Preface |
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v | |
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1 | (20) |
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1 | (2) |
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Chemometrics and the `Arch of Knowledge' |
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1 | (1) |
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2 | (1) |
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An overview of chemometrics |
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3 | (9) |
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Experiments and experimental design |
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3 | (1) |
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Extraction of information from data |
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3 | (1) |
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3 | (2) |
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5 | (1) |
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6 | (2) |
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8 | (2) |
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Chemical knowledge and (artificial) intelligence |
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10 | (1) |
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Chemical domains and quality aspects |
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10 | (1) |
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Mathematical and statistical tools |
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11 | (1) |
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11 | (1) |
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Some historical considerations |
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12 | (3) |
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Chemometrics in industry and academia |
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15 | (6) |
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18 | (3) |
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Statistical Description of the Quality of Processes and Measurements |
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21 | (26) |
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Introductory concepts about chemical data |
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21 | (11) |
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21 | (1) |
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22 | (1) |
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Histograms and distributions |
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23 | (3) |
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26 | (1) |
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Population parameters and their estimators |
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26 | (1) |
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Mean and other parameters for central location |
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27 | (1) |
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Standard deviation and variance |
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27 | (1) |
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Pooled standard deviation and standard deviation from paired data |
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28 | (2) |
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Range and its relation to the standard deviation |
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30 | (2) |
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32 | (1) |
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32 | (1) |
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Systematic versus random errors |
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33 | (1) |
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Quality of processes and statistical process control |
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33 | (6) |
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Process capability indexes for dispersion |
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34 | (1) |
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Process capability index for setting |
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35 | (1) |
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Process capability indexes for dispersion and setting |
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36 | (1) |
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Some other statistical process control tools and concepts |
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37 | (2) |
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Quality of measurements in relation to quality of processes |
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39 | (1) |
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Precision and bias of measurements |
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40 | (1) |
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Some other types of error |
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41 | (1) |
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42 | (2) |
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Rounding and rounding errors |
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44 | (3) |
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45 | (2) |
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47 | (26) |
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Population parameters and their estimators |
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47 | (2) |
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Moments of a distribution: mean, variance, skewness |
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49 | (1) |
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The normal distribution: description and notation |
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50 | (2) |
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Tables for the standardized normal distribution |
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52 | (4) |
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56 | (2) |
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Confidence intervals for the mean |
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58 | (2) |
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Small samples and the t-distribution |
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60 | (3) |
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Normality tests: a graphical procedure |
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63 | (7) |
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How to convert a non-normal distribution into a normal one |
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70 | (3) |
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72 | (1) |
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An Introduction To Hypothesis Testing |
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73 | (20) |
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Comparison of the mean with a given value |
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73 | (1) |
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Null and alternative hypotheses |
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74 | (1) |
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Using confidence intervals |
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75 | (1) |
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Comparing a test value with a critical value |
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76 | (2) |
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Presentation of results of a hypothesis test |
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78 | (1) |
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Level of significance and type I error |
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79 | (1) |
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79 | (3) |
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82 | (3) |
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85 | (3) |
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An alternative approach: interval hypotheses |
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88 | (5) |
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91 | (2) |
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Some Important Hypothesis Tests |
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93 | (28) |
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93 | (7) |
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Comparison of the means of two independent samples |
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93 | (1) |
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93 | (2) |
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95 | (2) |
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Comparison of the means of two paired samples |
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97 | (2) |
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99 | (1) |
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99 | (1) |
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100 | (2) |
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102 | (2) |
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104 | (5) |
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Comparison of two variances |
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104 | (3) |
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Comparison of a variance with a known value |
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107 | (2) |
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109 | (5) |
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109 | (3) |
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112 | (2) |
