In measurement errors, true scoring theory is a good model, but it cannot always be an accurate reflection of reality. In particular, it assumes that any observation is composed of the true value plus some random error value. But is that reasonable? What if all the errors aren’t random? Is it not possible for some errors to be systematic, to be maintained in most or in all members of a group? One way to address this notion is to review the simple actual scoring model by dividing the error component into two subcomponents, random error, and systematic error.
What is a random error?
Random error is caused by any factor that randomly affects the measurement of the variable throughout the sample. For example, each person’s mood can inflate or deflate their performance on any occasion. If mood affects your measurement performance, you can artificially inflate the scores observed for some children and artificially deflate them for others.
The important thing about the random error is that it has no consistent effect on the entire sample. Instead, push the observed scores up or down randomly. This means that if we could see all the random errors in a distribution they would have to add up to 0 – there would be as many negative and positive errors. The important property of the random error is that it adds variability to the data but does not affect the average performance of the group. Because of this, random error is sometimes considered noise.
Serious mistakes are due to human error. Serious error can only be avoided by taking the reading carefully.
For example – The experimenter reads the 31.5oC reading while the actual reading is 21.5C. This happens because of oversights. The experimenter takes the wrong reading and that is why the error occurs in the measurement.
This type of error is very common in measurement. Full removal of such an error is not possible. Some of the serious errors are easily detected by the experimenter, but others are hard to find. Two methods can eliminate the serious error.
Two methods can eliminate the serious error. These methods are
Reading should be taken very carefully.
Two or more readings of the measured quantity should be taken. The readings are taken by the different experimenter and at a different point to eliminate the error.
What is systematic error?
Systematic error is caused by any factor that systematically affects the measurement of the variable throughout the sample. For example, if there is noisy traffic passing right outside a classroom where students are taking an exam, this noise is likely to affect the scores of all children – in this case, by systematically reducing them. Unlike random error, systematic errors tend to be consistently positive or negative – because of this, systematic error is sometimes considered as a bias in measurement.
All measurements are prone to systematic errors, often of several different types. Sources of systematic errors can be imperfect calibration of measuring instruments, changes in the environment that interfere with the measurement process, and imperfect observation methods.
A systematic error makes the measured value always smaller or larger than the true value, but not both. An experiment can involve more than one systematic error, and these errors can override each other, but each alters the true value in one way. Accuracy (or validity) is a measure of systematic error.
If an experiment is accurate or valid, then the systematic error is very small. Accuracy is a measure of how well an experiment measures what it was trying to measure. This is difficult to evaluate unless you have an idea of the expected value (for example, a textbook value or a calculated value in a workbook). Compare its experimental value with the value of the literature. If you are within the margin of error of random errors, systematic errors are likely to be less than random errors. If it is older, then you need to determine where the errors occurred. When an accepted value is available for a result determined by the experiment, the error percentage can be calculated.
Types of Instrumental Errors
These errors are mainly due to three main reasons.
a) Deficiencies inherent in instruments – Such errors are incorporated into the instruments due to their mechanical structure. They may be due to the manufacture, calibration or operation of the device. For example – If the instrument uses the weak spring, then it gives the high value of the amount to be measured. The error occurs on the instrument due to loss of friction or hysteresis.
b) Misuse of the instrument – The error occurs on the instrument because of the operator. A good instrument used in an uns intelligent way can give a huge result.
For example – misuse of the instrument can cause the lack of zero adjustment of the instruments, a poor initial adjustment, the use of lead to too high resistance.
c) Load effect – This is the most common type of error that the instrument causes in measurement work. For example, when the voltmeter is connected to the high-strength circuit it gives a wrong reading, and when connected to the low-resistance circuit, it gives a reliable reading. This means that the voltmeter has a charging effect on the circuit.
The error caused by the charging effect can be overcome using the meters intelligently. For example, when measuring low resistance by the ammeter-voltmeter method, a voltmeter with a very high resistance value should be used.
These errors are due to the external condition of the measuring devices. Such errors occur mainly by the effect of temperature, pressure, humidity, dust, vibrations or by the magnetic or electrostatic field. The corrective measures used to eliminate or reduce these undesirable effects are
The arrangement should be made to keep conditions as constant as possible.
Using the equipment you are free of these effects.
Using techniques that eliminate the effect of these disturbances.
Applying calculated corrections.
These types of errors are due to mis-observation of reading. There are many sources of observational error. For example, the pointer of a voltmeter is slightly reset above the scale surface. Therefore, an error occurs (due to paralage) unless the observer’s line of sight is exactly above the pointer.
The error that is caused by the sudden change in the atmospheric condition, this type of error is called a random error.
Reduction of random errors
So how can we reduce measurement errors, random or systematic? One thing you can do is pilot your instruments, getting feedback from your respondents regarding how easy or difficult measurement was and information on how the test environment affected your performance.
Second, if you are gathering measures using people to collect data (such as interviewers or observers) you should make sure that you train them thoroughly so that they do not inadvertently introduce errors.
