How Can You Reduce Random Error
Contents |
of the measurement device. Random errors usually result from the experimenter's inability to take the same measurement in exactly example of random error the same way to get exact the same number. Systematic
Systematic Error Calculation
errors, by contrast, are reproducible inaccuracies that are consistently in the same direction. Systematic errors are random error examples physics often due to a problem which persists throughout the entire experiment. Note that systematic and random errors refer to problems associated with making measurements. Mistakes made
Random Error Calculation
in the calculations or in reading the instrument are not considered in error analysis. It is assumed that the experimenters are careful and competent! How to minimize experimental error: some examples Type of Error Example How to minimize it Random errors You measure the mass of a ring three times using the same zero error definition balance and get slightly different values: 17.46 g, 17.42 g, 17.44 g Take more data. Random errors can be evaluated through statistical analysis and can be reduced by averaging over a large number of observations. Systematic errors The cloth tape measure that you use to measure the length of an object had been stretched out from years of use. (As a result, all of your length measurements were too small.)The electronic scale you use reads 0.05 g too high for all your mass measurements (because it is improperly tared throughout your experiment). Systematic errors are difficult to detect and cannot be analyzed statistically, because all of the data is off in the same direction (either to high or too low). Spotting and correcting for systematic error takes a lot of care. How would you compensate for the incorrect results of using the stretched out tape measure? How would you correct the measurements from improperly tared scale?
assumes that any observation is composed of the true value plus some random error value. But is that reasonable? What if all error is not random? Isn't it possible that some errors are systematic, that they hold across most
Instrumental Error
or all of the members of a group? One way to deal with this notion
Systematic Error Formula
is to revise the simple true score model by dividing the error component into two subcomponents, random error and systematic error. here, types of errors in measurement we'll look at the differences between these two types of errors and try to diagnose their effects on our research. What is Random Error? Random error is caused by any factors that randomly affect measurement of the https://www2.southeastern.edu/Academics/Faculty/rallain/plab193/labinfo/Error_Analysis/05_Random_vs_Systematic.html variable across the sample. For instance, each person's mood can inflate or deflate their performance on any occasion. In a particular testing, some children may be feeling in a good mood and others may be depressed. If mood affects their performance on the measure, it may artificially inflate the observed scores for some children and artificially deflate them for others. The important thing about random error is that it does not have any consistent http://www.socialresearchmethods.net/kb/measerr.php effects across the entire sample. Instead, it pushes observed scores up or down randomly. This means that if we could see all of the random errors in a distribution they would have to sum to 0 -- there would be as many negative errors as positive ones. The important property of random error is that it adds variability to the data but does not affect average performance for the group. Because of this, random error is sometimes considered noise. What is Systematic Error? Systematic error is caused by any factors that systematically affect measurement of the variable across the sample. For instance, if there is loud traffic going by just outside of a classroom where students are taking a test, this noise is liable to affect all of the children's scores -- in this case, systematically lowering them. Unlike random error, systematic errors tend to be consistently either positive or negative -- because of this, systematic error is sometimes considered to be bias in measurement. Reducing Measurement Error So, how can we reduce measurement errors, random or systematic? One thing you can do is to pilot test your instruments, getting feedback from your respondents regarding how easy or hard the measure was and information about how the testing environment affected their performance. Second, if you are gathering measures using pe
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 http://www.physics.umd.edu/courses/Phys276/Hill/Information/Notes/ErrorAnalysis.html 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. random error 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 how can you 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