2 Types Of Experimental Error
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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 calibrated instrument such as a thermometer that reads 102 oC when immersed in boiling types of experimental error chemistry water and 2 oC when immersed in ice water at atmospheric pressure. Such a thermometer experimental error formula would result in measured values that are consistently too high. 2. Observational. For example, parallax in reading a meter scale. 3. Environmental. For
Experimental Error Examples
example, an electrical power ìbrown outî that causes measured currents 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
Sources Of Experimental Error
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 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 experimental error vs human error 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. They vary in random vary about an average value. If a systematic error is also included for example, your stop watch is not starting from zero, then your measurements will vary, not about the average value, but about a displaced value. Blunders A final source of error, called a blunder, is an outright mistake. A person may record a wrong value, misread a scale, forget a digit when reading a scale or recording a measurement, or make a similar blunder. These blunder should sti
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
Experimental Error Physics
in the wind. Random errors often have a Gaussian normal distribution (see experimental error biology Fig. 2). In such cases statistical methods may be used to analyze the data. The mean m of experimental percent error 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 http://www.physics.nmsu.edu/research/lab110g/html/ERRORS.html 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% http://www.physics.umd.edu/courses/Phys276/Hill/Information/Notes/ErrorAnalysis.html 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 sh
We're using the word "wrong" to emphasize a point. All experimental data is imperfect. Scientists know that their results always contain errors. However, http://www.digipac.ca/chemical/sigfigs/experimental_errors.htm one of their goals is to minimize errors, and to be aware of what the errors may be. Significant digits is one way of keeping track of how much error there is in a measurement. Since they know that all results contain errors, scientists almost never give definite answers. They are far more likely to say: "it is likely that ..." experimental error or "it is probable that ..." than to give an exact answer. As a science student you too must be careful to learn how good your results are, and to report them in a way that indicates your confidence in your answers. There are two kinds of experimental errors. Random Errors These errors are unpredictable. They are chance variations in the of experimental error measurements over which you as experimenter have little or no control. There is just as great a chance that the measurement is too big as that it is too small. Since the errors are equally likely to be high as low, averaging a sufficiently large number of results will, in principle, reduce their effect. Systematic Errors These are errors caused by the way in which the experiment was conducted. In other words, they are caused by the design of the system. Systematic errors can not be eliminated by averaging In principle, they can always be eliminated by changing the way in which the experiment was done. In actual fact though, you may not even know that the error exists. Which of the following are characteristics of random errors? Check all that apply. a) doing several trials and finding the average will minimize them b) the observed results will usually be consistently too high, or too low c) proper design of the experiment can eliminate them d) there is no way to know what they are It i
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