Population proportion

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

Mean proportion and population proportion: two answers to the same question?

Abstract: Two different, but equally correct, answers can be given to a question such as "What proportion of the cholesterol that is consumed comes from eggs?" This is because the question can have two different meanings, depending on whether one is referring to the mean proportion of cholesterol from eggs or the population proportion. The mean proportion of cholesterol from eggs for a group of persons is determined by first calculating the proportion of cholesterol from eggs for each person and then taking an arithmetic mean of all the proportions. The population proportion is calculated by summing the amount of cholesterol from eggs for all persons and then dividing that by the sum of the cholesterol from all foods for all persons. These two different formulas often yield similar results. Sometimes, however, the results can be quite different because of variation in the ratio, variation in the denominator, and/or the correlation between the ratio and the denominator. Each of these formulas is designed to answer a specific question: the mean proportion addresses the question about the average per person and the population proportion addresses the question of population intakes. But because either may be used to answer the same general question, confusion may result. This article discusses the factors influencing differences between the two formulas and the implications of those differences for reporting and interpreting dietary intake data.

Statistics: The Art and Science of Learning from Data

Abstract: Part 1: Gathering and Exploring Data 1. Statistics: The Art and Science of Learning from Data 1.1 Using Data to Answer Statistical Questions 1.2 Sample Versus Population 1.3 Using Calculators and Computers Chapter Summary Chapter Problems 2. Exploring Data with Graphs and Numerical Summaries 2.1 Different Types of Data 2.2 Graphical Summaries of Data 2.3 Measuring the Center of Quantitative Data 2.4 Measuring the Variability of Quantitative Data 2.5 Using Measures of Position to Describe Variability 2.6 Recognizing and Avoiding Misuses of Graphical Summaries Chapter Summary Chapter Problems 3. Association: Contingency, Correlation, and Regression 3.1 The Association Between Two Categorical Variables 3.2 The Association Between Two Quantitative Variables 3.3 Predicting the Outcome of a Variable 3.4 Cautions in Analyzing Associations Chapter Summary Chapter Problems 4. Gathering Data 4.1 Experimental and Observational Studies 4.2 Good and Poor Ways to Sample 4.3 Good and Poor Ways to Experiment 4.4 Other Ways to Conduct Experimental and Nonexperimental Studies Chapter Summary Chapter Problems Part 1 Review Part 1 Questions Part 1 Exercises Part 2: Probability, Probability Distributions, and Sampling Distributions 5. Probability in Our Daily Lives 5.1 How Probability Quantifies Randomness 5.2 Finding Probabilities 5.3 Conditional Probability: The Probability of A Given B 5.4 Applying the Probability Rules Chapter Summary Chapter Problems 6. Probability Distributions 6.1 Summarizing Possible Outcomes and Their Probabilities 6.2 Probabilities for Bell-Shaped Distributions 6.3 Probabilities When Each Observation Has Two Possible Outcomes Chapter Summary Chapter Problems 7. Sampling Distributions 7.1 How Sample Proportions Vary Around the Population Proportion 7.2 How Sample Means Vary Around the Population Mean 7.3 The Binomial Distribution Is a Sampling Distribution (Optional) Chapter Summary Chapter Problems Part 2 Review Part 2 Questions Part 2 Exercises Part 3: Inferential Statistics 8. Statistical Inference: Confidence Intervals 8.1 Point and Interval Estimates of Population Parameters 8.2 Constructing a Confidence Interval to Estimate a Population Proportion 8.3 Constructing a Confidence Interval to Estimate a Population Mean 8.4 Choosing the Sample Size for a Study 8.5 Using Computers to Make New Estimation Methods Possible Chapter Summary Chapter Problems 9. Statistical Inference: Significance Tests about Hypotheses 9.1 Steps for Performing a Significance Test 9.2 Significance Tests about Proportions 9.3 Significance Tests about Means 9.4 Decisions and Types of Errors in Significance Tests 9.5 Limitations of Significance Tests 9.6 The Likelihood of a Type II Error (Not Rejecting H0, Even Though It's False) Chapter Summary Chapter Problems 10. Comparing Two Groups 10.1 Categorical Response: Comparing Two Proportions 10.2 Quantitative Response: Comparing Two Means 10.3 Other Ways of Comparing Means and Comparing Proportions 10.4 Analyzing Dependent Samples 10.5 Adjusting for the Effects of Other Variables Chapter Summary Chapter Problems Part 3 Review Part 3 Questions Part 3 Exercises Part 4: Analyzing Association and Extended Statistical Methods 11. Analyzing the Association Between Categorical Variables 11.1 Independence and Association 11.2 Testing Categorical Variables for Independence 11.3 Determining the Strength of the Association 11.4 Using Residuals to Reveal the Pattern of Association 11.5 Small Sample Sizes: Fisher's Exact Test Chapter Summary Chapter Problems 12. Analyzing the Association Between Quantitative Variables: Regression Analysis 12.1 Model How Two Variables Are Related 12.2 Describe Strength of Association 12.3 Make Inference About the Association 12.4How the Data Vary Around the Regression Line 12.5 Exponential Regression: A Model for Nonlinearity Chapter Summary Chapter Problems 13. Multiple Regression 13.1 Using Several Variables to Predict a Response 13.2 Extending the Correlation and R-squared for Multiple Regression 13.3 Using Multiple Regression to Make Inferences 13.4 Checking a Regression Model Using Residual Plots 13.5 Regression and Categorical Predictors 13.6 Modeling a Categorical Response Chapter Summary Chapter Problems 14. Comparing Groups: Analysis of Variance Methods 14.1 One-Way ANOVA: Comparing Several Means 14.2 Estimating Differences in Groups for a Single Factor 14.3 Two-Way ANOVA Chapter Summary Chapter Problems 15. Nonparametric Statistics 15.1 Compare Two Groups by Ranking 15.2 Nonparametric Methods For Several Groups and for Matched Pairs Chapter Summary Chapter Problems PART 4 Review Part 4 Questions Part 4 Exercises Tables Answers Index Index of Applications Photo Credits