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114 | (7) |
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116 | (1) |
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117 | (3) |
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120 | (1) |
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121 | (30) |
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One-way analysis of variance |
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121 | (10) |
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121 | (3) |
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Estimating sources of variance and their significance |
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124 | (2) |
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Breaking up total variance in its components |
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126 | (2) |
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Random and fixed effect models |
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128 | (2) |
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130 | (1) |
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131 | (4) |
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Fixed effect models: testing differences between means of columns |
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135 | (2) |
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Random effect models: variance components |
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137 | (1) |
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Two-way and multi-way ANOVA |
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138 | (4) |
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142 | (2) |
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Incorporation of interaction in the residual |
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144 | (1) |
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Experimental design and modelling |
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145 | (1) |
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145 | (1) |
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Repeated testing by ANOVA |
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146 | (1) |
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147 | (4) |
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150 | (1) |
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151 | (20) |
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151 | (1) |
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151 | (10) |
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151 | (1) |
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151 | (4) |
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Application of the mean chart |
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155 | (3) |
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158 | (2) |
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Other charts for central location and spread |
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160 | (1) |
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Charts for the analytical laboratory |
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160 | (1) |
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161 | (1) |
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Moving average and related charts |
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161 | (8) |
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Moving average and range charts |
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161 | (2) |
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The cumulative sum (CUSUM) chart |
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163 | (3) |
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Exponentially weighted moving average charts |
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166 | (3) |
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169 | (2) |
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169 | (2) |
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Straight Line Regression and Calibration |
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171 | (60) |
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171 | (1) |
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172 | (47) |
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Estimation of the regression parameters |
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172 | (7) |
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179 | (1) |
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Analysis of the residuals |
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179 | (1) |
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180 | (6) |
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186 | (1) |
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187 | (1) |
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187 | (2) |
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Confidence intervals and hypothesis tests |
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189 | (1) |
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Confidence interval for the intercept and the slope |
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189 | (4) |
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Joint confidence region for slope and intercept |
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193 | (2) |
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Confidence interval for the true response at a given value of x |
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195 | (1) |
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Predictions made on the basis of the fitted line |
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196 | (1) |
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Prediction of new responses |
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196 | (1) |
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197 | (5) |
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202 | (5) |
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207 | (1) |
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207 | (1) |
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Comparison of the slopes of two regression lines |
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208 | (2) |
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The intersection of two regression lines |
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210 | (3) |
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Regression when both the predictor and the response variable are subject to error |
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213 | (3) |
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Straight line regression through a fixed point |
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216 | (1) |
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Linearization of a curved line |
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217 | (2) |
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219 | (12) |
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The correlation coefficient |
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221 | (2) |
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Hypothesis tests and confidence limits |
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223 | (5) |
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Correlation and regression |
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228 | (1) |
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229 | (2) |
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231 | (32) |
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The data table as data matrix |
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231 | (1) |
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232 | (17) |
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232 | (2) |
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234 | (1) |
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234 | (1) |
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Multiplication by a scalar |
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235 | (1) |
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236 | (1) |
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236 | (3) |
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239 | (1) |
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239 | (1) |
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240 | (1) |
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241 | (4) |
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Linear combinations, linear dependence and collinearity |
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245 | (2) |
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247 | (2) |
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249 | (14) |
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249 | (1) |
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250 | (1) |
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Addition and substraction |
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250 | (1) |
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Multiplication by a scalar |
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251 | (1) |
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251 | (2) |
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Examples of matrix multiplication |
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253 | (3) |
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Inverse of a square matrix |
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256 | (1) |
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Regression modelling and projection |
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257 | (2) |
