Measurement calculating final results

Notice that a result of this type, in order to be interpretable, must comprise three numbers the mean, the (relative) standard deviation, and the number of measurements that went into the calculation. All calculations are done using the full precision available, and only the final result is rounded to an appropriate precision. The calculator must be able to handle >4 significant digits in the standard deviation. (See file SYS SUITAB.xls.)... 

The measurement uncertainty is transformed into a corresponding uncertainty of the final result due to algebraic distortions and weighting factors, even if the calculator s accuracy is irrelevant. 

Author s comment] Because a general rendition of the Scientific Method cannot be cast in legally watertight wording, all possible outcomes of a series of measurements and pursuant actions must be in writing before the experiments are started. This includes but is not limited to the number of additional samples and measurements, and prescriptions on how to calculate and present final results. Off-the-cuff interpretations and decisions after the fact are viewed with suspicion. 

In contrast, a systematic error remains constant or varies in a predictable way over a series of measurements. This type of error differs from random error in that it cannot be reduced by making multiple measurements. Systematic error can be corrected for if it is detected, but the correction would not be exact since there would inevitably be some uncertainty about the exact value of the systematic error. As an example, in analytical chemistry we very often run a blank determination to assess the contribution of the reagents to the measured response, in the known absence of the analyte. The value of this blank measurement is subtracted from the values of the sample and standard measurements before the final result is calculated. If we did not subtract the blank reading (assuming it to be non-zero) from our measurements, then this would introduce a systematic error into our final result. 

To allow the uncertainty to be evaluated effectively, a model equation describing the method of analysis is required. The starting point is the equation used to calculate the final result. Intially, we will need to consider the uncertainties associated with the parameters that appear in this equation. It may be necessary to add terms to this equation (i.e. expand the model) to include other parameters that may influence the final result and therefore contribute to the measurement uncertainty. 

The error results were analyzed against final system pressure and volume of inert charge. The measured moles of CO2 were accurate at worst to within about 3% just using the Ideal Gas Law to calculate the result (no mass spectra were taken). The data were independent of the volume of the charge. 

In case of an odour measurement the inhaled air is supposed to be equal to the air delivered by the olfactometer. However if flowrates of the olfactometer are not equal to the respiration level, additional air from the experimental room will be used (see figure 2). Since it is a good practice to keep an experimental room free from odour contamination the additional air can be considered as diluting air. In that case the final dilution of the odour sample is higher than calculated. The result may be negative response in cases where a positive response should occur. An increase of the olfactometer flowrate will replace unaccounted diluting air by accounted air thus making the final dilution is closer to the desired dilution. 

If the treatment effect in each of the individual trials is the difference in the mean responses, then d represents the overall, adjusted mean difference. If the treatment effect in the individual trials is the log odds ratio, then d is the overall, adjusted log odds ratio and so on. In the case of overall estimates on the log scale we generally anti-log this final result to give us a measure back on the original scale, for example as an odds ratio. This is similar to the approach we saw in Section 4.4 when we looked at calculating a confidence interval for an odds ratio. 

The partition coefficient (K ) was used for the conversion of TBT concentrations in sediment and SPM to TBT concentrations in water. This Kp for TBT was calculated by multiplying the organic carbon partition coefficient (K ) with the measured fraction organic carbon (f ). Consequently, the K value has a strong impact on the final results of the risk prognosis. Generally, in risk predictions the lowest K value is applied to calculate concentrations in water (EC, 2003). This results in a worst-case water concentration, in accordance with the precautionary principle. However, with literature values for the K of TBT ranging from 3.0 - 6.2 (Lepper, 2002), it is more appropriate to base an assessment on local measured values. In this study the... 

Estimate of errors is fundamental to all branches of natural sciences that deal with experiments. Very frequently, the final result of an experiment cannot be measured directly. Rather, the value of the final result (u) will be calculated from several measured quantities (x, y, Z-., each of which has a mean value and an error) ... 

Laboratories use the concept of significant figures in manual calculations for standard and sample preparation, and in data reduction. The rule for determination of the number of significant figures in calculations is as follows When experimental quantities are multiplied and divided, the final result cannot be more accurate than the least precise measurement. 

Finally, it is important to note that the precision of quantities is often not arbitrary. Measuring tools have limits on the precision of measurement. Such measures will have a particular number of significant figures. Calculations with measurements may not result in an increase in the number of significant figures. There are two rules to follow to determine the number of significant figures in the result of calculations ... 

The method of symmetric points was used to determine the center of the interference curve. Extensive calculations showed that the line profile should be symmetric about the center frequency. The line center was then corrected for the second order Doppler shift, The Bloch-Siegert and rf Stark shifts, coupling between the rf plates, the residual F=1 hyperfine component, and distortion due to off axis electric fields. A small residual asymmetry in the average quench curve was attributed to a residual variation of the rf electric field across the line and corrected for on the assumption this was the correct explanation. Table 1 shows the measured interval and the corrections for one of the 8 data sets used to determine the final result. 

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