1 12 Ѕ. Multilevel Statistical Modeling The two widely used software packages are MLwiN and winBUGS. They perform multilevel modeling analysis and analysis of hierarchical datasets, Markov chain Monte Carlo MCMC methodology and Bayesian approaches. Further Readings Liao T.Statistical Group ComparisonWiley, 2002.

Antedependent Modeling for Repeated Measurements. Many techniques can be used to analyze such data. Antedependence modeling is a recently developed method which models the correlation between observations at different times. Split-half Analysis. Notice that this is like factor analysis itself an exploratorynot inferential technique, i.

hypothesis testing, confidence intervals etc. simply do not apply. Alternatively, randomly split the sample in half and then do an exploratory factor analysis on Sample 1. Use those results to do a confirmatory factor analysis with Sample 2. Sequential Acceptance Sampling. Sequential acceptance sampling minimizes the number of items tested when the early results show that the batch clearly meets, or fails to meet, the required standards. The procedure has the advantage of requiring fewer observations, on average, than fixed sample size tests for a similar degree of accuracy.

Local Influence. Cook defined local influence in 1986, and made some suggestions on how to use or interpret it; various slight variations have been defined iq option wallpaper then. But problems associated with its use have been pointed out by a number of workers since the very beginning. Variogram Analysis. A variogram summarizes the relationship between the variance of the difference in pairs of measurements and the distance of the corresponding points from each other.

Credit Scoring Consumer Credit Assessment. Accurate assessment of financial exposure is vital for continued business success. Accurate, and usable information are essential for good credit assessment in commercial decision making. The consumer credit environment is in a state of great change, driven by developments in computer technology, more demanding customers, availability of new products and increased competition.

Banks and other financial institutions are coming to rely more and more on increasingly sophisticated mathematical and statistical tools. These tools are used in a wide range of situations, including predicting default risk, estimating likely profitability, fraud detection, market segmentation, and portfolio analysis. The credit card market as an example, has changed the retail banking industry, and consumer loans. Both the tools, the behavioral scoring, and the characteristics of consumer credit data are usually the bases for a good decision.

The statistical tools include linear and logistic regression, mathematical programming, trees, nearest neighbor methods, stochastic process models, statistical market segmentation, and neural networks. These techniques are used to assess and predict consumers credit scoring. Further Readings Lewis E.Introduction to Credit ScoringFair, Isaac Co. Provides a general introduction to the issues of building a credit scoring model.

Components of the Interest Rates. The pure rate This is the time value of money. A promise of 100 units next year is not worth 100 units this year. The price-premium factor If prices go up 5 each year, interest rates go up at least 5. For example, under the Carter Administration, prices rose about 15 per year for a couple of years, interest was around 25. Same thing during the Civil War. In a deflationary period, prices may drop so this term can be negative. The risk factor A junk bond may pay a larger rate than a treasury note because of the chance of losing the principal.

Banks in a poor financial condition must pay higher rates to attract depositors for the same reason. Threat of confiscation by the government leads to high rates in some countries. Other factors are generally minor. Of course, the customer sees only the sum of these terms. These components fluctuate at different rates themselves. This makes it hard to compare interest rates across disparate time periods or economic condition.

The main questions are how are these components combined to form the index. A simple sum. A weighted sum. McNemar Change Test For the yes no questions under the two conditions, set up a 2x2 contingency table McNemar s test of correlated proportions is z f01 - f10 f01 f10 Ѕ. The same applies to other index numbers. Partial Least Squares. The method aims to identify the underlying factors, or linear combination of the X variables, which best model the Y dependent variables.

Growth Curve Modeling. Sometimes we simply wish to summarize growth observations in terms of a few parameters, perhaps in order to compare individuals or groups. Many growth phenomena in nature show an S shaped pattern, with initially slow growth speeding up before slowing down to approach a limit. These patterns can be modelled using several mathematical functions such as generalized logistic and Gompertz curves. Saturated Model Saturated Log Likelihood. Pattern recognition and Classification.

