Introduction to Sampling

Introduction. Some Basic Concepts and Terminology

Reasons Why Sampling May Be Preferred Over Complete Enumeration. Some Further Testimony.

Accuracy and Precision of Data

Accuracy of Data. Precision. Accuracy and Precision With Discrete Variables. Accuracy and Precision With Continuous Variables. Significant Figures. Rounding Off. Computations Using Approximate Numbers.

Data Arrangement

Introduction. Methods of Arrangement. Rules controlling Frequency Distributions. Cumulative Frequency Distributions. Relative Frequency Distributions. Graphical Presentations of Frequency Distributions. Descriptive Terms Used for Frequency Distributions.

Symbology

Introduction. Identification of Variables. Subscribing

Summation Symbology. Distinguishing Between Populations and Sample Values.

Averages

Introduction. Assessing Average. The Arithmetic Mean. The Median. The Mode. The Geometric Mean. The Harmonic Mean. The Quadratic Mean.

Measures of Dispersion

Introduction. The Range. The Interquartille and Semi-Interquartille Ranges. The Average Deviation. The Variance. The Standard Deviation. The Coefficient of Deviation. Probability. Some Basic Concepts and Terms. Relative Frequency. Empirical Probability. Classical Probability. Probability of Alternative Events. Probability of Multiple Events. Objective and Subjective Probabilities.

Probability Distributions

Random Variables. Probability Distribution and Empirical Relative Frequency Distributions. Discrete Probability Distributions. Cumulative Probability Distributions. The Mean of Random a Variable. Moments, Skewness, and Kurtosis. Moment Generating Functions.

Multi-Dimensional Probability Distributions

Multi-Dimensional Random Variables. Joint Probability Distributions. Marginal Probabilities. Conditional Probabilities. Joint Probability Distribution Functions. Functions of Multi-Dimensional Random Variables. Expectation of Functions of Multi-Dimensional Random Variables. The Regression of the Mean.

Discrete Probability Distributions

Introduction. The Rectangular Probability Distribution (D:M, YA, YB). The Binomial Probability Distribution (B:n,p). The Hypergeometric Probability Distribution (H:N, NS, n). The Poisson Probability Distribution (p:l). The Geometric Probability Distribution (G:p). The Negative Binomial and Pascal Probability Distribution s(NB:m,p and C:m,p). The Multinomial Probability Distribution (M:p1, p2...).

Continuous Probability Distributions

The Rectangular Probability Distribution (R:YA, YB). The Normal Probability Distribution (N:m, s). The Gamma Probability Distribution (G:r, a). The Exponential Probability Distribution (E:a). The Chi-Square Probability Distribution (x2:k). The Beta Probability Distribution (b:r1, r2). The Bivariate Normal Probability Distribution (N:m1, s1, N:m2, s2). The Weibull Probability Distribution (W:r, ya).

Sampling Theory

Introduction. Sampling Design. Sampling, Sampling Units, and Sampling Frames. Random Sampling and Random Numbers. Sampling Frames and Infinite Populations. The Sample Size and the Sampling Fraction. Sampling Distributions. Standard Answers. Bias. Precision. Sampling Distribution of Means. Sampling Distribution of Variances. Sampling Distribution of Standard Deviations. Sampling Distribution of Proportions. Sampling Distribution of Covariances. Sampling Distribution of Differences.

Estimation of Parameters

Introduction. Estimators and Estimates. Point Estimates. Criteria for Judging Estimators of Parameters. Laws of Large Numbers. Maximum Likelihood Estimators. Interval Estimates. Confidence Interval Estimates of Population Parameters Using the Normal Distribution. Confidence Interval Estimates of Population Means Using Students T-Distribution. Chebyshev's Theorem. Confidence Interval Estimates of Population Proportions. Confidence Interval Estimates of Population Variances and Standard Deviations. One-Sided Confidence Intervals. Sampling Errors, Allowable Errors, and Needed Sample Size.

Fundamentals of Hypothesis Testing

Introduction. Statistical Hypothesis. Type I and Type II Errors. Statistical Significance. Homogeneity Tests. One and Two-Tailed Test. The Power of the Test. Decision Rules. Test Procedures. Homogeneity Test Using a Sample Mean. Test of a Difference (Unpaired). Test of a Difference (Paired). The Linear Additive Model. The F-Distribution. Testing for Homogeneity of Variance Using F. Bartlett's Test for Homogeneity of Variance. Testing for Goodness of Fit Using x2. Testing for Normality. The Analysis of Variance. Transformations. Multiple Comparisons.

Regression and Correlation

Introduction. Theory of Regression. Fitting a Regression. Dummy Variables. Variance About the Regression. Confidence Intervals for Regression Estimates. Correlation. Hypothesis Testing in Regression Operations. Stepwise Variable Selection.

Stratified Random Sampling

Introduction. The Stratification Process. The Stratified Population. Estimation of the Parameters. Allocation of the Sample. Comparison of the Methods of Allocation. Stratification and the Estimation of Proportions. Effectiveness of Stratification. Stratum Sizes. Miscellany.

Cluster Sampling

Introduction. Types of Cluster Sampling. Cluster Configuration. Population Parameters. Estimation of the Parameters. The Intraclass Correlation Coefficient. Overlapping and Interlocking of Clusters. Examples. Variance of Functions. Cost Functions. Efficiency of Cluster Sampling. Sample Size Determination. Optimum Cluster Size. Cluster Sampling for Proportions. Three-Stage Sampling. Stratified Cluster Sampling.

Systematic Sampling

Introduction. Approaches to Systematic Sampling. Element Spacing and Sampling Intensity. Cluster Sampling Frames. Random and Arbitrary Starts. Population Types. Population Parameters. Variance of the Overall Total and Mean. Estimation of the Parameters. Approximations of the Variance of the Overall Mean.

Ratio Estimation

Introduction. Estimating R. Bias of R. Approximations of the Ratio Estimators. Using a Ratio to Estimate a Population Total and Mean. Variance of the Ratio Estimates. Sample Size. Efficiency of Ratio Estimators. Ratio Estimation and Stratified Sampling. Ratio Estimation and Cluster Sampling. Comments.

Double Sampling

Introduction. Using Regression. Using Ratio Estimators.

Sampling With Unequal Probabilities

Introduction. Mathematical Rationale. Sampling With Probability Proportional to Size (PPS). 3-P Sampling

Appendix

Literature Cited

Subject Index

Author Index