Possible Sources Of Random Error
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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 how to reduce random error to changes in the wind. Random errors often have a Gaussian random error examples physics normal distribution (see Fig. 2). In such cases statistical methods may be used to analyze the data. The random error calculation 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
How To Reduce Systematic Error
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 personal error < 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.
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until Oct 21, 2016. + Submit Comment Results 1 to 1 of 1 Section: 6.3 Sources of Random Error Section Tools Show Printable Version Email this Page… Subscribe http://www.physics.umd.edu/courses/Phys276/Hill/Information/Notes/ErrorAnalysis.html to this Thread… Search Section Advanced Search 07-23-201204:31 AM #1 6.3 Sources of Random Error Most random errors are due to sampling, measurement, or regression/extrapolation. 1. Sampling. Whenever a sample is selected to represent the population—whether the sample is of appliances, meters, accounts, individuals, households, premises, or organizations—there will be some amount of random https://ump.pnnl.gov/showthread.php/5124-6.3-Sources-of-Random-Error sampling error. Any selected sample is only one of a large number of possible samples of the same size and design that could have been drawn from that population. Sampling error and strategies for mitigating it are discussed in detail in the rest of this document. The primary topic of this chapter is the mitigation and quantification of sampling error. 2. Measurement. In a survey, random measurement error may be introduced by factors such as respondents’ incorrectly recalling dates, expenses, or by differences in a respondents’ mood or circumstances, which affect how they answer a question. Technical measurements can also be a source of measurement error. (See item 1 and footnote 18 in the systematic error list.) These types of random measurement error are generally assumed to “even out,” so that they do not introduce systematic bias, but only increase the variability. For this reason, researchers generally do not attempt to quantify the potential for bias due to random measurement error. 3. Regr
of this type result in measured values that are consistently too high or consistently too low. Systematic errors may be of four kinds: 1. Instrumental. For example, a poorly http://www.physics.nmsu.edu/research/lab110g/html/ERRORS.html calibrated instrument such as a thermometer that reads 102 oC when immersed in boiling water and 2 oC when immersed in ice water at atmospheric pressure. Such a thermometer would result in measured values that are consistently too high. 2. Observational. For example, parallax in reading a meter scale. 3. Environmental. For example, an electrical power ìbrown outî that causes measured currents random error to be consistently too low. 4. Theoretical. Due to simplification of the model system or approximations in the equations describing it. For example, if your theory says that the temperature of the surrounding will not affect the readings taken when it actually does, then this factor will introduce a source of error. Random Errors Random errors are positive and negative fluctuations how to reduce that cause about one-half of the measurements to be too high and one-half to be too low. Sources of random errors cannot always be identified. Possible sources of random errors are as follows: 1. Observational. For example, errors in judgment of an observer when reading the scale of a measuring device to the smallest division. 2. Environmental. For example, unpredictable fluctuations in line voltage, temperature, or mechanical vibrations of equipment. Random errors, unlike systematic errors, can often be quantified by statistical analysis, therefore, the effects of random errors on the quantity or physical law under investigation can often be determined. Example to distinguish between systematic and random errors is suppose that you use a stop watch to measure the time required for ten oscillations of a pendulum. One source of error will be your reaction time in starting and stopping the watch. During one measurement you may start early and stop late; on the next you may reverse these errors. These are random errors if both situations are equally likely. Repeated measurements produce a series of times that are all slightly different. T
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