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Determinant of a square matrix |
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259 | (2) |
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261 | (1) |
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261 | (2) |
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Multiple and Polynomial Regression |
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263 | (42) |
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263 | (1) |
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Estimation of the regression parameters |
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264 | (6) |
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270 | (14) |
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Examination of the overall regression equation |
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270 | (1) |
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270 | (3) |
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The coefficient of multiple determination |
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273 | (1) |
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Analysis of the residuals |
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274 | (1) |
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Importance of the predictor variables |
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275 | (3) |
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Selection of predictor variables |
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278 | (4) |
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Validation of the prediction accuracy of the model |
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282 | (2) |
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284 | (2) |
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286 | (3) |
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289 | (3) |
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Multicomponent analysis by multiple linear regression |
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292 | (4) |
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296 | (4) |
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300 | (5) |
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302 | (3) |
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305 | (34) |
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305 | (1) |
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306 | (16) |
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308 | (1) |
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Least-squares parameter estimation |
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309 | (1) |
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Gauss-Newton linearization |
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310 | (4) |
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Steepest descent and Marquardt procedure |
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314 | (1) |
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315 | (6) |
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321 | (1) |
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322 | (17) |
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322 | (1) |
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323 | (1) |
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323 | (4) |
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327 | (2) |
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329 | (1) |
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329 | (3) |
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332 | (4) |
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336 | (1) |
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336 | (3) |
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339 | (40) |
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Methods based on the median |
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339 | (22) |
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339 | (1) |
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The median and the interquartile range |
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339 | (2) |
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341 | (3) |
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Hypothesis tests based on ranking |
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344 | (1) |
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The sign test for two related samples |
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344 | (1) |
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The Wilcoxon signed rank test or the Wilcoxon T-test for two paired samples |
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345 | (2) |
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Mann-Witney U-test for two independent samples |
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347 | (2) |
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Kruskal-Wallis one-way analysis of variance by ranks |
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349 | (1) |
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The Spearman rank correlation coefficient |
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350 | (1) |
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Detection of trends by the runs test |
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351 | (3) |
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Median-based robust regression |
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354 | (1) |
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355 | (1) |
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356 | (2) |
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The least median of squares (LMS) method |
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358 | (3) |
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Comparison of least squares and different median based robust regression procedures |
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361 | (1) |
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Biweight and winsorized mean |
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361 | (4) |
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Iteratively reweighted least squares |
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365 | (2) |
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367 | (2) |
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369 | (10) |
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Probabilistic MC for statistical methods |
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370 | (2) |
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Probabilistic MC for physical systems |
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372 | (2) |
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374 | (2) |
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376 | (3) |
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Internal Method Validation |
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379 | (62) |
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Definition and types of method validation |
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379 | (2) |
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The golden rules of method validation |
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381 | (1) |
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Types of internal method validation |
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381 | (2) |
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383 | (10) |
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383 | (1) |
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384 | (4) |
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An intermediate precision measure: within-laboratory reproducibility |
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388 | (1) |
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Requirements for precision measurements |
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389 | (1) |
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390 | (3) |
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393 | (24) |
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393 | (4) |
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Restricted concentration range --- reconstitution of sample possible |
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397 | (1) |
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Restricted concentration range --- reference material available |
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398 | (1) |
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Large concentration range --- blank material available |
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399 | (5) |
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Large concentration range --- blank material not available |
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404 | (4) |
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Comparison of two methods or two laboratories |
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408 | (6) |
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An alternative approach to hypothesis testing in method validation |
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414 | (1) |
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Comparison of more than two methods or laboratories |
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414 | (3) |
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Linearity of calibration lines |
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417 | (5) |
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The correlation coefficient |
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418 | (1) |
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418 | (3) |
