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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 z 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 F-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 t-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 Q 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 via 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

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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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