Biostatistics: Basic Concepts and Methodology for the Health Sciences

Abstract: Preface. 1. Introduction To Biostatistics. 1.1 Introduction. 1.2 Some Basic Concepts. 1.3 Measurement and Measurement Scales. 1.4 Sampling and Statistical Inference. 1.5 The Scientific Method and the Design of Experiments. 1.6 Computers and Biostatistical Analysis. 1.7 Summary. Review Questions and Exercises. References. 2. Descriptive Statistics. 2.1 Introduction. 2.2 The Ordered Array. 2.3 Grouped Data: The Frequency Distribution. 2.4 Descriptive Statistics: Measures of Central Tendency. 2.5 Descriptive Statistics: Measures of Dispersion. 2.6 Summary. Review Questions and Exercises. References. 3. Some Basic Probability Concepts. 3.1 Introduction. 3.2 Two Views of Probability: Objective and Subjective. 3.3 Elementary Properties of Probability. 3.4 Calculating the Probability of an Event. 3.5 Bayes' Theorem, Screening Tests, Sensitivity, Specificity, and Predictive Value Positive and Negative. Summary. Review Questions and Exercises. References. 4. Probability Distributions. 4.1 Introduction. 4.2 Probability Distributions of Discrete Variables. 4.3 The Binomial Distribution. 4.4 The Poisson Distribution. 4.5 Continuous Probability Distributions. 4.6 The Normal Distribution. 4.7 Normal Distribution Applications. 4.8 Summary. Review Questions and Exercises. References. 5. Some Important Sampling Distributions. 5.1 Introduction. 5.2 Sampling Distributions. 5.3 Distribution of the Sample Mean. 5.4 Distribution of the Difference Between Two Sample Means. 5.5 Distribution of the Sample Proportion. 5.6 Distribution of the Difference Between Two Sample Proportions. 5.7 Summary. Review Questions and Exercises. References. 6. Estimation. 6.1 Introduction. 6.2 Confidence Interval for a Population Mean. 6.3 The t Distribution. 6.4 Confidence Interval for the Difference Between Two Population Means. 6.5 Confidence Interval for a Population Proportion. 6.6 Confidence Interval for the Difference Between Two Population Proportions. 6.7 Determination of Sample Size for Estimating Means. 6.8 Determination of Sample Size for Estimating Proportions. 6.9 Confidence Interval for the Variance of a Normally Distributed Population. 6.10 Confidence Interval for the Ratio of the Variances of Two Normally Distributed Populations. 6.11 Summary. Review Questions and Exercises. References. 7. Hypothesis Testing. 7.1 Introduction. 7.2 Hypothesis Testing: A Single Population Mean. 7.3 Hypothesis Testing: The Difference Between Two Population Means. 7.4 Paired Comparisons. 7.5 Hypothesis Testing: A Single Population Proportion. 7.6 Hypothesis Testing: The Difference Between Two Population Proportions. 7.7 Hypothesis Testing: A Single Population Variance. 7.8 Hypothesis Testing: The Ratio of Two Population Variances. 7.9 The Type II Error and the Power of a Test. 7.10 Determining Sample Size to Control Type II Errors. 7.11 Summary. Review Questions and Exercises. References. 8. Analysis Of Variance. 8.1 Introduction. 8.2 The Completely Randomized Design. 8.3 The Randomized Complete Block Design. 8.4 The Repeated Measures Design. 8.5 The Factorial Experiment. 8.6 Summary. Review Questions and Exercises. References. 9. Simple Linear Regression And Correlation. 9.1 Introduction. 9.2 The Regression Model. 9.3 The Sample Regression Equation. 9.4 Evaluating the Regression Equation. 9.5 Using the Regression Equation. 9.6 The Correlation Model. 9.7 The Correlation Coefficient. 9.8 Some Precautions. 9.9 Summary. Review Questions and Exercises. References. 10. Multiple Regression And Correlation. 10.1 Introduction. 10.2 The Multiple Linear Regression Model. 10.3 Obtaining the Multiple Regression Equation. 10.4 Evaluating the Multiple Regression Equation. 10.5 Using the Multiple Regression Equation. 10.6 The Multiple Correlation Model. 10.7 Summary. Review Questions and Exercises. References. 11. Regression Analysis: Some Additional Techniques. 11.1 Introduction. 11.2 Qualitative Independent Variables. 11.3 Variable Selection Procedures. 11.4 Logistic Regression. 11.5 Summary. Review Questions and Exercises. References. 12. The Chi-Square Distribution And The Analysis Of Frequencies. 12.1 Introduction. 12.2 The Mathematical Properties of the Chi-Square Distribution. 12.3 Tests of Goodness-of-Fit. 12.4 Tests of Independence. 12.5 Tests of Homogeneity. 12.6 The Fisher Exact Test. 12.7 Relative Risk, Odds Ratio, and the Mantel-Haenszel Statistic. 12.8 Survival Analysis. 12.9 Summary. Review Questions and Exercises. References. 13. Nonparametric And Distribution-Free Statistics. 13.1 Introduction. 13.2 Measurement Scales. 13.3 The Sign Test. 13.4 The Wilcoxon Signed-Rank Test for Location. 13.5 The Median Test. 13.6 The Mann-Whitney Test. 13.7 The Kolmogorov-Smirnov Goodness-of-Fit Test. 13.8 The Kruskal-Wallis One-Way Analysis of Variance by Ranks. 13.9 The Friedman Two-Way Analysis of Variance by Ranks. 13.10 The Spearman Rank Correlation Coefficient. 13.11 Nonparametric Regression Analysis. 13.12 Summary. Review Questions and Exercises. References. 14. Vital Statistics. 14.1 Introduction. 14.2 Death Rates and Ratios. 14.3 Measures of Fertility. 14.4 Measures of Morbidity. 14.5 Summary. Review Questions and Exercises. References. Appendix. Statistical Tables. Answers To Odd-Numbered Exercises. Index.