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The F-test for lack of fit |
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421 | (1) |
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Test of the significance of b2 |
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421 | (1) |
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Use of robust regression or non-parametric methods |
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422 | (1) |
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Detection limit and related quantities |
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422 | (13) |
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423 | (2) |
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425 | (1) |
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426 | (1) |
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427 | (2) |
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429 | (1) |
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430 | (1) |
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431 | (1) |
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Determination of the concentration limits from the calibration line |
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432 | (3) |
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435 | (1) |
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Sensitivity in quantitative analysis |
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435 | (1) |
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Sensitivity and specificity in qualitative analysis |
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436 | (1) |
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Selectivity and interferences |
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436 | (5) |
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438 | (3) |
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Method Validation by Interlaboratory Studies |
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441 | (20) |
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Types of interlaboratory studies |
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441 | (1) |
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Method-performance studies |
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441 | (10) |
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Definition of reproducibility and repeatability |
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441 | (2) |
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Method-performance precision experiments |
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443 | (1) |
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Repeatability and reproducibility in a method-performance experiment |
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444 | (1) |
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Statistical analysis of the data obtained in a method-performance experiment |
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444 | (5) |
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449 | (2) |
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Method-performance bias experiments |
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451 | (1) |
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Laboratory-performance studies |
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451 | (10) |
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451 | (1) |
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452 | (1) |
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452 | (2) |
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Mandel's h and k consistency statistics |
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454 | (3) |
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457 | (1) |
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457 | (3) |
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460 | (1) |
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461 | (14) |
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Introduction --- probabilities |
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461 | (2) |
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The binomial distribution |
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463 | (4) |
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An example: the counter-current distribution |
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463 | (2) |
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465 | (1) |
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Applications in quality control: the np and p charts |
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466 | (1) |
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The hypergeometric distribution |
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467 | (1) |
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468 | (3) |
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Rare events and the Poisson distribution |
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468 | (2) |
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Application in quality control: the c and u-charts |
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470 | (1) |
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Interrelationships between the binomial, Poisson and normal distributions |
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471 | (1) |
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The negative exponential distribution and the Weibull distribution |
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471 | (1) |
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Extreme value distributions |
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472 | (3) |
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473 | (2) |
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The 2x2 Contingency Table |
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475 | (44) |
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475 | (14) |
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Variables, categories, frequencies and marginal totals |
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475 | (1) |
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Probability and conditional probability |
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476 | (2) |
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Sensitivity and specificity |
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478 | (3) |
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481 | (1) |
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Posterior and prior probabilities, Bayes' theorem and likelihood ratio |
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482 | (1) |
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483 | (2) |
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485 | (2) |
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Receiver operating characteristic |
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487 | (2) |
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489 | (30) |
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Test of hypotheses for 2 x 2 contingency tables |
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489 | (2) |
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Fisher's exact test for two independent samples |
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491 | (2) |
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Pearson's X2 test for two independent samples |
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493 | (3) |
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Graphical X2 test for two independent samples |
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496 | (2) |
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Large-scale X2 test statistic for two independent samples |
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498 | (1) |
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McNemar's X2 test statistic for two related samples |
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498 | (2) |
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500 | (1) |
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Mantel-Haenszel X2 test statistic for multiple 2 x 2 contingency tables |
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501 | (3) |
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504 | (1) |
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505 | (4) |
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Multiple 2 x 2 contingency tables, meta-analysis |
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509 | (2) |
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Logistic regression, confounding, interaction |
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511 | (2) |
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513 | (2) |
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General contingency table |
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515 | (2) |
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517 | (2) |
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519 | (38) |
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519 | (8) |
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527 | (3) |
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530 | (6) |
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536 | (2) |
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Applications in method validation |
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538 | (3) |
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Comparison of two methods |
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538 | (1) |
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539 | (2) |
