PREFACE xv
 
ACKNOWLEDGMENTS xix
 
1 Introduction 1
 
1.1 Introduction / 1
 
1.2 Direct and Indirect Measurements / 2
 
1.3 Measurement Error Sources / 2
 
1.4 Definitions / 3
 
1.5 Precision versus Accuracy / 4
 
1.6 Redundant Observations in Surveying and Their Adjustment / 7
 
1.7 Advantages of Least Squares Adjustment / 8
 
1.8 Overview of the Book / 10
 
Problems / 10
 
2 Observations and Their Analysis 13
 
2.1 Introduction / 13
 
2.2 Sample versus Population / 13
 
2.3 Range and Median / 14
 
2.4 Graphical Representation of Data / 15
 
2.5 Numerical Methods of Describing Data / 18
 
2.6 Measures of Central Tendency / 18
 
2.7 Additional Definitions / 19
 
2.8 Alternative Formula for Determining Variance / 22
 
2.9 Numerical Examples / 24
 
2.10 Root Mean Square Error and Mapping Standards / 28
 
2.11 Derivation of the Sample Variance (Bessel's Correction) / 31
 
2.12 Software / 32
 
Problems / 34
 
Practical Exercises / 37
 
3 Random Error Theory 39
 
3.1 Introduction / 39
 
3.2 Theory of Probability / 39
 
3.3 Properties of the Normal Distribution Curve / 42
 
3.4 Standard Normal Distribution Function / 44
 
3.5 Probability of the Standard Error / 47
 
3.6 Uses for Percent Errors / 50
 
3.7 Practical Examples / 50
 
Problems / 53
 
Programming Problems / 55
 
4 Confidence Intervals 57
 
4.1 Introduction / 57
 
4.2 Distributions Used in Sampling Theory / 59
 
4.3 Confidence Interval for the Mean: t Statistic / 63
 
4.4 Testing the Validity of the Confidence Interval / 66
 
4.5 Selecting a Sample Size / 67
 
4.6 Confidence Interval for a Population Variance / 68
 
4.7 Confidence Interval for the Ratio of Two Population Variances / 70
 
4.8 Software / 72
 
Problems / 75
 
5 Statistical Testing 79
 
5.1 Hypothesis Testing / 79
 
5.2 Systematic Development of a Test / 82
 
5.3 Test of Hypothesis for the Population Mean / 84
 
5.4 Test of Hypothesis for the Population Variance / 85
 
5.5 Test of Hypothesis for the Ratio of Two Population Variances / 89
 
5.6 Software / 92
 
Problems / 93
 
6 Propagation of Random Errors in Indirectly Measured Quantities 97
 
6.1 Basic Error Propagation Equation / 97
 
6.2 Frequently Encountered Specific Functions / 102
 
6.3 Numerical Examples / 103
 
6.4 Software / 107
 
6.5 Conclusions / 109
 
Problems / 109
 
Practical Exercises / 112
 
7 Error Propagation in Angle and Distance Observations 113
 
7.1 Introduction / 113
 
7.2 Error Sources in Horizontal Angles / 113
 
7.3 Reading Errors / 114
 
7.4 Pointing Errors / 116
 
7.5 Estimated Pointing and Reading Errors with Total Stations / 117
 
7.6 Target-Centering Errors / 118
 
7.7 Instrument Centering Errors / 120
 
7.8 Effects of Leveling Errors in Angle Observations / 123
 
7.9 Numerical Example of Combined Error Propagation in a Single Horizontal Angle / 126
 
7.10 Using Estimated Errors to Check Angular Misclosure in a Traverse / 127
 
7.11 Errors in Astronomical Observations for Azimuth / 130
 
7.12 Errors in Electronic Distance Observations / 135
 
7.13 Centering Errors When Using Range Poles / 136
 
7.14 Software / 137
 
Problems / 138
 
Programming Problems / 141
 
8 Er