无论您多么小心,测量中总会出现错误。错误不是“错误” – 这是测量过程的一部分。在科学中,测量误差称为实验误差或观测误差。有两大类观察误差:随机误差和系统误差。随机误差从一个测量到另一个测量不可预测地变化,而系统误差对于每个测量具有相同的值或比例。随机错误导致一个测量值与下一个测量值略有不同。它来自实验期间不可预测的变化。系统误差总是会影响相同数量或相同比例的测量,前提是每次读取的方式相同。这是可以预测的。实验中无法消除随机误差,但可以减少大多数系统误差。如果进行多次测量,则值会围绕真值进行聚类。因此,随机误差主要影响精度。通常,随机误差会影响测量的最后一个有效数字。随机误差的主要原因是仪器的限制,环境因素和程序的轻微变化。例如:在秤上称重时,每次都会略微不同。在烧瓶中读取体积读数时,您可以每次从不同的角度读取该值。测量分析天平上样品的质量可能会产生不同的值,因为气流会影响平衡或水进入和离开样品。测量您的身高会受到轻微姿势变化的影响。测量风速取决于测量的高度和时间。必须采取多个读数并取平均值,因为阵风和方向变化会影响该值。当读数落在秤上的标记之间或考虑到测量标记的厚度时,必须估算读数。由于随机错误总是发生且无法预测,因此采用多个数据点并对其进行平均以获得变化量并估计真实值非常重要。系统误差是可预测的,或者是恒定的,或者与测量成比例。系统误差主要影响测量的准确性。系统误差的典型原因包括观测误差,不完美的仪器校准和环境干扰。例如:忘记皮重或零平衡会产生质量测量,这些测量总是“关闭”相同的量。由于在使用仪器之前未将仪器设置为零而导致的错误称为偏移误差。对于体积测量而言,不在视线水平读取弯月面将始终导致读数不准确。该值将始终为低或高,具体取决于读数是从标记的上方还是下方获取。由于材料的热膨胀,使用金属尺测量长度将在冷温度下产生与在高温下不同的结果。校准不正确的温度计可以在一定温度范围内提供准确的读数,但在更高或更低的温度下变得不准确。使用新的布料卷尺与较旧的拉伸卷尺测量的距离是不同的。这种比例误差称为比例因子误差。当连续读数随时间变得一直变低或变高时,就会发生漂移。电子设备往往容易漂移。随着设备升温,许多其他仪器会受到(通常为正)漂移的影响。一旦确定其原因,系统误差可能会降低到一定程度。通过常规校准设备,使用实验中的控制,在读取之前预热仪器,以及将值与标准进行比较,可以最小化系统误差。虽然可以通过增加样本量和平均数据来最小化随机误差,但是更难以补偿系统误差。避免系统误差的最佳方法是熟悉仪器的局限性并正确使用它们。测量误差的两种主要类型是随机误差和系统误差。随机错误导致一个测量值与下一个测量值略有不同。它来自实验期间不可预测的变化。系统误差总是会影响相同数量或相同比例的测量,前提是每次读取的方式相同。这是可以预测的。无法从实验中消除随机误差,但可以减少大多数系统误差。

美国杜克大学物理学Essay代写:随机误差与系统误差

No matter how careful you are, there is always error in a measurement. Error is not a “mistake”—it’s part of the measuring process. In science, measurement error is called experimental error or observational error. There are two broad classes of observational errors: random error and systematic error. Random error varies unpredictably from one measurement to another, while systematic error has the same value or proportion for every measurement. Random error causes one measurement to differ slightly from the next. It comes from unpredictable changes during an experiment. Systematic error always affects measurements the same amount or by the same proportion, provided that a reading is taken the same way each time. It is predictable. Random errors cannot be eliminated from an experiment, but most systematic errors can be reduced. If you take multiple measurements, the values cluster around the true value. Thus, random error primarily affects precision. Typically, random error affects the last significant digit of a measurement. The main reasons for random error are limitations of instruments, environmental factors, and slight variations in procedure. For example: When weighing yourself on a scale, you position yourself slightly differently each time. When taking a volume reading in a flask, you may read the value from a different angle each time. Measuring the mass of a sample on an analytical balance may produce different values as air currents affect the balance or as water enters and leaves the specimen. Measuring your height is affected by minor posture changes. Measuring wind velocity depends on the height and time at which a measurement is taken. Multiple readings must be taken and averaged because gusts and changes in direction affect the value. Readings must be estimated when they fall between marks on a scale or when the thickness of a measurement marking is taken into account. Because random error always occurs and cannot be predicted, it’s important to take multiple data points and average them to get a sense of the amount of variation and estimate the true value. Systematic error is predictable and either constant or else proportional to the measurement. Systematic errors primarily influence a measurement’s accuracy. Typical causes of systematic error include observational error, imperfect instrument calibration, and environmental interference. For example: Forgetting to tare or zero a balance produces mass measurements that are always “off” by the same amount. An error caused by not setting an instrument to zero prior to its used is called an offset error. Not reading the meniscus at eye level for a volume measurement will always result in an inaccurate reading. The value will be consistently low or high, depending on whether the reading is taken from above or below the mark. Measuring length with a metal ruler will give a different result at a cold temperature than at a hot temperature, due to thermal expansion of the material. An improperly calibrated thermometer may give accurate readings within a certain temperature range, but become inaccurate at higher or lower temperatures. Measured distance is different using a new cloth measuring tape versus an older, stretched one. Proportional errors of this type are called scale factor errors. Drift occurs when successive readings become consistently lower or higher over time. Electronic equipment tends to be susceptible to drift. Many other instruments are affected by (usually positive) drift, as the device warms up. Once its cause is identified, systematic error may be reduced to an extent. Systematic error can be minimized by routinely calibrating equipment, using controls in experiments, warming up instruments prior to taking readings, and comparing values against standards. While random errors can be minimized by increasing sample size and averaging data, it’s harder to compensate for systematic error. The best way to avoid systematic error is to be familiar with the limitations of instruments and experienced with their correct use. The two main types of measurement error are random error and systematic error. Random error causes one measurement to differ slightly from the next. It comes from unpredictable changes during an experiment. Systematic error always affects measurements the same amount or by the same proportion, provided that a reading is taken the same way each time. It is predictable. Random errors cannot be eliminated from an experiment, but most systematic errors may be reduced.

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