Ranked set sampling for efficient estimation of a population proportion.

Abstract: Ranked set sampling (RSS) is a sampling procedure that can be considerably more efficient than simple random sampling (SRS). It involves preliminary ranking of the variable of interest to aid in sample selection. Although ranking processes for continuous variables that are implemented through either subjective judgement or via the use of a concomitant variable have been studied extensively in the literature, the use of RSS in the case of a binary variable has not been investigated thoroughly. In this paper we propose the use of logistic regression to aid in the ranking of a binary variable of interest. We illustrate the application of RSS to estimation of a population proportion with an example based on the National Health and Nutrition Examination Survey III data set. Our results indicate that this use of logistic regression improves the accuracy of the preliminary ranking in RSS and leads to substantial gains in precision for estimation of a population proportion.

Essentials of Statistics

Abstract: (Each Chapter begins with an Overview) 1. Introduction to Statistics The Nature of Data Uses and Abuses of Statistics Design of Experiments 2. Describing, Exploring, and Comparing Data Summarizing Data with Frequency Tables Pictures of Data Measures of Center Measures of Variation. Measures of Position Exploratory Data Analysis (EDA) 3. Probability Fundamentals Addition Rule Multiplication Rule: Basics Multiplication Rule: Complements and Conditional Probability Counting 4. Probability Distributions Random Variables Binomial Probability Distributions Mean, Variance, and Standard Deviation for the Binomial Distribution 5. Normal Probability Distributions The Standard Normal Distribution Nonstandard Normal Distributions: Finding Probabilities Nonstandard Normal Distributions: Finding Values The Central Limit Theorem Normal Distribution as Approximation to Binomial Distribution 6. Estimates and Sample Sizes Estimating a Population Mean: Large Samples Estimating a Population Mean: Small Samples Determining Sample Size Estimating a Population Proportion Estimating a Population Variance 7. Hypothesis Testing Fundamentals of Hypothesis Testing Testing a Claim about a Mean: Large Samples Testing a Claim about a Mean: Small Samples Testing a Claim about a Proportion Testing a Claim about a Standard Deviation or Variance 8. Inferences from Two Samples Inferences about Two Means: Independent and Large Samples Inferences about Two Means: Matched Pairs Inferences about Two Proportions 9. Correlation and Regression Correlation Regression Variation and Prediction Intervals 10. Chi-Square and Analysis of Variance Multinomial Experiments: Goodness-0f-Fit Contingency Tables: Independence and Homogeneity One-Way ANOVA Appendices Appendix A: Tables Appendix B: Data Sets Appendix C: TI-83 Plus Reference Appendix D: Answers to Odd-Numbered Exercises (and All Review Chapter Exercises and All Cumulative Review Exercises) Credits