Topic
Population proportion
About: Population proportion is a research topic. Over the lifetime, 247 publications have been published within this topic receiving 4099 citations.
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15 Jan 2020
TL;DR: In this article, the authors derive uniformly most powerful (UMP) tests for simple and one-sided hypotheses for a population proportion within the framework of differential privacy, optimizing finite sample performance.
Abstract: We derive uniformly most powerful (UMP) tests for simple and one-sided hypotheses for a population proportion within the framework of Differential Privacy (DP), optimizing finite sample performance. We show that in general, DP hypothesis tests can be written in terms of linear constraints, and for exchangeable data can always be expressed as a function of the empirical distribution. Using this structure, we prove a `Neyman-Pearson lemma' for binomial data under DP, where the DP-UMP only depends on the sample sum. Our tests can also be stated as a post-processing of a random variable, whose distribution we coin ``Truncated-Uniform-Laplace'' (Tulap), a generalization of the Staircase and discrete Laplace distributions. Furthermore, we obtain exact p-values, which are easily computed in terms of the Tulap random variable.
Using the above techniques, we show that our tests can be applied to give uniformly most accurate one-sided confidence intervals and optimal confidence distributions. We also derive uniformly most powerful unbiased (UMPU) two-sided tests, which lead to uniformly most accurate unbiased (UMAU) two-sided confidence intervals. We show that our results can be applied to distribution-free hypothesis tests for continuous data. Our simulation results demonstrate that all our tests have exact type I error, and are more powerful than current techniques.
15 citations
TL;DR: The combination of the randomized response technique (RRT) and NSUM obtained a high response rate and produced a reliable estimate of the size of a high-risk population.
14 citations
Book•
10 Sep 1998
TL;DR: This book discusses data analysis for improved decision making, management Scenarios and Data Sets, and the need for Statistical Inference methods to minimize Managerial Judgment Errors.
Abstract: PART I: UNIVARIATE DATA 1. DATA ANALYSIS FOR IMPROVED DECISION MAKING Introduction / Types of Problems / Mental Models and Effective Problem Solving / Types of Variation / Types of Data Business Professionals Use / Data Measurement Scales / Data Sources for Improved Decision Making / Data Collection through Surveys / Summary / Exercises / Appendices 2. DESCRIBING UNIVARIATE DATA Introduction / Management Scenarios and Data Sets / Displaying Cross-Sectional Data for Quantitative Variables / Summarizing Cross-Sectional Data for Quantitative Variables / Assessing Assignable Cause Variation: Cross-Sectional Data for Quantitative Variables / Cross-Sectional Data for Qualitative Variables / Displaying Time-Ordered Data / Summarizing Time-Ordered Data / Assessing Assignable-Cause Variation for Time-Ordered Data / Guide to Data-Analysis Methods / Exercises / Appendices 3. BASIC PROBABILITY CONCEPTS AND PROBLEMS IN ASSESSING PROBABILITIES Introduction / Types of Probability / Computing Conditional Probabilities and Statistical Independence / Using Probability Trees to Minimize Managerial Judgment Errors / Key Ideas / Exercises 4. SAMPLING AND SAMPLING DISTRIBUTIONS The Need for Statistical Inference Methods / Exploring the Distribution of the Sample Mean / The Normal Distribution / Exploring the Distribution of the Sample Proportion / Exploring the Distribution of the Sample Variance / Key Ideas and Overview / Exercises / Appendices 5. STATISTICAL INFERENCE I: CONFIDENCE INTERVALS The Statistical Inference Process / Management Scenarios and Data Sets / General Principles of Confidence Intervals / Confidence Intervals on an Unknown Population Mean / Confidence Interval on an Unknown Population Proportion / Determining the Sample Size / Confidence Interval on an Unknown Population Variance / Key Ideas and Overview / Exercises / Appendices 6. STATISTICAL INFERENCE II: HYPOTHESIS TESTING ON ONE POPULATION PARAMETER Introduction / Management Scenarios and Data Sets / Hypothesis Testing on One Population Mean / Hypothesis Testing on One Population Proportion / Key Ideas and Summary / Exercises / Appendices PART II: MULTIVARIATE DATA 7. DESCRIBING MULTIVARIATE DATA Introduction / Management Scenarios and Data Sets / Analyzing Mixed Cross-Sectional Data / Analyzing Qualitative Cross-Sectional Data / Analyzing Quantitative Cross-Sectional Data / Analyzing Time-Ordered Quantitative Data / Analyzing Time-Ordered Quantitative Data: Autoregressive Equations / Correlation and Cross-Correlation / Guidelines for Using Chapter's Descriptive Methods / Exercises / Appendices 8. HYPOTHESIS TESTING ON TWO POPULATION PARAMETERS Statistical Inference Process / Management Scenarios and Data Sets / Hypothesis Testing on the Difference in the Means of Two Independent Populations Having Equal Variances / Hypothesis Testing on the Difference in the Means of Two Independent Populations Having Unequal Variances / Testing for the Difference between the Means of Two Related Populations: The Paired Sample t-Test for the Matched Pair Design / Testing for the Difference between the Proportions of Two Independent Populations / Testing for the Equality of Variances from Two Independent Populations: The F-test / Roadmap for the Chapter / Exercises / Appendices 9. REGRESSION ANALYSIS AND CHI-SQUARE TEST OF INDEPENDENCE Introduction / Management Scenarios and Data Sets / Introduction to Regression Analysis / Scatter Diagramming and the Analysis of Variance / Evaluating the Regression Model Assumptions: Graphical Analysis of Residuals / Using the Estimated Regression Models for Making Predictions / Multicollinearity / Chi-Square Test of Independence / Chapter Overview / Exercises / Appendices 10. FORECASTING AND TIME SERIES ANALYSIS Data Patterns and Forecasting / Management Scenarios and Data Bases / Forecasting Meandering Patterns / Forecasting Seasonal Patterns / Summary / Exercises / Appendices PART III: QUALITY AREA 11. QUALITY IMPROVEMENT AND STATISTICAL PROCESS CONTROL Quality Improvement, Productivity, and Business Success / Types of Quality / The "Big 8" Quality Improvement Tools / Management Scenarios and Data Sets / Control Charts for Variables: x [overbar] and Standard Deviation / Control Charts for Proportion Nonconforming / Control Charts for the Number of Nonconformities: The Demerit Chart / Ideas and Overview / Exercises / Appendices 12. DESIGN OF EXPERIMENTS The Role of Experimentation in Process and Product Improvement / Management Scenarios and Data Sets / Designing Experiments / One Factor Completely Random Design / The Two-Factor Completely Random Design / Exercises / Appendices / INDEX
13 citations
13 citations
TL;DR: This paper illustrates via real-life examples that in contrast to classical test theory, fuzzy hypothesis testing provides an additional partial and gradual consideration of the indifference zone for both complementary and non-complementary hypotheses.
13 citations