Third, when the data for the study are collected, the data should be thoroughly verified. All data entered for computer analysis must be “double-drilled” and verified. This means that the data is entered twice, the second time causing the data entry machine to verify that exactly the same data is being entered as the first time.
Fourth, you can use statistical procedures to adjust the measurement error. These range from fairly simple formulas that can be applied directly to data to very complex modeling procedures to model the error and its effects.
Finally, one of the best things you can do to address measurement errors, especially systematic errors, is to use multiple measurements of the same construction. Especially if the different measures do not share the same systematic errors, you will be able to triangulate through the multiple measures and get a more accurate sense of what is going on.
The Uncertainty of Measurements
Some numerical statements are accurate: Mary has 3 siblings, and 2 + 2 x 4. However, all measurements have some degree of uncertainty that can come from a variety of sources. The process of assessing the uncertainty associated with the outcome of a measurement is often referred to as uncertainty analysis or error analysis.
The complete declaration of a measured value must include an estimate of the confidence level associated with the value. Proper statement of an experimental result along with its uncertainty allows others to make judgments about the quality of the experiment, and facilitates meaningful comparisons with other similar values or a theoretical prediction. Without an estimate of uncertainty, it is impossible to answer the basic scientific question: “Does my result match a theoretical prediction or the results of other experiments?”
Exact and True Values
When we make a measurement, we generally assume that there is some exact or true value based on how we define what is being measured. While we may never know this true value accurately, we try to find this ideal amount as best as possible with the time and resources available. As we make measurements by different methods, or even when we make multiple measurements using the same method, we can get slightly different results. So how do we report our findings for our best estimate of this elusive real value? The most common way to display the range of values that we think includes true value is:
( 1 ) measurement (best estimate ± uncertainty) units
Examples of True and Accurate Values
Let’s take an example. Suppose you want to find the mass of a gold ring you’d like to sell to a friend. You don’t want to jeopardize your friendship, so you want to get an exact mass of the ring to charge a fair market price. You estimate that the dough is between 10 and 20 grams for the weight you feel in your hand, but it’s not a very accurate estimate. After searching, you find an electronic balance that gives a mass reading of 17.43 grams. Although this measurement is much more accurate than the original estimate, how do you know it is accurate, and how confident do you are that this measurement represents the true value of the ring mass? Since the digital display of the balance is limited to 2 decimal places, you could report the mass as
17.43 ± 0.01 g.
Suppose you use the same electronic balance and get several more readings: 17.46 g, 17.42 g, 17.44 g, so that the average mass appears to be in the range of
17.44 ± 0.02 g.
By now you may feel confident that you know the mass of this ring at the nearest hundredth of a gram, but how do you know that the true value is definitely between 17.43 g and 17.45 g? Since you want to be honest, you decide to use another balance that gives a reading of 17.22 g. This value is clearly below the range of values found on the first balance, and under normal circumstances, you may not care, but you want to be fair to your friend. So, what are you doing now? The answer is to know something about the accuracy of each instrument.
Accuracy and Measurement.
To help answer these questions, we must first define the terms accuracy and accuracy:
Accuracy is the closeness of agreement between a measured value and a true or accepted value. The measurement error is the amount of inaccuracy.
Accuracy is a measure of how well a result can be determined (without reference to a theoretical or true value). It is the degree of consistency and agreement between independent measurements of the same amount; reliability or reproducibility of the result.
The estimation of the uncertainty associated with a measurement should take into account both the accuracy and accuracy of the measurement.
Note: Unfortunately, the terms error and uncertainty are often used interchangeably to describe both inaccuracy and inaccuracy. This use is so common that it is impossible to avoid completely. Whenever you encounter these terms, be sure to understand whether they refer to accuracy or accuracy, or both.
Note that to determine the accuracy of a particular measurement, we need to know the ideal and true value. Sometimes we have a measured “textbook” value, which is well known, and we assume that this is our “ideal” value, and we use it to estimate the accuracy of our result. Other times we know a theoretical value, which is calculated from basic principles, and this can also be taken as an “ideal” value. But physics is an empirical science, which means that theory must be validated through experiments, not the other way around. We can escape these difficulties and maintain a useful definition of accuracy assuming that even when we don’t know the true value, we can rely on the best accepted value available to compare our experimental value with.
For our example with the gold ring, there is no accepted value to compare with, and both measured values have the same accuracy, so we have no reason to believe one more than the other. We may look for the precision specifications of each balance as supplied by the manufacturer (the Appendix at the end of this lab manual contains precision data for most instruments to be used), but the best way to evaluate the accuracy of a measurement is to compare it to a known standard. For this situation, it may be possible to calibrate the balances with a standard mass that is precise within a narrow tolerance and traceable to a primary mass standard at the National Institute of Standards and Technology (NIST). Calibration of balances should eliminate discrepancy between readings and provide more accurate mass measurement.