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- https://chem.libretexts.org/Bookshelves/Analytical_Chemistry/Analytical_Chemistry_2.1_(Harvey)/07%3A_Obtaining_and_Preparing_Samples_for_Analysis/7.01%3A_The_Importance_of_SamplingThis page discusses the importance of sampling in achieving accurate and precise chemical analyses, specifically related to ACS Reagent Grade specifications. A key point is that accurate sampling is c...This page discusses the importance of sampling in achieving accurate and precise chemical analyses, specifically related to ACS Reagent Grade specifications. A key point is that accurate sampling is crucial to minimize errors and meet standards, such as limiting iron in NaBr to under 5 ppm. The text also explains variance in sampling and analytical methods, illustrating the propagation of uncertainty through examples and exercises.
- https://chem.libretexts.org/Courses/University_of_Arkansas_Little_Rock/Chem_1402%3A_General_Chemistry_1_(Kattoum)/Text/1.B%3A_Review_of_the_Tools_of_Quantitative_Chemistry/1B.2%3A__Making_Measurements%3A__Experimental_Error%2C_Accuracy%2C_Precision%2C_Standard_Deviation_and_Significant_FiguresIn figure 1B.2.4 we see two distributions based on the two scales in 1B.2.2, where on the left, the centimeter scale was used, and the values reported have a greater spread (between the certain values...In figure 1B.2.4 we see two distributions based on the two scales in 1B.2.2, where on the left, the centimeter scale was used, and the values reported have a greater spread (between the certain values of 1 and 2cm), than on the right, where the more precise millimeter scale was used, and the spread is between the certain values of 1.6 and 1.7 cm.
- https://chem.libretexts.org/Bookshelves/Analytical_Chemistry/Analytical_Chemistry_2.1_(Harvey)/05%3A_Standardizing_Analytical_Methods/5.04%3A_Linear_Regression_and_Calibration_CurvesThis page discusses different approaches to identifying the relationship between signal and concentration in quantitative analysis. It outlines methodologies for single-point and multiple-point extern...This page discusses different approaches to identifying the relationship between signal and concentration in quantitative analysis. It outlines methodologies for single-point and multiple-point external standardization, emphasizing the limitations and considerations for each, such as determinate errors. It further delves into unweighted and weighted linear regression techniques, detailing equations for calculating slope and y-intercept while addressing error management.
- https://chem.libretexts.org/Bookshelves/Analytical_Chemistry/Instrumental_Analysis_(LibreTexts)/35%3A_Appendicies/35.02%3A_Single-Sided_Normal_DistributionFor example, the proportion of the area under a normal distribution to the right of a deviation of 0.04 is 0.4840 (see entry in red in the table), or 48.40% of the total area (see the area shaded blue...For example, the proportion of the area under a normal distribution to the right of a deviation of 0.04 is 0.4840 (see entry in red in the table), or 48.40% of the total area (see the area shaded blue in Figure \PageIndex1). This divides the normal distribution curve into three regions: the area that corresponds to our answer (shown in blue), the area to the right of this, and the area to the left of this.
- https://chem.libretexts.org/Bookshelves/Physical_and_Theoretical_Chemistry_Textbook_Maps/Thermodynamics_and_Chemical_Equilibrium_(Ellgen)/03%3A_Distributions_Probability_and_Expected_Values/3.10%3A_Statistics_-_the_Mean_and_the_Variance_of_a_DistributionThere are two important statistics associated with any probability distribution, the mean of a distribution and the variance of a distribution.
- https://chem.libretexts.org/Courses/Lakehead_University/Analytical_I/4%3A_Evaluating_Analytical_Data/4.01%3A_Characterizing_Measurements_and_ResultsOne way to characterize data from multiple measurements/runs is to assume that the measurements are randomly scattered around a central value that provides the best estimate of expected, or “true” va...One way to characterize data from multiple measurements/runs is to assume that the measurements are randomly scattered around a central value that provides the best estimate of expected, or “true” value. There are two common ways to estimate central tendency: the mean and the median.
- https://chem.libretexts.org/Courses/Los_Angeles_Trade_Technical_College/Analytical_Chemistry/2%3A_Analytical_Chemistry_2.0_(Harvey)/15%3A_Developing_a_Standard_Method/15.3%3A_Validating_the_Method_as_a_Standard_MethodFor an analytical method to be useful, an analyst must be able to achieve results of acceptable accuracy and precision. Verifying a method, as described in the previous section, establishes this goal ...For an analytical method to be useful, an analyst must be able to achieve results of acceptable accuracy and precision. Verifying a method, as described in the previous section, establishes this goal for a single analyst. Another requirement for a useful analytical method is that an analyst should obtain the same result from day to day, and different labs should obtain the same result when analyzing the same sample. The process by which we approve method for general use is known as validation.
- https://chem.libretexts.org/Bookshelves/Analytical_Chemistry/Analytical_Chemistry_2.1_(Harvey)/04%3A_Evaluating_Analytical_Data/4.06%3A_Statistical_Methods_for_Normal_DistributionsThis page discusses the use of statistical tests to compare means and variances in analytical chemistry. Key methods include the t-test for comparing sample means, the F-test for variances, and signif...This page discusses the use of statistical tests to compare means and variances in analytical chemistry. Key methods include the t-test for comparing sample means, the F-test for variances, and significance tests for outliers like Dixon's Q-test, Grubb's test, and Chauvenet's criterion. The tests help determine if observed differences are significant or due to chance, aiding in validating analytical methods or identifying errors in analyses.
- https://chem.libretexts.org/Bookshelves/Analytical_Chemistry/Analytical_Chemistry_2.1_(Harvey)/04%3A_Evaluating_Analytical_Data/4.07%3A_Detection_LimitsThe page discusses the IUPAC's definition of a method's detection limit as the smallest signal indicating the presence of an analyte, distinct from a blank signal. It delves into statistical concepts ...The page discusses the IUPAC's definition of a method's detection limit as the smallest signal indicating the presence of an analyte, distinct from a blank signal. It delves into statistical concepts like type 1 and type 2 errors, explaining the probability associated with detecting an analyte.
- https://chem.libretexts.org/Courses/Los_Angeles_Trade_Technical_College/Analytical_Chemistry/2%3A_Analytical_Chemistry_2.0_(Harvey)/16%3A_Quality_Assurance/16.4%3A_Evaluating_Quality_Assurance_DataNow we turn our attention to how we incorporate this quality assessment data into a complete quality assurance program. There are two general approaches to developing a quality assurance program: a pr...Now we turn our attention to how we incorporate this quality assessment data into a complete quality assurance program. There are two general approaches to developing a quality assurance program: a prescriptive approach, in which we prescribe an exact method of quality assessment, and a performance-based approach in which we can use any form of quality assessment, provided that we can demonstrate an acceptable level of statistical control.
- https://chem.libretexts.org/Bookshelves/Physical_and_Theoretical_Chemistry_Textbook_Maps/Statistical_Thermodynamics_(Jeschke)/02%3A_Probability_Theory/2.01%3A_Discrete_Probability_TheoryAccording to the central limit theorem, the mean value ⟨S⟩/N of the sum of all these random numbers is approximately normally distributed, regardless of the probability distribution ...According to the central limit theorem, the mean value ⟨S⟩/N of the sum of all these random numbers is approximately normally distributed, regardless of the probability distribution of the individual random numbers, as long all the probability distributions of all individual random numbers are identical.
