Кездейсоқ және жүйелік қателіктер. Өлшеудің дәлдігі мен нақтылығы №1 Зертханалық жұмыс. Бұрыш жасай бағытталған күштерді қосу. Физика, 10 сынып, дидактикалық материал.

Random Errors

Random errors in experimental measurements are caused by unknown and unpredictable changes in the experiment. These changes may occur in the measuring instruments or in the environmental conditions.

Examples of causes of random errors are:

• electronic noise in the circuit of an electrical instrument,
• irregular changes in the heat loss rate from a solar collector due to changes in the wind.

Random errors often have a Gaussian normal distribution (see Fig. 2). In such cases statistical methods may be used to analyze the data. The mean m of a number of measurements of the same quantity is the best estimate of that quantity, and the standard deviation s of the measurements shows the accuracy of the estimate. The standard error of the estimate m is s/sqrt(n), where n is the number of measurements.

Fig. 2. The Gaussian normal distribution. m = mean of measurements. s = standard deviation of measurements. 68% of the measurements lie in the interval m - s < x < m + s; 95% lie within m - 2s < x < m + 2s; and 99.7% lie within m - 3s < x < m + 3s.

The precision of a measurement is how close a number of measurements of the same quantity agree with each other. The precision is limited by the random errors. It may usually be determined by repeating the measurements.

Systematic Errors

Systematic errors in experimental observations usually come from the measuring instruments. They may occur because:

• there is something wrong with the instrument or its data handling system, or
• because the instrument is wrongly used by the experimenter.

Two types of systematic error can occur with instruments having a linear response:

• Offset or zero setting error in which the instrument does not read zero when the quantity to be measured is zero.
• Multiplier or scale factor error in which the instrument consistently reads changes in the quantity to be measured greater or less than the actual changes.

These errors are shown in Fig. 1. Systematic errors also occur with non-linear instruments when the calibration of the instrument is not known correctly.

Fig. 1. Systematic errors in a linear instrument (full line).Broken line shows response of an ideal instrument without error.

Examples of systematic errors caused by the wrong use of instruments are:

• errors in measurements of temperature due to poor thermal contact between the thermometer and the substance whose temperature is to be found,
• errors in measurements of solar radiation because trees or buildings shade the radiometer.

The accuracy of a measurement is how close the measurement is to the true value of the quantity being measured. The accuracy of measurements is often reduced by systematic errors, which are difficult to detect even for experienced research workers.

Taken from R. H. B. Exell, www.jgsee.kmutt.ac.th/exell/PracMath/ErrorAn.htm

What is Systematic Error?

Systematic error (also called systematic bias) is consistent, repeatable error associated with faulty equipment or a flawed experiment design. These errors are usually caused by measuring instruments that are incorrectly calibrated or are used incorrectly. However, they can creep into your experiment from many sources, including:

• A worn out instrument. For example, a plastic tape measure becomes slightly stretched over the years, resulting in measurements that are slightly too high.
• An incorrectly calibrated or tared instrument, like a scale that doesn’t read zero when nothing is on it.
• A person consistently takes an incorrect measurement. For example, they might think the 3/4″ mark on a ruler is the 2/3″ mark.

What is Random Error?

Random error (also called unsystematic error, system noise or random variation) has no pattern. One minute your readings might be too small. The next they might be too large. You can’t predict random error and these errors are usually unavoidable.

Systematic vs. Random Errors

The main differences between these two error types are:

• Random errors are (like the name suggests) completely random. They are unpredictable and can’t be replicated by repeating the experiment again.
• Systematic Errors produce consistent errors, either a fixed amount (like 1 lb) or a proportion (like 105% of the true value). If you repeat the experiment, you’ll get the same error.

Systematic errors are consistently in the same direction (e.g. they are always 50 g, 1% or 99 mm too large or too small). In contrast, random errors produce different values in random directions. For example, you use a scale to weigh yourself and get 148 lbs, 153 lbs, and 132 lbs.

Types of Systematic Error

1. Offset Error is a type of systematic error where the instrument isn’t set to zero when you start to weigh items. For example, a kitchen scale includes a “tare” button, which sets the scale and a container to zero before contents are placed in the container. This is so the weight of the container isn’t included in the readings. If the tare isn’t set properly, all readings will have offset error.

Offset errors results in consistently wrong readings.

2. Scale Factor Errors. These are errors that are proportional to the true measurement. For example, a measuring tape stretched to 101% of its original size will consistently give results that are 101% of the true value.

Scale factor errors increase (or decrease) the true value by a proportion or percentage.

Compare the above two error patterns with random errors, which have no pattern:

Random errors do not follow a pattern.

Preventing Errors

Random error can be reduced by:

• Using an average measurement from a set of measurements, or
• Increasing sample size.

It’s difficult to detect — and therefore prevent — systematic error. In order to avoid these types of error, know the limitations of your equipment and understand how the experiment works. This can help you identify areas that may be prone to systematic errors.

If you prefer an online interactive environment to learn R and statistics, this free R Tutorial by Datacamp is a great way to get started. If you're are somewhat comfortable with R and are interested in going deeper into Statistics, try this Statistics with R track.