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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/Courses/Grinnell_College/CHM_363%3A_Physical_Chemistry_1_(Grinnell_College)/16%3A_Math_Chapters/16.01%3A_Probability_and_StatisticsA random variable X can have more than one value x as an outcome. Which value the variable has in a particular case is a matter of chance and cannot be predicted other than that we associate a probabi...A random variable X can have more than one value x as an outcome. Which value the variable has in a particular case is a matter of chance and cannot be predicted other than that we associate a probability to the outcome. Probability p is a number between 0 and 1 that indicates the likelihood that the variable X has a particular outcome x . The set of outcomes and their probabilities form a probability distribution.
- https://chem.libretexts.org/Bookshelves/Analytical_Chemistry/Analytical_Chemistry_2.1_(Harvey)/16%3A_Appendix/16.07%3A_Critical_Values_for_Grubb's_TestThe page provides critical values for Grubb's Test, used to identify outliers in data. It explains that the test involves calculating a value \(G_{10}\) for a single suspected outlier, compared agains...The page provides critical values for Grubb's Test, used to identify outliers in data. It explains that the test involves calculating a value \(G_{10}\) for a single suspected outlier, compared against a critical threshold \(G(\alpha, n)\). The table details these critical values for different sample sizes (n) and significance levels (\(\alpha\)), allowing users to determine if an outlier can be statistically rejected based on the given data set size and alpha values.
- https://chem.libretexts.org/Bookshelves/Physical_and_Theoretical_Chemistry_Textbook_Maps/Chemical_Thermodynamics_(Supplement_to_Shepherd_et_al.)/04%3A_Fundamental_2_-_Counting_Configurations/4.05%3A_Combinatorics_and_MultiplicityCombinatorics is the branch of math related to counting events and outcomes, while multiplicity is the statistical thermodynamics variable equal to the number of possible outcomes. They are intricate...Combinatorics is the branch of math related to counting events and outcomes, while multiplicity is the statistical thermodynamics variable equal to the number of possible outcomes. They are intricately connected.
- https://chem.libretexts.org/Bookshelves/Physical_and_Theoretical_Chemistry_Textbook_Maps/Physical_Chemistry_(LibreTexts)/32%3A_Math_Chapters/32.04%3A_Spherical_CoordinatesThis page explores various coordinate systems like Cartesian, polar, and spherical, focusing on their applications in mathematics and physics, as well as their significance for different problems. It ...This page explores various coordinate systems like Cartesian, polar, and spherical, focusing on their applications in mathematics and physics, as well as their significance for different problems. It highlights the necessity of adapting integration methods, particularly in quantum mechanics for normalizing wave functions using double and triple integrals.
- https://chem.libretexts.org/Bookshelves/Physical_and_Theoretical_Chemistry_Textbook_Maps/Physical_Chemistry_(LibreTexts)/03%3A_The_Schrodinger_Equation_and_a_Particle_in_a_Box/3.06%3A_Wavefunctions_Must_Be_NormalizedThis page explains the calculation of probabilities in quantum mechanics using wavefunctions, highlighting the importance of their absolute square as a probability density. It includes examples for on...This page explains the calculation of probabilities in quantum mechanics using wavefunctions, highlighting the importance of their absolute square as a probability density. It includes examples for one to three-dimensional scenarios and illustrates normalization to ensure total probabilities sum to one.
- 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/Bookshelves/Analytical_Chemistry/Analytical_Chemistry_2.1_(Harvey)/16%3A_Appendix/16.06%3A_Critical_Values_for_Dixon's_Q-TestThis page discusses Dixon's Q-test, a statistical method used to identify outliers in a data set. The focus is on Q10, a specific calculation for detecting a single outlier by comparing an outlier's d...This page discusses Dixon's Q-test, a statistical method used to identify outliers in a data set. The focus is on Q10, a specific calculation for detecting a single outlier by comparing an outlier's deviation from its nearest data point with the total range of the sample set. If the calculated value (Qexp) exceeds a critical value depending on the significance level alpha and the sample size (n), the outlier is rejected.
- 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/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/Bookshelves/Physical_and_Theoretical_Chemistry_Textbook_Maps/Physical_Chemistry_(LibreTexts)/17%3A_Boltzmann_Factor_and_Partition_Functions/17.05%3A_Pressure_can_be_Expressed_in_Terms_of_the_Canonical_Partition_FunctionThis page explains the derivation of pressure from the canonical partition function in statistical mechanics, linking it to thermodynamic principles and the ideal gas law. It includes equations that r...This page explains the derivation of pressure from the canonical partition function in statistical mechanics, linking it to thermodynamic principles and the ideal gas law. It includes equations that relate average pressure to energy and the partition function, along with a thought experiment illustrating gas compression with a piston.