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The singular value decomposition |
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541 | (5) |
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541 | (2) |
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Score and loading matrices |
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543 | (3) |
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The resolution of mixtures by evolving factor analysis and the HELP method |
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546 | (6) |
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Principal component regression and multivariate calibration |
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552 | (1) |
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Other latent variable methods |
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553 | (4) |
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556 | (1) |
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557 | (16) |
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Uncertainty and information |
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557 | (4) |
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An application to thin layer chromatography |
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561 | (3) |
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The information content of combined procedures |
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564 | (3) |
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567 | (2) |
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Information theory in data analysis |
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569 | (4) |
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570 | (3) |
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573 | (14) |
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Conventional set theory and fuzzy set theory |
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573 | (3) |
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Definitions and operations with fuzzy sets |
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576 | (3) |
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579 | (8) |
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Identification of patterns |
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579 | (4) |
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583 | (3) |
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586 | (1) |
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586 | (1) |
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Process Modelling and Sampling |
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587 | (56) |
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587 | (1) |
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Measurability and controllability |
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588 | (3) |
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Estimators of system states |
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591 | (2) |
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Models for process fluctuations |
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593 | (11) |
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593 | (1) |
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594 | (1) |
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Autocorrelation function and time constant |
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594 | (7) |
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The autoregressive moving average model (ARMA) |
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601 | (3) |
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Measurability and measuring system |
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604 | (3) |
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Choice of an optimal measuring system: cost considerations |
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607 | (4) |
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Multivariate statistical process control |
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611 | (7) |
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Sampling for spatial description |
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618 | (1) |
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Sampling for global description |
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619 | (4) |
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619 | (1) |
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620 | (1) |
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621 | (2) |
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623 | (13) |
|
h-scatter plots, autocorrelogram, covariogram and variogram |
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|
624 | (5) |
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629 | (1) |
|
Interpolation methods using only location information |
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630 | (1) |
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631 | (2) |
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633 | (1) |
|
Assessing the uncertainty of the prediction |
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|
634 | (2) |
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636 | (7) |
|
Operating characteristic curve |
|
|
637 | (1) |
|
Sequential sampling plans |
|
|
638 | (2) |
|
|
640 | (3) |
|
An Introduction to Experimental Design |
|
|
643 | (16) |
|
Definition and terminology |
|
|
643 | (1) |
|
Aims of experimental design |
|
|
644 | (3) |
|
|
647 | (2) |
|
|
649 | (2) |
|
|
651 | (3) |
|
Response functions: the model |
|
|
654 | (2) |
|
An overview of simultaneous (factorial) designs |
|
|
656 | (3) |
|
|
658 | (1) |
|
Two-level Factorial Designs |
|
|
659 | (24) |
|
Terminology: a pharmaceutical technology example |
|
|
659 | (3) |
|
Direct estimation of effects |
|
|
662 | (3) |
|
Yates' method of estimating effects |
|
|
665 | (2) |
|
An example from analytical chemistry |
|
|
667 | (1) |
|
Significance of the estimated effects: visual interpretation |
|
|
668 | (4) |
|
|
668 | (2) |
|
|
670 | (2) |
|
Significance of the estimated effects: by using the standard deviation of the effects |
|
|
672 | (3) |
|
Determination of the standard deviation of the effects by using duplicated experiments |
|
|
672 | (1) |
|
Determination of the standard deviation of the effects by neglecting higher interactions |
|
|
673 | (1) |
|
Determination of the standard deviation of the effects by using the centre point |
|
|
674 | (1) |
|
Significance of the estimated effects: by ANOVA |
|
|
675 | (2) |
|
|
677 | (2) |
|
|
679 | (4) |
|
Effect of aberrant values |
|
|
679 | (1) |
|
Blocking and randomization |
|
|
680 | (1) |
|
|
681 | (1) |
|
|
682 | (1) |
|
Fractional Factorial Designs |
|
|
683 | (18) |
|
Need for fractional designs |
|
|
683 | (1) |
|
Confounding: example of a half-fraction factorial design |
|
|
684 | (4) |
|
Defining contrasts and generators |
|
|
688 | (3) |
|
|
691 | (2) |
|
|
693 | (1) |
|
Selection of additional experiments |
|
|
693 | (1) |
|
|
694 | (7) |
|
Saturated fractional factorial designs |
|
|
694 | (3) |
|
|
697 | (2) |
|
|
699 | (2) |
|
|
701 | (38) |
|
Linear and quadratic response surfaces |
|
|
701 | (3) |
|
|
704 | (4) |
|
|
704 | (3) |
|
Rotatability, uniformity and variance-related criteria |
|
|
707 | (1) |
|
Classical symmetrical designs |
|
|
708 | (14) |
|
Three-level factorial designs |
|
|
709 | (2) |
|
Central composite designs |
|
|
711 | (5) |
|
|
716 | (2) |
|
Doehlert uniform shell design |
|
|
718 | (4) |
|
|
722 | (7) |
|
|
722 | (4) |
|
Uniform mapping algorithms |
|
|
726 | (3) |
|
Response surface methodology |
|
|
729 | (5) |
|
|
734 | (1) |
|
|
735 | (4) |
|
|
737 | (2) |
|
|
739 | (32) |
|
|
739 | (2) |
|
|
741 | (2) |
|
Introduction to the Simplex design |
|
|
743 | (3) |
|
Simplex lattice and -centroid designs |
|
|
746 | (11) |
|
The (3,2) Simplex lattice design |
|
|
746 | (2) |
|
(k,m) Simplex lattice designs |
|
|
748 | (4) |
|
|
752 | (1) |
|
|
753 | (1) |
|
Designs based on inner points |
|
|
754 | (2) |
|
Regression modelling of mixture designs |
|
|
756 | (1) |
|
|
757 | (4) |
|
|
761 | (5) |
|
Combining mixture and process variables |
|
|
766 | (5) |
|
|
768 | (3) |
|
Other Optimization Methods |
|
|
771 | (34) |
|
|
771 | (1) |
|
Sequential optimization methods |
|
|
771 | (9) |
|
|
771 | (3) |
|
|
774 | (4) |
|
The modified Simplex method |
|
|
778 | (1) |
|
Advantages and disadvantages of Simplex methods |
|
|
779 | (1) |
|
|
780 | (3) |
|
Multicriteria decision making |
|
|
783 | (16) |
|
|
783 | (2) |
|
|
785 | (3) |
|
|
788 | (1) |
|
|
788 | (2) |
|
Pareto optimality methods |
|
|
790 | (2) |
|
Electre outranking relationships |
|
|
792 | (4) |
|
|
796 | (3) |
|
|
799 | (6) |
|
|
799 | (1) |
|
|
799 | (4) |
|
|
803 | (2) |
|
Genetic Algorithms and Other Global Search Strategies |
|
|
805 | (44) |
|
|
805 | (1) |
|
|
806 | (1) |
|
Principle of genetic algorithms |
|
|
807 | (14) |
|
Candidate solutions: representation |
|
|
807 | (4) |
|
Flowchart of genetic algorithms |
|
|
811 | (1) |
|
|
811 | (1) |
|
Evaluation and termination |
|
|
812 | (1) |
|
|
813 | (3) |
|
Recombination and mutation |
|
|
816 | (5) |
|
|
821 | (1) |
|
Performance measure of a generation |
|
|
821 | (1) |
|
Configuration of genetic algorithms |
|
|
821 | (2) |
|
Search behaviour of genetic algorithms |
|
|
823 | (1) |
|
Search accuracy and precision |
|
|
823 | (1) |
|
Behaviour of genetic algorithms in the presence of multiple optima |
|
|
824 | (1) |
|
Hybridization of genetic algorithms |
|
|
824 | (2) |
|
|
826 | (14) |
|
|
840 | (1) |
|
|
841 | (3) |
|
Principle of simulated annealing |
|
|
841 | (2) |
|
Configuration parameters for the simulated annealing algorithm |
|
|
843 | (1) |
|
|
844 | (1) |
|
|
844 | (5) |
|
|
845 | (4) |
Index |
|
849 | |