What is Biostatistics. Recent advancement in human genome marks a major step in the advancement of understanding how the human body works at a molecular level. The biomedical statistics identifies the need for computational statistical tools to meet important challenges in biomedical studies. The active areas are Clustering of very large dimensional data such as the micro-array. Clustering algorithms that support biological meaning. Network models and simulations of biological pathways.

Pathway estimation from data. Integration of multi-format and multi-type data from heterogeneous databases. Information and knowledge visualization techniques for biological systems. Further Reading Cleophas T. Zwinderman, and T. Cleophas, Statistics Applied to Clinical TrialsKluwer Academic Publishers, 2002. Shmulevich, Computational and Statistical Approaches to GenomicsKluwer Academic Publishers, 2002. Evidential Statistics. In most cases the index is form both empirically and assigned on basis of some criterion of importance.

Should this observation lead me to believe that condition C is present. Does this observation justify my acting as if condition C were present. Is this observation evidence that condition C is present. We must distinguish among these three questions in terms of the variables and principles that determine their answers. It is already recognized that for answering the evidential question current statistical methods are seriously flawed which could be corrected by a applying the the Law of Likelihood.

This law suggests how the dominant statistical paradigm can be altered so as to generate appropriate methods for objective, quantitative representation of the evidence embodied in a specific set of observations, as well as measurement and control of the probabilities that a study will produce weak or misleading evidence. Questions of the third type, concerning the evidential interpretation of statistical data, are central to many applications of statistics in many fields.Statistical Evidence A Likelihood ParadigmChapman Hall, 1997.

Further Reading Royall R. Statistical Forensic Applications. One consequence of the failure to recognize the benefits that an organized approach can bring is our failure to move evidence as a discipline into volume case analytics. There has been an over emphasis on the formal rules of admissibility rather than the rules and principles of a methodological scientific approach. As the popularity of using DNA evidence increases, both the public and professionals increasingly regard it as the last word on a suspect s guilt or innocence.

As citizens go about their daily lives, pieces of their identities are scattered in their wake. It could as some critics warn, one day place an innocent person at the scene of a crime. The traditional methods of statistical forensic, for example, for facial reconstruction date back to the Victorian Era. Tissue depth data was collected from cadavers at a small number of landmark sites on the face.

Samples were tiny, commonly numbering less than ten. Although these data sets have been superceded recently by tissue depths collected from the living using ultrasound, the same twenty-or-so landmarks are used and samples are still small and under-representative of the general population. A number of aspects of identity--such as age, height, geographic ancestry and even sex--can only be estimated from the skull.

Current research is directed at the recovery of volume tissue depth data from magnetic resonance imaging scans of the head of living individuals; and the development of simple interpolation simulation models of obesity, ageing and geographic ancestry in facial reconstruction. Any cursory view of the literature reveals that work has centered on thinking about single cases using narrowly defined views of what evidential reasoning involves.Statistical Science in the CourtroomSpringer Verlag, 2000.

Spatial Statistics. Further Readings Diggle P.The Statistical Analysis of Spatial Point PatternsAcademic Press, 1983.Spatial StatisticsWiley, 1981. What Is the Black-Sholes Model. Further Readings Clewlow L. Strickland, Implementing Derivatives ModelsJohn Wiley Sons, 1998. What Is a Classification Tree. There are several methods of deciding when to stop.

Further Reading Gastwirth J. The simplest method is to split the data into two samples. A tree is developed with one sample and tested with another. As the number of nodes used changes the mis-classification rate changes. The mis-classification rate is calculated by fitting the tree to the test data set and increasing the number of branches one at a time. The number of nodes which minimize the mis-classification rate is chosen. Graphical Tools for High-Dimensional Classification Statistical algorithmic classification methods include techniques such as trees, forests, and neural nets.

Such methods tend to share two common traits. They can often have far greater predictive power than the classical model-based methods. And they are frequently so complex as to make interpretation very difficult, often resulting in a black box appearance. An alternative approach is iq option wallpaper graphical tool to facilitate investigation of the inner workings of such classifiers. Additional information can be visually incorporated as to true class, predicted class, and casewise variable importance.

