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Chapter 1
Chemical Applications of Statistical Analyses

SI Units: 2019 Redefinition
Measurement is an indispensable part of analytical chemistry. The result of measurement helps quantify a substance's physical property and…
Degrees of Freedom
The degree of freedom for a particular statistical calculation is the number of values that are free to vary. As a result, the minimum number of…
Statistical Analysis: Overview
When we take repeated measurements on the same or replicated samples, we will observe inconsistencies in the magnitude. These inconsistencies are…
Types of Errors: Detection and Minimization
Error is the deviation of the obtained result from the true, expected value or the estimated central value. Errors are expressed in absolute or…
Systematic Error: Methodological and Sampling Errors
In the case of systematic errors, the sources can be identified, and the errors can be subsequently minimized by addressing these sources. According…
Random Error
Random or indeterminate errors originate from various uncontrollable variables, such as variations in environmental conditions, instrument…
Standard Deviation of Calculated Results
Standard deviation measures the spread of data around the mean value. Many large data sets follow a Gaussian distribution, also known as a normal…
Introduction to <em>z</em> Scores
A z score (or standardized value) is measured in units of the standard deviation. It indicates how many standard deviations the value x is above (to…
Uncertainty: Overview
In analytical chemistry, we often perform repetitive measurements to detect and minimize inaccuracies caused by both determinate and indeterminate…
Propagation of Uncertainty from Random Error
An experiment often consists of more than a single step. In this case, measurements at each step give rise to uncertainty. Because the measurements…
Propagation of Uncertainty from Systematic Error
The atomic mass of an element varies due to the relative ratio of its isotopes. A sample's relative proportion of oxygen isotopes influences its…
Uncertainty: Confidence Intervals
The confidence interval is the range of values around the mean that contains the true mean. It is expressed as a probability percentage. The…
Significance Testing: Overview
Significance testing is a set of statistical methods used to test whether a claim about a parameter is valid. In analytical chemistry, significance…
Identifying Statistically Significant Differences: The <em>F</em>-Test
The F-test is used to compare two sample variances to each other or compare the sample variance to the population variance. It is used to decide…
Comparing Experimental Results: Student's <em>t</em>-Test
The t-test is a statistical method used to compare the sample mean with a population mean or compare two means from two data sets. The test statistic…
Detection of Gross Error: The <em>Q</em> Test
When one or more data points appear far from the rest of the data, there is a need to determine whether they are outliers and whether they should be…
Calibration Curves: Linear Least Squares
A calibration curve is a plot of the instrument's response against a series of known concentrations of a substance. This curve is used to set the…
Calibration Curves: Correlation Coefficient
In a linear calibration curve, there is a value called the calibration coefficient, denoted by 'r,' which measures the strength and the…
Correlation and Regression
In statistics, correlation describes the degree of association between two variables. In the subfield of linear regression, correlation is…
Difference from Background: Limit of Detection
The limit of detection (LOD) is the smallest amount of analyte that can be distinguished from the background noise. The LOD value corresponds to the…
Quantifying and Rejecting Outliers: The Grubbs Test
Sometimes, a data set can have a recorded numerical observation that greatly  deviates from the rest of the data. Assuming that the data is…
What is ANOVA?
The Analysis of Variance or ANOVA is a statistical test developed by Ronald Fisher in 1918. It is performed on three or more samples to check for…
Synthesis of Protein Bioconjugates <em>via</em> Cysteine-maleimide Chemistry
The chemical linking or bioconjugation of proteins to fluorescent dyes, drugs, polymers and other proteins has a broad range of applications, such as…
Measuring Lactase Enzymatic Activity in the Teaching Lab
Understanding how enzymes work, and relating this to real life examples, is critical to a wide range of undergraduate degrees in the biological and…
Spectrophotometric Methods for the Study of Eukaryotic Glycogen Metabolism
Glycogen is synthesized as a storage form of glucose by a wide array of organisms, ranging from bacteria to animals. The molecule comprises linear…

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