Population proportion

About: Population proportion is a research topic. Over the lifetime, 247 publications have been published within this topic receiving 4099 citations.

Statistics for management and economics

Abstract: 1. WHAT IS STATISTIC?. Introduction to Statistics. Key Statistical Concepts. How Managers Use Statistics. Statistics and the Computer. World Wide Web and Learning Center. Part I. DESCRIPTIVE TECHNIQUES AND PROBABILITY. 2. Graphical Descriptive Techniques. Introduction. Types of Data. Graphical Techniques for Quantitative Data. Scatter Diagrams. Pie Charts, Bar Charts, and Line Charts. Summary. Case 2.1 Pacific Salmon Catches. Case 2.2 Bombardier Inc. Case 2.3 The North American Free Trade Agreement (NAFTA). Appendix 2.A Minitab Instructions. Appendix 2.B Excel Instructions. 3. Art and Science of Graphical Presentations. Introduction. Graphical Excellence. Graphical Deception. Summary. Case 3.1 Canadian Federal Budget. 4. Numerical Descriptive Measures. Introduction. Measures of Central Location. Measures of Variability. Interpreting Standard Deviation. Measures of Relative Standing and Box Plots. Measures of Association. General Guidelines on the Exploration of Data. Summary. Appendix 4.A Minitab Instructions. Appendix 4.B Summation Notation. 5. Data Collection and Sampling. Introduction. Sources of Data. Sampling. Sampling Plans. Errors Involved in Sampling. Use of Sampling in Auditing. Summary. 6. Probability and Discrete Probability Distributions. Introduction. Assigning Probabilities to Events. Probability Rules and Trees. Random Variables and Probability Distributions. Expected Value and Variance. Bivariate Distributions. Binomial Distribution. Poisson Distribution. Summary. Case 6.1 Let's Make a Deal. Case 6.2 Gains from Market Timing. Case 6.3 Calculating Probabilities Associated with the Stock Market. Appendix 6.A Minitab Instructions. Appendix 6.B Excel Instructions. 7. Continuous Probability Distributions. Introduction. Continuous Probability Distributions. Normal Distribution. Exponential Distribution. Summary. Appendix 7.A Minitab Instructions. Appendix 7.B Excel Instructions. Part II. STATISTICALl INFERENCE. 8. Sampling Distributions. Introduction. Sampling Distribution of the Mean. Summary. 9. Introduction to Estimation. Introduction. Concepts of Estimation. Estimating the Population Mean When the Population Variance Is Known. Selecting the Sample Size. Summary. Appendix 9.A Minitab Instructions. Appendix 9.B Excel Instructions. 10. Introduction to Hypothesis Testing. Introduction. Concepts of Hypothesis Testing. Testing the Population Mean When the Population Variance Is Known. The p-Value of a Test of Hypothesis. Calculating the Probability of a Type II Error. The Road Ahead. Summary. Appendix 10.A Minitab Instructions. Appendix 10.B Excel Instructions. 11. Inference about the Description of a Single Population. Introduction. Inference about a Population Mean When the Population Variance Is Unknown. Inference about a Population Variance. Inference about a Population Proportion. The Myth of the Law of Averages. Case 11.1 Number of Uninsured Motorists. Case 11.2 National Patent Development Corporation.