The A generalization of the ideas such as the data image, and the color histogram allows simultaneous examination of dozens to hundreds of variables across similar numbers of observations. Careful choice of orderings across cases and variables can clearly indicate clusters, irrelevant or redundant variables, and other features of the classifier, leading to substantial improvements in classifier interpretability.

The various programs vary in how they operate. For making splits, most programs use definition of purity. More sophisticated methods of finding the stopping rule have been developed and depend on the software package. What Is a Regression Tree. The Tree-based models known also as recursive partitioning have been used in both statistics and machine learning. Most of their applications to date have, however, been in the fields of regression, classification, and density estimation.

S-PLUS statistical package includes some nice features such as non-parametric regression and tree-based models. Further Readings Breiman L. Olshen and C. Stone, Classification and Regression TreesCRC Press, Inc.Boca Raton, Florida, 1984. Cluster Analysis for Correlated Variables. characterize a specific group of interest, compare two or more specific groups, discover a pattern among several variables. Cluster analysis is used to classify observations with respect to a set of variables.

The widely used Ward s method is predisposed to find spherical clusters and may perform badly with very ellipsoidal clusters generated by highly correlated variables within clusters. To deal with high correlations, some model-based methods are implemented in the S-Plus package. However, a limitation of their approach is the need to assume the clusters have a multivariate normal distribution, as well as the need to decide in advance what the likely covariance structure of the clusters is.

Another option is to combine the principal component analysis with cluster analysis. Further Readings Baxter M.Exploratory Multivariate Analysis in Archaeologypp. 167-170, Edinburgh University Press, Edinburgh, 1994.Multivariate Statistical Methods A PrimerChapman and Hall, London, 1986. Capture-Recapture Methods. Tchebysheff Inequality and Its Improvements. P X - m k s 1 k 2for any k 1. The symmetric property of Tchebysheff s inequality is useful, constructing control limits is the quality control process.

However the limits are very conservative because of lack of knowledge about the underlying distribution. This bounds can be improved i.becomes tighter if we have some knowledge about the population distribution. For example, if the population is homogeneous, that is its distribution is unimodal, then. 25k 2for any k 1.

The above inequality is known as the Camp-Meidell inequality. Contains a test for multimodality that is based on the Gaussian kernel density estimates and then test for multimodality by using the window size approach. Leavenworth, Statistical Quality ControlMcGraw-Hill, 1996.Statistical Methods for Quality ImprovementJohn Wiley Sons, 2000.

A very good book for a starter. Frechet Bounds for Dependent Random Variables. max 0, P A P B - 1 P A and B min P AP B. Frechet Bounds is often used in stochastic processes with the effect of dependencies, such as estimating an upper and or a lower bound on the queue length in a queuing system with two different but known marginal inter-arrivals times distributions of two types of customers.

Statistical Data Analysis in Criminal Justice. Further Readings McKean J.and Bryan Byers, Data Analysis for Criminal Justice and CriminologyAllyn Bacon, 2000.Statistics in Criminal Justice Analysis and InterpretationAspen Publishers, Inc. What is Intelligent Numerical Computation. Software Engineering by Project Management. The software project scheduling and tracking is to create a network of software engineering tasks that will enable you to get the job done on time.

Once the network is created, you have to assign responsibility for each task, make sure it gets done, and adapt the network as risks become reality. Further Readings Ricketts I.Managing Your Software Project A Student s GuideLondon, Springer, 1998. Chi-Square Analysis for Categorical Grouped Data. Group Yes Uncertain No 1 10 21 23 2 12 15 18. One may first construct an equivalent alternative categorical table as follows.

Group Reply Count 1 Y 10 1 U 21 1 N 23 2 Y 12 2 U 15 2 N 18. Now, weight the data by counts and then perform the Chi-Square analysis. Further Reading Agresti A.Categorical Data AnalysisWiley, 2002. O Muircheartaigh, and J. Lepkowski, Collected Papers of Leslie KishWiley, 2002. Cohen s Kappa A Measures of Data Consistency. Kappa k observed concordance - concordance by chance 1- concordance by chance. Where by chance is calculated as in chi-square multiply row marginal times column marginal and divide by n.

