MeasureErrAnal

MeasureErrAnal - Experimental Error Introduction....

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1 Experimental Error Introduction . Experiments are designed to test hypotheses and the conclusion to an experiment is that the experiment either supported or negated the hypothesis. The conclusion is usually based on the analysis of quantitative data obtained by making measurements with appropriate instruments. While learning how to operate research instruments it is also important to learn that all physical measurements are subject to experimental errors that limit the reproducibility of the measurements. These errors cannot be totally eliminated, but can be reduced to acceptable levels. To establish reproducibility usually requires that experiments be repeated so as to obtain several measurements made in exactly the same way (called replicates). In independent study, time will generally limit the number of replicate measurements to five or less. Based on this small number of results you will have to conclude whether your experiment supported or negated your hypothesis. Fortunately, statistics makes it possible to draw conclusions based on a small number of measurements having limited reproducibilities. Data sets consisting of a large number of replicate measurements (called populations). In statistics, a data set having a large number of replicate measurements is called a population and measurements made on populations are called parameters . Table 1 shows a population consisting of 24 replicate measurements on a metal strip. Table 1. Mass measurements (in grams) for a metal strip. dePaula, J.C., Experimental Errors and Data Analysis, http://www.haverford.edu/chem/302/data.pdf , accessed 6/4/10. Table 1 shows that these mass measurements made under the same conditions contain small variations tin the last two digits that are called experimental errors. This is true in general of physical measurements of any continuous variable.
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2 Figure 1 shows a histogram of the above data in which the frequency of occurrence of values is plotted as a function of values. Figure 1. Histogram of mass measurements from Table 1. dePaula, J.C., Experimental Errors and Data Analysis, http://www.haverford.edu/chem/302/data.pdf , accessed 6/4/10. Figure 2 shows what happens to the histogram in Figure 1 if the measurements are repeated a very large number of times . μ σ Values Figure 2. Histogram for a large number of repeated mass measurements. Eeling, D.L., Introduction to the normal distribution, http://www.comfsm.fm/%7Edleeling/statistics/notes007.html , accessed 6/4/10. Generalizations about large data sets 1. The smooth line drawn through the midpoints of the histogram intervals in Figure 2 produces a bell-shaped curve called a normal distribution curve. Frequency
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3 The same type of distribution curve is obtained for large numbers of replicate measurements of many physical properties.
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This note was uploaded on 10/19/2011 for the course CHEM 197 taught by Professor Bonk during the Summer '11 term at Duke.

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MeasureErrAnal - Experimental Error Introduction....

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