Statistics for business and economics

Abstract: 1. Statistics, Data, and Statistical Thinking. 1.1 The Science of Statistics 1.2 Types of Statistical Applications 1.3 Fundamental Elements of Statistics 1.4 Processes (Optional) 1.5 Types of Data 1.6 Collecting Data 1.7 The Role of Statistics in Managerial Decision-Making Statistics in Action: A "20/20" View of Survey Results - Fact or Fiction? Using Technology: Creating and Listing Data in SPSS, MINITAB, and EXCEL 2. Methods for Describing Sets of Data. 2.1 Describing Qualitative Data 2.2 Graphical Methods for Describing Quantitative Data 2.3 Summation Notation 2.4 Numerical Measures of Central Tendency 2.5 Numerical Measures of Variability 2.6 Interpreting the Standard Deviation 2.7 Numerical Measures of Relative Standing 2.8 Methods for Detecting Outliers (Optional) 2.9 Graphing Bivariate Relationships (Optional) 2.10 The Time Series Plot (Optional) 2.11 Distorting the Truth with Descriptive Techniques Statistics In Action: Characteristics of Physicians who Use or Refuse Ethics Consultation Using Technology: Describing Data using SPSS, MINITAB, and EXCEL/PHStat2 APPLYING STATISTICS TO THE REAL WORLD: THE KENTUCKY MILK CASE C PART I (A Case Covering Chapters 1 and 2) 3. Probability. 3.1 Events, Sample Spaces, and Probability 3.2 Unions and Intersections 3.3 Complementary Events 3.4 The Additive Rule and Mutually Exclusive Events. 3.5 Conditional Probability 3.6 The Multiplicative Rule and Independent Events 3.7 Random Sampling 3.8 Bayes' Rule (Optional) Statistics In Action: Lottery Buster! Using Technology: Generating a Random Sample Using SPSS, MINITAB, and EXCEL/PHStat2 4. Discrete Random Variables. 4.1 Two Types of Random Variables 4.2 Probability Distributions for Discrete Random Variables 4.3 Expected Values of Discrete Random Variables 4.4 The Binomial Random Variable 4.5 The Poisson Random Variable (Optional) 4.6 The Hypergeometric Random Variable (Optional) Statistics in Action: Probability in a Reverse Cocaine Sting Using Technology: Binomial, Poisson, and Hypergeometric Probabilities using SPSS, MINITAB, and EXCEL/PHStat2 5. Continuous Random Variables 5.1Continuous Probability Distributions 5.2The Uniform Distribution (Optional) 5.3The Normal Distribution 5.4Descriptive Methods for Assessing Normality 5.5Approximating a Binomial Distribution with a Normal Distribution 5.6The Exponential Distribution (Optional) Statistics in Action: Super Weapons Development - Optimizing the Hit Ratio Using Technology: Cumulative Probabilities and Normal Probability Plots using SPSS, MINITAB, and EXCEL/PHStat2 6. Sampling Distributions 6.1The Concept of Sampling Distributions 6.2Properties of Sampling Distributions: Unbiasedness and Minimum Variance (Optional) 6.3The Sampling Distribution of and the Central Limit Theorem Statistics in Action: The Insomnia Pill Using Technology: Simulating a Sampling Distribution using MINITAB and EXCEL/PHStat2 APPLYING STATISTICS TO THE REAL WORLD: THE FURNITURE FIRE CASE (A Case Covering Chapters 3-6) 7. Inferences Based on a Single Sample: Estimation with Confidence Intervals 7.1Large-Sample Confidence Interval for a Population Mean 7.2Small-Sample Confidence Interval for a Population Mean 7.3Large-Sample Confidence Interval for a Population Proportion 7.4Determining the Sample Size 7.5Finite Population Correction for Simple Random Sampling (Optional) 7.6Sample survey Designs (Optional) Statistics in Action: Scallops, Sampling, and the Law Using Technology: Confidence Intervals using SPSS, MINITAB and EXCEL/PHStat2 8. Inferences Based on a Single Sample: Tests of Hypothesis 8.1The Elements of a Test of Hypothesis 8.2Large-Sample Test of Hypothesis About a Population Mean 8.3Observed Significance Levels: p-Values 8.4Small-Sample Test of Hypothesis About a Population Mean 8.5Large-Sample Test of Hypothesis About a Population Proportion 8.6Calculating Type II Error Probabilities: More About _ (Optional) 8.7Test of Hypothesis About a Population Variance (Optional) Statistics in Action: Diary of a Kleenex User Using Technology: Tests of Hypotheses using SPSS, MINITAB and EXCEL/PHStat2 9. Inferences Based on a Two Samples: Confidence Intervals and Tests of Hypotheses 9.1Comparing Two Population Means: Independent Sampling 9.2Comparing Two Population Means: Paired Difference Experiments 9.3Comparing Two Population Proportions: Independent Sampling 9.4Determining the Sample Size 9.5Comparing Two Population Variances: Independent Sampling Statistics in Action: The Effect of Self-Managed Work Teams on Family Life Using Technology: Two-Sample Inferences using SPSS, MINITAB and EXCEL/PHStat2 APPLYING STATISTICS TO THE REAL WORLD: THE KENTUCKY MILK CASE C PART II (A Case Covering Chapters 7-9) 10. Design of Experiments and Analysis of Variance 10.1Elements of a Designed Experiment 10.2The Completely Randomized Design 10.3Multiple Comparisons of