2-Data Handling and Statistics

2-Data Handling and Statistics - DataHandlingandStatistics...

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Data Handling and Statistics  in Chemical Analysis  CHEM 2211
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Errors Systematic , or determinate errors affect the accuracy of results. Random , or indeterminate errors affect the precision of measurement. * Instrument Errors - caused by imperfections in measuring devices and instabilities in their components. * Method Errors - arise from nonideal chemical or physical behavior of reagents and reactions upon which the analysis is based. * Personal Errors - caused by carelessness, inattention, or personal limitations of the experimenter.
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Impact of Systematic Errors Constant Errors independent of the size of the sample. Their impact increases with decreasing sample size. Proportional Errors magnitude is directly dependent upon size of sample. Detection of Systematic Errors Analysis of standard reference materials (available from NIST). Analysis by two or more independent, reliable measurement methods. Perform blank determinations. Demonstrate that the analysis is independent of sample size.
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Indeterminate Errors Random , or indeterminate errors affect the precision of measurement. Statistical treatment of results allows one: to look at the data in different ways make objective and intelligent decisions regarding their quality and use.
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Different Methods, Different Analysts Low Random Low Systematic Large Random Low Systematic Low Random Large Systematic Large Random Large Systematic Biased method! Careless Analyst! AND Careless Analyst!
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Quantitative Estimation of Errors: Precision vs. Accuracy How would you define precision and accuracy? What is more important in chemical analysis, to be accurate or precise?
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Precision vs. Accuracy Low accuracy High accuracy Low precision High precision
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Precision vs. Accuracy
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Precision vs. Accuracy Systematic error Random error around mean value
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Measuring Accuracy Absolute Error (aka bias) Relative Error true X i X E - = 100 - = true X true X i X relative E True value needs to be known! If not known, we can make use of the mean value obtained with a reference method or by a certified lab or a reference material.
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Mathematical concepts used in evaluating accuracy and precision
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Mean Mean, arithmetic mean, average (all synonyms). (Average function in Excel) n x x n i i = = 1 Value of property x Value of property y y x , Are both affected by the outlier
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Median Is the middle result when replicate measurements are ordered in ascending order. Tolerant to outliers. Always compare to the mean.
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Evaluation of Precision Variance Standard Deviation Relative Standard Deviation Coefficient of Variation 1 ) ( 2 1 2 - - = = N X X s i n i X s RSD = variance = s 100 = RSD CV
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variables measured affect the overall precision of the analytical result? In experimental work, the quantity to be
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2-Data Handling and Statistics - DataHandlingandStatistics...

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