Experimental Error Lab Report
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Overview Keeping a lab notebook Writing research papers Dimensions & units Using figures (graphs) Examples of graphs Experimental error Representing error Applying statistics Overview Principles of microscopy Solutions & dilutions Protein assays Spectrophotometry Fractionation & centrifugation Radioisotopes and detection Error Analysis and Significant Figures
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Errors using inadequate data are much less than those using no data at all. lab report experimental design C. Babbage] No measurement of a physical quantity can be entirely accurate. It is important to know, therefore, just how much experimental error in a scientific experiment the measured value is likely to deviate from the unknown, true, value of the quantity. The art of estimating these deviations should probably be called uncertainty analysis, but for historical reasons is referred to as http://reference.wolfram.com/applications/eda/ExperimentalErrorsAndErrorAnalysis.html error analysis. This document contains brief discussions about how errors are reported, the kinds of errors that can occur, how to estimate random errors, and how to carry error estimates into calculated results. We are not, and will not be, concerned with the “percent error” exercises common in high school, where the student is content with calculating the deviation from some allegedly authoritative number. You might also be interested in our http://www.ruf.rice.edu/~bioslabs/tools/data_analysis/errors_sigfigs.html tutorial on using figures (Graphs). Significant figures Whenever you make a measurement, the number of meaningful digits that you write down implies the error in the measurement. For example if you say that the length of an object is 0.428 m, you imply an uncertainty of about 0.001 m. To record this measurement as either 0.4 or 0.42819667 would imply that you only know it to 0.1 m in the first case or to 0.00000001 m in the second. You should only report as many significant figures as are consistent with the estimated error. The quantity 0.428 m is said to have three significant figures, that is, three digits that make sense in terms of the measurement. Notice that this has nothing to do with the "number of decimal places". The same measurement in centimeters would be 42.8 cm and still be a three significant figure number. The accepted convention is that only one uncertain digit is to be reported for a measurement. In the example if the estimated error is 0.02 m you would report a result of 0.43 ± 0.02 m, not 0.428 ± 0.02 m. Students frequently are confused about when to count a zero as a significant figure. The rule is: If the zero has a non-zero digit
of this type result in measured values that are consistently too high or consistently too low. Systematic errors may be of four kinds: 1. http://www.physics.nmsu.edu/research/lab110g/html/ERRORS.html Instrumental. For example, a poorly 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. experimental error Environmental. For 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 that the temperature of the surrounding will not affect the readings taken when it actually does, then experimental error in 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 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 sta