准确度与精密度Accuracy and precision

系统误差（可测误差）由固定原因引起，使结果系统偏高或偏低，具有单向性和重复性，包括方法误差、仪器误差、试剂误差和操作误差，可通过对照试验、空白试验、校准仪器和方法校正来减小，影响准确度。随机误差（偶然误差）由难以控制的微小波动引起，服从正态分布，可通过增加平行测定次数来减小，影响精密度。过失误差（如读错数、溅失）应剔除。

Systematic (determinate) errors have fixed causes and bias results consistently high or low; they include method, instrument, reagent and operator errors, are reduced by control and blank experiments, calibration and method correction, and affect accuracy. Random (indeterminate) errors arise from small uncontrollable fluctuations, follow a normal distribution, are reduced by more replicate measurements, and affect precision. Gross errors such as misreadings or spills must be discarded.

绝对误差 E = x − T，相对误差 E_r = (x − T)/T × 100%；平均偏差 d̄ = Σ|xᵢ − x̄|/n；标准偏差 s = √[Σ(xᵢ − x̄)²/(n − 1)]；相对标准偏差（变异系数）RSD = s/x̄ × 100%。平均值的置信区间 μ = x̄ ± t·s/√n。可疑值用 Q 检验或格鲁布斯检验判断是否舍弃；用 t 检验比较平均值与标准值是否存在系统误差，用 F 检验比较两组数据的精密度。

Absolute error E = x − T and relative error E_r = (x − T)/T × 100%; mean deviation d̄ = Σ|xᵢ − x̄|/n; standard deviation s = √[Σ(xᵢ − x̄)²/(n − 1)]; and relative standard deviation (coefficient of variation) RSD = s/x̄ × 100%. The confidence interval of the mean is μ = x̄ ± t·s/√n. Outliers are tested with the Q test or Grubbs's test; a t test compares a mean with a reference value for systematic error, and an F test compares the precision of two data sets.

常用打靶图说明：弹孔密集且集中在靶心——准确又精密；弹孔密集但偏离靶心——精密但不准确（存在系统误差）；弹孔分散但平均位置在靶心——准确但不精密；分散且偏离——既不准确也不精密。国际标准 ISO 5725 中，“准确度”包括正确度（系统误差）和精密度（随机误差）两方面。

The dartboard picture: shots tightly grouped on the bullseye are accurate and precise; tightly grouped off-centre, precise but inaccurate (systematic error); scattered around the centre, accurate on average but imprecise; scattered and off-centre, neither. In ISO 5725, accuracy comprises trueness (systematic error) and precision (random error).