Means 10.4The Randomized Block Design (Optional) 10.5Factorial Experiments Statistics in Action: The Ethics of Downsizing Using Technology: Analysis of Variance using SPSS, MINITAB and EXCEL/PHStat2 11. The Chi-Square Test and the Analysis of Contingency Tables 11.1Categorical Data and the Multinomial Distribution 11.2Testing Category Probabilities: One-Way Table 11.3Testing Category Probabilities: Two-Way (Contingency) Table 11.4A Word of Caution About Chi-Square Tests Statistics in Action: A Study of Coupon Users-Mail versus the Internet Using Technology: Chi-Square Analyses using SPSS, MINITAB and EXCEL/PHStat2 APPLYING STATISTICS TO THE REAL WORLD: DISCRIMINATION IN THE WORKPLACE (A Case Covering Chapters 10-11) 12. Simple Linear Regression 12.1Probabilistic Models 12.2Fitting the Model: The Least Squares Approach 12.3Model Assumptions 12.4An Estimator of _2 12.5Making Inferences About the Slope _1 12.6The Coefficient of Correlation 12.7The Coefficient of Determination 12.8Using the Model for Estimation and Prediction 12.9A Complete Example Statistics in Action: Can "Dowsers" Really Detect Water? Using Technology: Simple Linear Regression using SPSS, MINITAB and EXCEL/PHStat2 13. Multiple Regression and Model Building 13.1Multiple Regression Models 13.2The First-Order Model: Estimating and Interpreting the _-Parameters 13.3Model Assumptions 13.4Inferences About the Individual _ Parameters 13.5Checking the Overall Utility of a Model 13.6Using the Model for Estimation and Prediction 13.7Model Building: Interaction Models 13.8Model Building: Quadratic and other Higher-Order Models 13.9Model Building: Qualitative (Dummy) Variable Models 13.10Model Building: Models with both Quantitative and Qualitative Variables (Optional) 13.11Model Building: Comparing Nested Models (Optional) 13.12Model Building: Stepwise Regression (Optional) 13.13Residual Analysis: Checking the Regression Assumptions 13.14Some Pitfalls: Estimability, Multicollinearity, and Extrapolation Statistics in Action: Bid-Rigging in the Highway construction Industry Using Technology: Multiple Regression using SPSS, MINITAB and EXCEL/PHStat2 APPLYING STATISTICS TO THE REAL WORLD: THE CONDO SALES CASE (A Case Covering Chapters 12-13) 14. Methods for Quality Improvement 14.1Quality, Processes, and Systems 14.2Statistical Control 14.3The Logic of Control Charts 14.4A Control Chart for Monitoring the Mean of a Process: The -Chart 14.5A Control Chart for Monitoring the Variation of a Process: The R-Chart 14.6A Control Chart for Monitoring the Proportion of Defectives Generated by a Process: The p-Chart 14.7Diagnosing the Causes of Variation (Optional) 14.8Capability Analysis (Optional) Statistics in Action: Testing Jet Fuel Additive for Safety Using Technology: Control Charts using SPSS, MINITAB and EXCEL/PHStat2 15. Time Series: Descriptive Analyses, Models, and Forecasting 15.1Descriptive Analysis: Index Numbers 15.2Descriptive Analysis: Exponential Smoothing 15.3Time Series Components 15.4Forecasting: Exponential Smoothing 15.5Forecasting Trends: The Holt-Winters Model (Optional) 15.6Measuring Forecast Accuracy: MAD and RMSE 15.7Forecasting Trends: Simple Linear Regression 15.8Seasonal Regression Models 15.9Autocorrelation and the Durbin-Watson Test Statistics In Action: Forecasting the Monthly Sales of a New Cold Medicine Using Technology: Forecasting using SPSS, MINITAB and EXCEL/PHStat2 APPLYING STATISTICS TO THE REAL WORLD: THE GASKET MANUFACTURING CASE (A Case Covering Chapters 14-15) 16. Nonparametric Statistics 16.1Single Population Inferences: The Sign Test 16.2Comparing Two Populations: The Wilcoxon Rank Sum Test for Independent Samples 16.3Comparing Two Populations: The Wilcoxon Signed Rank Test for the Paired Difference Experiment 16.4The Kruskal-Wallis H-Test for a Completely Randomized Design 16.5The Friedman Fr - Test for a Randomized Block Design (Optional) 16.6Spearman's Rank Correlation Coefficient Statistics in Action: Deadly Exposure-Agent Orange and Vietnam Vets Using Technology: Nonparametric Analyses using SPSS, MINITAB and EXCEL/PHStat2 Appendix ABasic Counting Rules Appendix BTables Table IRandom Numbers Table IIBinomial Probabilities Table IIIPoisson Probabilities Table IVNormal Curve Areas Table VExponentials Table VICritical Values of t Table VIICritical Values of _2 Table VIIIPercentage Points of the F Distribution, _=.10 Table IX Percentage Points of the F Distribution, _=.05 Table X Percentage Points of the F Distribution, _=.025 Table XI Percentage Points of the F Distribution, _=.01 Table XIICritical Values of TL and TU for the Wilcoxon Rank Sum Test: Independent Samples Table XIIICritical Values of T0 in the Wilcoxon Paired Difference Signed Rank Test Table XIVCritical Values of Spearman's Rank Correlation Coefficient Appendix CCalculation Formulas for Analysis of Variance Short Answers to Selected Odd-Numbered Exercises Index

