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Unformatted text preview: 1 125:315 BME MEASUREMENTS AND ANALYSIS LABORATORY MEASUREMENT AND UNCERTAINTY PDF Created with deskPDF PDF Writer - Trial :: http://www.docudesk.com 2 I. Objectives The objective of this laboratory exercise is to: 1. Find the average value, the median value, the standard deviation, and the standard deviation of the mean for a set of measurements that conform to a normal distribution. 2. Use these values for a set of measurements to fit a Gaussian distribution to the actual data. 3. Test for statistical significance. 4. Become proficient in the use of Excel for data analysis. II. Introduction II.1 Measurements: Error and Uncertainty Measurements are made using instruments that are imperfect and thus contain errors due to the measuring device. The 'truth' of a measurement is that value that a measurement would have were it free of the error introduced by the measurement instrument. measurement = truth + measurement error There is no true value in biological systems. Here the 'truth' of a measurement takes on a somewhat different meaning. truth = average value + biological variability . measurement = average value + biological variability + measurement error After we identify the measurement errors, we can proceed to characterize and quantify the biological variability. Sometimes we find that we cannot isolate the measurement error by quantifying this error from the measurements. Measurement errors are classified as either systematic or random. Systematic errors cause a measurement to be skewed in a certain direction, i.e., to be consistently larger or consistently smaller. For example, weighing yourself repeatedly on a bathroom scale that has an initial reading of 20 lbs will result in the reading of your weight to be greater than your 'true' weight. The addition of 20 lbs is a systematic error. This form of error can be reduced once identified in this case you can zero the scale using the little ridged knob (calibration). A systematic measurement error may also be called a measurement bias . Other sources of bias include one-sided error arising from various sources such as flaws in study design or data collection methods. Random errors are statistical fluctuations in the measured data due to limitations on the precision of the measurement device. They are bi-directional (as opposed to the unidirectional nature of a bias). If you weighed yourself on ten different bathroom scales (or weighed yourself ten times on one bathroom scale) over the period of a few minutes, you would record a range of values even though you know your weight is essentially not changing. This sort of error cannot be eliminated, but can be managed by taking many measurements to get a closer estimate of the mean....
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- Spring '09