北京大学分析化学02误差

Systematic Error 具单向性、重现性，为可测误差 Method error方法误差
⎯Most difficult to determine amongst systematic error ⎯Comes from non-ideal chemical or physical behavior of the reagents and reactions
It is mistake!!!!!!!
Random/Indeterminate Error随机误差
Accidental, can not be avoided 偶然误差 — Follow mathematical laws of probability
服从统计规律
— Random errors in analytical results follow a
Chapter 2 Data Process and Analysis 数据处理与分析
• Errors in chemical analysis误差 • Random errors in chemical analysis 随机误差 • Statistical data treatment and evaluation 数据的统计学处理和评价 • Sampling, Standardization, and Calibration 取样、标定和校准 (To be lectured at the end of the semester)
Reagent Errors试剂不纯引起的误差 Running reagent blank Personal Errors 个人（操作）误差 Prejudice or bias Color observation颜色观察
Gross (Error)过失(误差) Personal Errors
Lead to outliers 离群值
总体标准差
μ
0
− 1 f ( x) = e σ 2π ( x − μ )2 2σ 2
x
x−μ
极大值在x=μ处. 拐点在x=μ±σ处. 于x=μ对称.
0.4 0.3
Standard Normal (z) Distribution 标准正态分布曲线: N（0,1）
y
0.2 0.1 0 -4 -3 -2 -1 0
测定结果与“真值”接近的程度, 以误差表示 通常反映测定方法的系统误差
Absolute error绝对误差 E r = x − T
Ea Relative error相对误差 E r = × 100% ☺ T
Accuracy and Precision
Precision
Degree of agreement between replicate measurements of the same quantity. It describes the reproducibility of the measurements. Denoted as random error. 平行测定的结果互相靠近的程度. 以偏差表示
4. 5.
Determine at a given probability level whether the precision of two sets of measurements differs. Decide with a certain probability whether an apparent outlier in a set of replication measurements is the result of a gross error and can thus be rejected or not.
Population Standard Deviation 总体标准偏差：σ = ( xi − μ )2 ∑ n
Sample Standard Deviation 样本标准偏差：s = ( xi − x) 2 ∑ n −1 (n-1)为自由度， f (freedom)表示 用
相对标准差Relative Standard Deviation s RSD= x
– Standard Deviation标准偏差 – Coefficient of Variance 变异系数
Accuracy versus Precision 准确度与精密度的关系
S来自百度文库oog p94
Classification of Errors, Source and Way to Eliminate or Reduce Errors
The Confidence Interval (CI)
总体均值的置信区间 The true value falls within the confidence limit with a certain probability. 在一定的置信度下(把握性), 估计总体均 值可能存在的区间, 称置信区间。
– An experimental mean and a true value or – Two experimental means are different That is, whether the difference is real or simply the result of random error
相对标准差 (Coefficient of variation变异系数 ) CV=(s/x ) × 100%
Statistical Data Treatment and Evaluation Based on Sample or Subset
有限数据的统计处理
总体 population sampling 抽样 样本 sample Observation 观测 数据 Data
– Accuracy准确度: Refers to the difference between a measured value and the “true” or Known value – Precision精密度: Denotes the estimated uncertainty in a measurement or experiment
Objectives 目的
• Minimize errors • Estimate the size of errors with acceptable accuracy • Estimate the “true” value
– To define limits within which the true value of a measured quantity lies with a given level of probability
1. 2. 3. Define the confidence interval (CI) related to the standard deviation of the mean Determine n required to ensure that experimental mean falls within a certain range with a given level of probability. Estimate the probability that
• What maximum error can I tolerate in the result? • How many determinations are necessary, then?
Measurement Errors Are an Inherent Part of the Skoog P90 Quantitized World in Which We Live The two meanings of Errors
误差的分类、产生的原因及减免办法
Systematic/Determinate Error系统误差
Affect accuracy of results
Random/Indeterminate Error随机误差
Affect measurement precision
Gross Error过失误差
Lead to outliers 离群值
Systematic Error
Instrument Errors仪器误差
⎯ Uncalibrated Instrument 仪器未校准 ⎯ Uncalibrated/ worn weights砝码磨损 ⎯ Uncalibrated glassware刻度不准 ⎯ Calibrating is the way to do it 校准 (绝对、相对)
19.4, 20.1, 20.3, 19.5, 19.6,19.8 ( 21.2)
Accuracy and Precision
Accuracy
The closeness of a measured value to the “True” or accepted value. Denoted as Error which indicates systematic error of a method.
Normal Distribution/Gaussian Curve 分析结果中的偶然误差服从正态分布或高斯曲线
正态分布曲线
The Normal (Gaussian) Distribution
f (x )
A
y: relative frequency频率密度 x: data测量值
σA σB
B
μ: population mean总体平均值 x-μ: deviation from mean随机误差 σ : population standard deviation
Confidence Interval (CI)
无限多次的测定， (x -1.96 σ, x +1.96 σ ) 范围内包含 μ 的 概率p = 95.0% (x -1.96 σ, x +1.96 σ ) has 95% probability containing the true population mean μ.
68.3 % 95.5% 99.7%
Z in most English
Textbook
1 2 3 4
z
u=
x−μ
σ
u : the deviation of a result from the population
Mean relative to the standard deviation.
Area under the Curve 曲线下面积
⎯Slowness, incompleteness of reaction Solubility ⎯Instability of some species ⎯Non-specificity of most reagents ⎯Side-reaction
⎯Calibrating by other method or Analysis of standard samples
Statistical analysis 统计方法
样本容量n: 样本所含的个体数.
The number of measurements in the sample set The number of total number of measurements in the population
Objectives again
area =
∫ 2π
|u|
1
− u2 du u 2 e −u
正态分布概率积分表
area 0.500 0.683 0.900 0.950 0.954 0.990 0.997 1.000 0.674 1.000 1.645 1.960 2.000 2.576 3.000 ∞
Statistical Treatment of Random Error
½α
½α
μ -1.96σ
μ +1.96 σ
x = μ ± uσ ↔ μ = x ± uσ
置信水平Confidence Level
The probability that the true mean lies within a confidence interval 真值处于某一区间的可能性 Significance Level-α value显著性水平 The probability that a result is outside the confidence interval