Post-Stratification: A Modeler's Perspective

Abstract: Post-stratification is a common technique in survey analysis for incorporating population distributions of variables into survey estimates. The basic technique divides the sample into post-strata, and computes a post-stratification weight w ih = rP h /r h for each sample case in post-stratum h, where r h is the number of survey respondents in post-stratum h, P h is the population proportion from a census, and r is the respondent sample size. Survey estimates, such as functions of means and totals, then weight cases by w h . Variants and extensions of the method include truncation of the weights to avoid excessive variability and raking to a set of two or more univariate marginal distributions. Literature on post-stratification is limited and has mainly taken the randomization (or design-based) perspective, where inference is based on the sampling distribution with population values held fixed. This article develops Bayesian model-based theory for the method. A basic normal post-stratification mod...

Using R for Introductory Statistics

Abstract: DATA What Is Data? Some R Essentials Accessing Data by Using Indices Reading in Other Sources of Data UNIVARIATE DATA Categorical Data Numeric Data Shape of a Distribution BIVARIATE DATA Pairs of Categorical Variables Comparing Independent Samples Relationships in Numeric Data Simple Linear Regression MULTIVARIATE DATA Viewing Multivariate Data R Basics: Data Frames and Lists Using Model Formula with Multivariate Data Lattice Graphics Types of Data in R DESCRIBING POPULATIONS Populations Families of Distributions The Central Limit Theorem SIMULATION The Normal Approximation for the Binomial for loops Simulations Related to the Central Limit Theorem Defining a Function Investigating Distributions Bootstrap Samples Alternates to for loops CONFIDENCE INTERVALS Confidence Interval Ideas Confidence Intervals for a Population Proportion, p Confidence Intervals for the Population Mean, u Other Confidence Intervals Confidence Intervals for Differences Confidence Intervals for the Median SIGNIFICANCE TESTS Significance Test for a Population Proportion Significance Test for the Mean (t-Tests) Significance Tests and Confidence Intervals Significance Tests for the Median Two-Sample Tests of Proportion Two-Sample Tests of Center GOODNESS OF FIT The Chi-Squared Goodness-of-Fit Test The Chi-Squared Test of Independence Goodness-of-Fit Tests for Continuous Distributions LINEAR REGRESSION The Simple Linear Regression Model Statistical Inference for Simple Linear Regression Multiple Linear Regression ANALYSIS OF VARIANCE One-Way ANOVA Using lm() for ANOVA ANCOVA Two-Way ANOVA TWO EXTENSIONS OF THE LINEAR MODEL Logistic Regression Nonlinear Models APPENDIX A: GETTING, INSTALLING, AND RUNNING R Installing and Starting R Extending R Using Additional Packages APPENDIX B: GRAPHICAL USER INTERFACES AND R The Windows GUI The Mac OS X GUI Rcdmr APPENDIX C: TEACHING WITH R APPENDIX D: MORE ON GRAPHICS WITH R Low- and High-Level Graphic Functions Creating New Graphics in R APPENDIX E: PROGRAMMING IN R Editing Functions Using Functions Using Files and a Better Editor Object-Oriented Programming with R INDEX

Modeling microbial abundances and dysbiosis with beta-binomial regression

Abstract: Using a sample from a population to estimate the proportion of the population with a certain category label is a broadly important problem. In the context of microbiome studies, this problem arises when researchers wish to use a sample from a population of microbes to estimate the population proportion of a particular taxon, known as the taxon's relative abundance. In this paper, we propose a beta-binomial model for this task. Like existing models, our model allows for a taxon's relative abundance to be associated with covariates of interest. However, unlike existing models, our proposal also allows for the overdispersion in the taxon's counts to be associated with covariates of interest. We exploit this model in order to propose tests not only for differential relative abundance, but also for differential variability. The latter is particularly valuable in light of speculation that dysbiosis, the perturbation from a normal microbiome that can occur in certain disease conditions, may manifest as a loss of stability, or increase in variability, of the counts associated with each taxon. We demonstrate the performance of our proposed model using a simulation study and an application to soil microbial data.