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- https://chem.libretexts.org/Bookshelves/Analytical_Chemistry/Analytical_Chemistry_2.1_(Harvey)/04%3A_Evaluating_Analytical_Data/4.09%3A_ProblemsThe page outlines various statistical analysis exercises involving data sets from different scientific experiments. The tasks include calculating descriptive statistics such as mean, median, standard ...The page outlines various statistical analysis exercises involving data sets from different scientific experiments. The tasks include calculating descriptive statistics such as mean, median, standard deviation, and variance; performing hypothesis tests to determine statistical significance; analyzing data distributions and detecting outliers. It also includes problems on data uncertainty, accuracy verification of equipment, and chemical analysis through different methods.
- https://chem.libretexts.org/Bookshelves/Analytical_Chemistry/Analytical_Chemistry_2.1_(Harvey)/05%3A_Standardizing_Analytical_Methods/5.06%3A_Using_Excel_and_R_for_a_Linear_RegressionThe page details methods for performing linear regression analysis using Excel and R. It explains how to fit a straight-line model to data, obtain relevant statistical information, and visualize the r...The page details methods for performing linear regression analysis using Excel and R. It explains how to fit a straight-line model to data, obtain relevant statistical information, and visualize the regression model using Excel. Three approaches in Excel include using built-in functions, employing Data Analysis ToolPak, and programming formulas directly into a spreadsheet.
- https://chem.libretexts.org/Bookshelves/Physical_and_Theoretical_Chemistry_Textbook_Maps/Physical_Chemistry_(LibreTexts)/32%3A_Math_Chapters/32.11%3A_The_Binomial_Distribution_and_Stirling's_AppromixationThis page discusses Stirling's approximation, developed by James Stirling, which estimates the factorial of large numbers, essential in statistics. It states that \(\ln N!\) approximates \(N \ln N - N...This page discusses Stirling's approximation, developed by James Stirling, which estimates the factorial of large numbers, essential in statistics. It states that \(\ln N!\) approximates \(N \ln N - N\), improving with larger \(N\). The approximation's accuracy is supported by evaluations at different \(N\) and its application in thermodynamics for large quantities like Avogadro's number, utilizing concepts from the Euler-MacLaurin formula and integration techniques.
- https://chem.libretexts.org/Bookshelves/Analytical_Chemistry/Instrumental_Analysis_(LibreTexts)/35%3A_AppendiciesThe appendices gathered here provide a lengthy introduction to the analysis of data, a variety of tables that contain critical values for the statistical analysis of data and standard oxidation-reduct...The appendices gathered here provide a lengthy introduction to the analysis of data, a variety of tables that contain critical values for the statistical analysis of data and standard oxidation-reduction potential, a discussion of activity, and a list of acronyms and abbreviations used in this textbook and in other resources for analytical chemistry.
- 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 \(\PageIndex{1}\)). 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/Ancillary_Materials/Worksheets/Worksheets%3A_Analytical_Chemistry_II/Statistics_(Mullaugh)The table below summarizes the results of an analysis of the child’s blood lead level (BLL, in µg/dL) initially and after a month of treatment. At the 95% confidence level, does the athlete’s caffeine...The table below summarizes the results of an analysis of the child’s blood lead level (BLL, in µg/dL) initially and after a month of treatment. At the 95% confidence level, does the athlete’s caffeine level exceed the acceptable level? (Another way of asking this is, “Does the maximum acceptable value of 12.00 μg/mL fall within the 95% confidence interval?”) Based on the results of the F-test, use the appropriate form of the t-test to determine if the child’s BLL is decreasing significantly.
- https://chem.libretexts.org/Bookshelves/Physical_and_Theoretical_Chemistry_Textbook_Maps/Physical_Chemistry_(LibreTexts)/32%3A_Math_ChaptersThis page covers essential mathematical concepts in physical chemistry, such as complex numbers, probability, vectors, and matrices. It highlights the significance of multivariate calculus, probabilit...This page covers essential mathematical concepts in physical chemistry, such as complex numbers, probability, vectors, and matrices. It highlights the significance of multivariate calculus, probability distributions, and numerical methods in solving experimental and theoretical problems in the physical sciences. Topics like Fourier analysis, partial differentiation, and the binomial distribution are also discussed for their practical applications.
- https://chem.libretexts.org/Ancillary_Materials/Worksheets/Worksheets%3A_Analytical_Chemistry_II/Statistics_(Gray)2) Write the numbers above in scientific notation maintaining the same number of significant figures. 1) Find the absolute and percent relative uncertainty and express each answer with the correct num...2) Write the numbers above in scientific notation maintaining the same number of significant figures. 1) Find the absolute and percent relative uncertainty and express each answer with the correct number of significant figures. 1) Given the following data, are the precisions of the two datasets significantly different at the 95% confidence level? 2) Using both the Grubbs and the Q-test, can the last data point be excluded at the 95% CI?
- https://chem.libretexts.org/Courses/Remixer_University/Construction_Guide_for_LibreTexts_2e/01%3A_LibreTexts_Fundamentals/1.02%3A_Project_OrganizationThe content in the Libretexts is organized in the following sections (which may not be fully implemented in each constituent librarian of the project the chemistry library is most developed).
- https://chem.libretexts.org/Bookshelves/Analytical_Chemistry/Instrumental_Analysis_(LibreTexts)/35%3A_Appendicies/35.05%3A_Critical_Values_for_Dixon's_Q-TestThe following table provides critical values for \(Q(\alpha, n)\), where \(\alpha\) is the probability of incorrectly rejecting the suspected outlier and \(n\) is the number of samples in the data set...The following table provides critical values for \(Q(\alpha, n)\), where \(\alpha\) is the probability of incorrectly rejecting the suspected outlier and \(n\) is the number of samples in the data set. There are several versions of Dixon’s Q-Test, each of which calculates a value for Q ij where i is the number of suspected outliers on one end of the data set and j is the number of suspected outliers on the opposite end of the data set.
- https://chem.libretexts.org/Bookshelves/Analytical_Chemistry/Instrumental_Analysis_(LibreTexts)/35%3A_Appendicies/35.04%3A_Critical_Values_for_F-TestThe following tables provide values for \(F(0.05, \nu_\text{num}, \nu_\text{denom})\) for one-tailed and for two-tailed F-tests. To use these tables, we first decide whether the situation calls for a ...The following tables provide values for \(F(0.05, \nu_\text{num}, \nu_\text{denom})\) for one-tailed and for two-tailed F-tests. To use these tables, we first decide whether the situation calls for a one-tailed or a two-tailed analysis and calculate F exp Next, we compare Fexp to \(F(0.05, \nu_\text{num}, \nu_\text{denom})\) and reject the null hypothesis if \(F_\text{exp} > F(0.05, \nu_\text{num}, \nu_\text{denom})\). Table \(\PageIndex{1}\): Critical Values of F for a One-Tailed F-Test