Kappa k Interpretation k 0. One may use this measure as a decision-making tool. 60 Moderate 0. 80 Substantial 0. 80 k Almost Perfect. Further Reading Looney S.Biostatistical Methodsed.Humana Press, 2002. Cooil, Reliability measures for qualitative data Theory and implications, Journal of Marketing Research31 11-14, 1994.

Modeling Dependent Categorical Data. Further Readings Agresti A.Iq option wallpaper Introduction to Categorical Data AnalysisWiley, 1996. The Deming Paradigm. Further Reading Thompson J. Koronacki, Statistical Process Control The Deming Paradigm and BeyondCRC Press, 2001. Reliability Repairable System. The primary intent of reliability engineering is to improve reliability, and almost all systems of interest to reliability engineers are designed to be repairable, this is the most important reliability concept.

It is also the simplest, in sharp contrast, spacing between order statistics of the times to failure of non-repairable items eventually become stochastically larger. Even under any physically plausible model of wearout. Moreover, if parts are put on test simultaneously and operated continuously, the spacing between order statistics, which are times between failures, occur exactly in calendar time. Because of non-zero repair times, this is never exactly true for a repairable system.

As long as a system is non-repairable, the focus usually should be on the underlying distribution s hazard function. Correspondingly, if it is repairable, the focus usually should be on the underlying process s intensity function. However, even though hazard and intensity functions can be - and sometimes have to be - represented by the same mathematical function, the differences in interpretation are significantly different. Further Reading Ascher H.

Feingold, Repairable Systems Reliability Modeling, Inference, Misconceptions and Their CausesMarcel Dekker, 1984. Computation of Standard Scores. where m raw score mean. s raw score standard deviation. s new standard deviation. Suppose a population of psychological test scores has a mean of 70 and a standard deviation of 8 and it is desired to convert these scores to standard scores with a mean of 100 and a standard deviation of 20.

If 40 is one of the raw scores in the population, we may apply the foregoing equation to convert this to a standard score by substituting. m 70, s 8, X 40, m 100, s 20 to obtain. Quality Function Deployment QFD. Further Readings Franceschini F.Advanced Quality Function DeploymentSt. Lucie Press, 2002. Event History Analysis. Further Readings Brown H. Prescott, Applied Mixed Models in MedicineWiley, 1999.

Factor Analysis. Further Reading Reyment R. Joreskog, Applied Factor Analysis in the Natural ScienceCambridge University Press, 1996. It covers multivariate analysis and applications to environmental fields such as chemistry, paleoecology, sedimentology, geology and marine ecology. Tabachick B. Fidell, Using Multivariate StatisticsHarper Collins, New York, 1996.

Kinds of Lies Lies, Damned Lies and Statistics. However it often happens that people manipulating statistics in their own advantage or in advantage of their boss or friend. The following are some examples as how statistics could be misused in advertising, which can be described as the science of arresting human unintelligence long enough to get money from it.

The founder of Revlon says In factory we make cosmetics; in the store we sell hope. In most cases, the deception of advertising is achieved by omission. The Incredible Expansion Toyota How can it be that an automobile that s a mere nine inches longer on the outside give you over two feet more room on the inside. Toyota Camry Ad. Where is the fallacy in this statement. Taking volume as length. For example 3x6x4 72 feet cubic3x6x4.

5 feet cubic. It could be even more than 2 feet. Pepsi Cola Ad. In recent side-by-side blind taste tests, nationwide, more people preferred Pepsi over Coca-Cola. The questions are, Was it just some of taste tests, what was the sample size. It does not say In all recent. Consortium of Electric Companies Ad. May be it s the new math. 96 of streets in the US are under-lit and, moreover, 88 of crimes take place on under-lit streets. Dependent or Independent Events. If the probability of someone carrying a bomb on a plane is.

