Data error

Mathematical Consistency Requirements. Theoretical equations provide a method by which a data set s internal consistency can be tested or missing data can be derived from known values of related properties. The abiUty of data to fit a proven model may also provide insight into whether that data behaves correctiy and follows expected trends. For example, poor fit of vapor pressure versus temperature data to a generally accepted correlating equation could indicate systematic data error or bias. A simple sermlogarithmic form, (eg, the Antoine equation, eq. 8), has been shown to apply to most organic Hquids, so substantial deviation from this model might indicate a problem. Many other simple thermodynamics relations can provide useful data tests (1—5,18,21). 

The major limitation of velocity transducers is their sensitivity to mechanical and thermal damage. Normal use can cause a loss of calibration and, therefore, a strict recalibration program is required to prevent data errors. At a minimum, velocity transducers should be re-calibrated every six months. Even with periodic re-calibration, however, velocity transducers are prone to provide distorted data due to loss of calibration. 

Validation of the data management system is typically done in two rounds. First, correctly completed data forms are entered to ensure that the system is not flagging any good data. In the second round, completed data forms with intentional data errors are entered. All errors must be identified by the system. 

The local user performs data entry by directly entering data into the system s database stored on the local computer with customized electronic forms. The system performs edit checks, which include range, across-form, and across-visit checks at the time of entry. This feature greatly reduces data error rates. 

Fig. 4.3. (A) Composite multispecies benthic foraminiferal Mg/Ca records from three deep-sea sites DSDP Site 573, ODP Site 926, and ODP Site 689. (B) Species-adjusted Mg/Ca data. Error bars represent standard deviations of the means where more than one species was present in a sample. The smoothed curve through the data represents a 15% weighted average. (C) Mg temperature record obtained by applying a Mg calibration to the record in (B). Broken line indicates temperatures calculated from the record assuming an ice-free world. Blue areas indicate periods of substantial ice-sheet growth determined from the S 0 record in conjunction with the Mg temperature. (D) Cenozoic composite benthic foraminiferal S 0 record based on Atlantic cores and normalized to Cibicidoides spp. Vertical dashed line indicates probable existence of ice sheets as estimated by (2). 3w, seawater S 0. (E) Estimated variation in 8 0 composition of seawater, a measure of global ice volume, calculated by substituting Mg temperatures and benthic 8 0 data into the 8 0 paleotemperature equation (Lear et al., 2000).

Some points should be noted from this example. Firstly, ideal gas behavior has been assumed. This is an approximation, but it is reasonable for the low pressure assumed in the calculation. Later the calculation will be repeated at higher pressure when the ideal gas approximation will be poor. Also, it should be clear that the calculation is very sensitive to the thermodynamic data. Errors in the thermodynamic data can lead to a significantly different result. Thermodynamic data, even from reputable sources, should be used with caution. 

It should also be again noted that firstly ideal gas behavior has been assumed, which is reasonable at this pressure, and secondly that small data errors might lead to significant errors in the calculations. 

Errors in system output measurements can produce calibration errors because the model user will be attempting to calibrate against inaccurate or missing data. Errors associated with system outputs are discussed below. 

For these reasons, the thermodynamic data on which a model is based vary considerably in quality. At the minimum, data error limits the resolution of a geochemical model. The energetic differences among groups of silicates, such as the clay minerals, is commonly smaller than the error implicit in estimating mineral stability. A clay mineralogist, therefore, might find less useful information in the results of a model than expected. 

All arrays are scanned with the exact same scanner settings. Otherwise, it can result in image data errors between samples. 

There are three types of data error random error in the reference laboratory values, random error in the optical data, and systematic error in the relationship between the two. The proper approach to data error depends on whether the affected variables are reference values or spectroscopic data. Calibrations are usually performed empirically and are problem specific. In this situation, the question of data error becomes an important issue. However, it is difficult to decide if the spectroscopic error is greater than the reference laboratory method error, or vice versa. The noise of current NIR instrumentation is usually lower than almost anything else in the calibration. The total error of spectroscopic data includes... 

Fig. 7. A simulation of the Hamiltonian identification concept in Fig. 6 for a 10-state quantum system, with the observations being state populations. The data errors were taken as 1%. The closed loop optimal inversion was capable of finding a single experiment, which dramatically filtered out the data noise to produce Hamiltonian matrix elements with an order of magnitude better quality than that of the data noise. In contrast, a standard inversion involving 5000 observations gave significantly poorer results, including amplification of the laboratory noise.

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