Page 5 - Modern Analytical Chemistry

1400-Fm 9/9/99 7:37 AM Page iv

iv Modern Analytical Chemistry

3E Developing the Procedure 45 4E.4 Errors in Significance Testing 84
3E.1 Compensating for Interferences 45 4F Statistical Methods for Normal Distributions 85
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3E.2 Calibration and Standardization 47 4F.1 Comparing X to m 85
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3E.3 Sampling 47 4F.2 Comparing s to s 2 87
3E.4 Validation 47 4F.3 Comparing Two Sample Variances 88
3F Protocols 48 4F.4 Comparing Two Sample Means 88
3G The Importance of Analytical Methodology 48 4F.5 Outliers 93
3H Key Terms 50 4G Detection Limits 95
3I Summary 50 4H Key Terms 96
3J Problems 51 4I Summary 96
3K Suggested Readings 52 4J Suggested Experiments 97
3L References 52 4K Problems 98
Chapter 4 4L Suggested Readings 102
4M References
102
Evaluating Analytical Data 53
Chapter 5

4A Characterizing Measurements and Results 54
4A.1 Measures of Central Tendency 54 Calibrations, Standardizations,
and Blank Corrections 104
4A.2 Measures of Spread 55
4B Characterizing Experimental Errors 57
5A Calibrating Signals 105
4B.1 Accuracy 57
5B Standardizing Methods 106
4B.2 Precision 62
5B.1 Reagents Used as Standards 106
4B.3 Error and Uncertainty 64
5B.2 Single-Point versus Multiple-Point
4C Propagation of Uncertainty 64 Standardizations 108
4C.1 A Few Symbols 65 5B.3 External Standards 109
4C.2 Uncertainty When Adding or Subtracting 65 5B.4 Standard Additions 110
4C.3 Uncertainty When Multiplying or 5B.5 Internal Standards 115
Dividing 66
5C Linear Regression and Calibration Curves 117
4C.4 Uncertainty for Mixed Operations 66
5C.1 Linear Regression of Straight-Line Calibration
4C.5 Uncertainty for Other Mathematical Curves 118
Functions 67
5C.2 Unweighted Linear Regression with Errors
4C.6 Is Calculating Uncertainty Actually Useful? 68 in y 119
4D The Distribution of Measurements and 5C.3 Weighted Linear Regression with Errors
Results 70 in y 124
4D.1 Populations and Samples 71 5C.4 Weighted Linear Regression with Errors
4D.2 Probability Distributions for Populations 71 in Both x and y 127
4D.3 Confidence Intervals for Populations 75 5C.5 Curvilinear and Multivariate
4D.4 Probability Distributions for Samples 77 Regression 127
4D.5 Confidence Intervals for Samples 80 5D Blank Corrections 128
4D.6 A Cautionary Statement 81 5E Key Terms 130
4E Statistical Analysis of Data 82 5F Summary 130
4E.1 Significance Testing 82 5G Suggested Experiments 130
4E.2 Constructing a Significance Test 83 5H Problems 131
4E.3 One-Tailed and Two-Tailed Significance 5I Suggested Readings 133
Tests 84 5J References 134