Random Error In Physics Lab
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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 to changes in the wind. Random errors often have a Gaussian normal distribution (see Fig. 2). In such cases how to reduce random error statistical methods may be used to analyze the data. The mean m of a number systematic error calculation of measurements of the same quantity is the best estimate of that quantity, and the standard deviation s of the measurements shows the accuracy how to reduce systematic error 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 random error calculation 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
Personal Error
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.categories. 5.1. Random Errors 5.2. Systematic Errors << Previous Page Next Page >> Home - Credits - Feedback © Columbia University
or experimental values. This calculation will help you to evaluate the relevance of your results. It is helpful to know http://physics.appstate.edu/undergraduate-programs/laboratory/resources/error-analysis by what percent your experimental values differ from your lab partners' values, or to some established value. In most cases, a percent error or difference of less than 10% will be acceptable. If your comparison shows a difference of more than 10%, there is a great likelihood that some mistake has occurred, and you should look back over your random error lab to find the source of the error. These calculations are also very integral to your analysis analysis and discussion. A high percent error must be accounted for in your analysis of error, and may also indicate that the purpose of the lab has not been accomplished. Percent error: Percent error is used when you are comparing your result to how to reduce a known or accepted value. It is the absolute value of the difference of the values divided by the accepted value, and written as a percentage. Percent difference: Percent difference is used when you are comparing your result to another experimental result. It is the absolute value of the difference of the values divided by their average, and written as a percentage. A measurement of a physical quantity is always an approximation. The uncertainty in a measurement arises, in general, from three types of errors. Systematic errors: These are errors which affect all measurements alike, and which can be traced to an imperfectly made instrument or to the personal technique and bias of the observer. These are reproducible inaccuracies that are consistently in the same direction. Systematic errors cannot be detected or reduced by increasing the number of observations, and can be reduced by applying a correction or correction factor to compensate for the effect. Random errors: These are errors for which the causes are unknown or indeterminate, but are usually small and follow the laws of chance.