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Chapter 1

Chemical Applications of Statistical Analyses

SI Units: 2019 Redefinition
SI Units: 2019 Redefinition
Measurement is integral to analytical chemistry. Each record comprises a number – denoting the magnitude  – and the unit – a ...
Degrees of Freedom
Degrees of Freedom
The degree of freedom is the number of independent pieces of information or sample values required to perform any calculation. The degrees of freedom vary ...
Statistical Analysis: Overview
Statistical Analysis: Overview
An analysis is usually conducted by replicated sampling or repeated measurements on the same sample. This leads to scattered results rather than a single ...
Types of Errors: Detection and Minimization
Types of Errors: Detection and Minimization
Error is the deflection of an obtained result from the expected or true results of an experiment. This happens due to the uncertainty associated with the ...
Systematic Error: Methodological and Sampling Errors
Systematic Error: Methodological and Sampling Errors
Systematic errors, depending on their source, are of four types – sampling, instrumental, method, and personal errors. Sampling errors occur due to ...
Random Error
Random Error
Indeterminate or random errors arise from several uncontrollable variables in successive measurements. Since these errors can neither be predicted nor ...
Standard Deviation of Calculated Results
Standard Deviation of Calculated Results
A plot of relative deviation from the mean and its frequency of occurrence appears as a Gaussian curve. This probability distribution curve of a ...
Introduction to <em>z</em> Scores
Introduction to z Scores
The z score, or standardized score, is the number of standard deviations that a given value is away from the mean. It is one of the commonly used measures ...
Uncertainty: Overview
Uncertainty: Overview
The uncertainty reflects the possible range of values in which the result of a measurement can exist. However, uncertainty varies from error, which is the ...
Propagation of Uncertainty from Random Error
Propagation of Uncertainty from Random Error
In an experiment, multiple arithmetic operations are often required. Here, the uncertainty associated with the first measurement propagates to the next in ...
Propagation of Uncertainty from Systematic Error
Propagation of Uncertainty from Systematic Error
The atomic mass of an element obtained from different sources changes slightly due to the variation in relative isotope concentration from one source to ...
Uncertainty: Confidence Intervals
Uncertainty: Confidence Intervals
Standard deviation provides a measure of nearness between the sample mean and the true mean reliably for a large number of measurements. So, when there ...
Significance Testing: Overview
Significance Testing: Overview
Is the difference between the two values due to an unexplainable random error or a systematic error that can be rationalized by a hypothetical model? The ...
Identifying Statistically Significant Differences: The <em>F</em>-Test
Identifying Statistically Significant Differences: The F-Test
The F-test checks if the difference between two variances is too large to be explained by an indeterminate error. It compares the variance of a sample and ...
Comparing Experimental Results: Student's <em>t</em>-Test
Comparing Experimental Results: Student's t-Test
The influence of changing the method, the sample, or the analyst on the analysis results is studied by altering only one in a pair of experiments. The ...
Detection of Gross Error: The <em>Q</em> Test
Detection of Gross Error: The Q Test
Outliers are those data points extremely different from the rest of the data set. Dixon's Q-test is a significance test that helps determine whether ...
Calibration Curves: Linear Least Squares
Calibration Curves: Linear Least Squares
A calibration curve is a mathematical relationship between the instrument's signal and known analyte concentrations. This curve equation predicts the ...
Calibration Curves: Correlation Coefficient
Calibration Curves: Correlation Coefficient
A correlation coefficient is a statistical test to evaluate the degree and the direction of linear correlation between two variables. The Pearson ...
Correlation and Regression
Correlation and Regression
Regression and correlation are statistical techniques that examine the relationship between two variables.  While regression is used to understand ...
Difference from Background: Limit of Detection
Difference from Background: Limit of Detection
Background noise is intrinsic to any measurement interfering with the detection of the analyte signal. To analyze if the measured signal is from the ...
Quantifying and Rejecting Outliers: The Grubbs Test
Quantifying and Rejecting Outliers: The Grubbs Test
Grubbs' test, like Dixon's Q-test, is a statistical test to identify the outliers in data with a normal distribution. Here, the number of ...
What is ANOVA?
What is ANOVA?
The analysis of variance—abbreviated as ANOVA —is used when the means of three or more samples need to be tested for equality. For example, ...
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