001, then the chance of two people carrying a bomb is. Therefore, I should start carrying a bomb on every flight. Paperboard Packaging Council s concerns University studies show paper milk cartons give you more vitamins to the gallon. How was the design of experiment. The council sponsored the research. Paperboard sales is declining. All the vitamins or just one. You d have to eat four bowls of Raisin Bran to get the vitamin nutrition in one bowl of Total.

Six Times as Safe Last year 35 people drowned in boating accidents. Only 5 were wearing life jackets. The rest were not. Always wear life jacket when boating. What percentage of boaters wears life jackets. Is it a conditional probability. A Tax Accountant Firm Ad. One of our officers would accompany you in the case of Audit. This sounds like a unique selling proposition, but it conceals the fact that the statement is a US Law.

Dunkin Donuts Ad. Free 3 muffins when you buy three at the regular 1 2 dozen price. There have been many other usual misuses of statistics dishonest and or ignorant survey methods, loaded survey questions, graphs and picto-grams that suppress that which is not in the proof program, and survey respondents who are the autos select because they have an axe to grind about the issue; very interesting stuff, and, of course, those amplifying that which the data really minimizes.

Further Readings.Slippery Math in Public Affairs Price Tag and DefenseDekker. Examines flawed usage of math in public affairs through actual cases of how mathematical data and conclusions can be distorted and misrepresented to influence public opinion. Highlights how slippery numbers and questionable mathematical conlusions emerge and what can be done to safeguard against them.200 of NothingJohn Wiley, 1993.

Based on his articles about math abuse in Scientific American, Dewdney lists the many ways we are manipulated with fancy mathematical footwork and faulty thinking in print ads, the news, company reports and product labels. He shows how to detect the full range of math abuses and defend against them. Hardin, Common Errors in StatisticsWiley, 2003.

Schindley W.The Informed Citizen Argument and Analysis for TodayHarcourt Brace, 1996. This rhetoric reader explores the study and practice of writing argumentative prose. The interacting in communities theme and the high-interest readings engage students, while helping them develop informed opinions, effective arguments, and polished writing. Spirer, and A. Jaffe, Misused StatisticsDekker, 1998. The focus is on exploring current issues in communities, from the classroom to cyberspace.

Illustrating misused statistics with well-documented, real-world examples drawn from a wide range of areas, public policy, and business and economics. Entropy Measure. where, sum is over all the categories and p i is the relative frequency of the i th category. It represents a quantitative measure of uncertainty associated with p. It is interesting to note that this quantity is maximized when all p i s, are equal. For a rXc contingency table it is E S S p ij ln p ij - S S p ij ln S p ij - S S p ij ln S p ij.

The sums are over all i and j, and j and i s. or the variation distance. where P i and Q i are the probabilities for the i-th category for the two populations. Further Reading Kesavan H. Kapur, Entropy Optimization Principles with ApplicationsAcademic Press, New York, 1992. Warranties Statistical Planning and Analysis. Warranty decisions involve both technical and commercial considerations. Because of the possible financial consequences of these decisions, effective warranty management is critical for the financial success of a manufacturing firm.

This requires that management at all levels be aware of the concept, role, uses and cost and design implications of warranty. The aim is to understand the concept of warranty and its uses; warranty policy alternatives; the consumer manufacturer perspectives with regards warranties; the commercial technical aspects of warranty and their interaction; strategic warranty management; methods for warranty cost prediction; warranty administration.

Further Reading Brennan J.Warranties Planning, Analysis, and ImplementationMcGraw Hill, 1994. Tests for Normality. Kolmogrov-Smirinov-Lilliefors Test This test is a special case of the Kolmogorov-Smirnov goodness-of-fit test for normality of population s distribution. In applying the Lilliefors test a comparison is made between the standard normal cumulative distribution function, and a sample cumulative distribution function with standardized random variable. If there is a close agreement between the two cumulative distributions, the hypothesis that the sample was drawn from population with a normal distribution function is supported.

If, however, there is a discrepancy between the two cumulative distribution functions too great to be attributed to chance alone, then the hypothesis is rejected.

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