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Chapter 1

Chemical Applications of Statistical Analyses

SI-Einheiten: Neudefinition 2019
SI-Einheiten: Neudefinition 2019
Measurement is integral to analytical chemistry. Each record comprises a number – denoting the magnitude  – and the unit – a ...
Freiheitsgrade
Freiheitsgrade
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 ...
Statistische Analyse: Überblick
Statistische Analyse: Überblick
An analysis is usually conducted by replicated sampling or repeated measurements on the same sample. This leads to scattered results rather than a single ...
Arten von Fehlern: Erkennung und Minimierung
Arten von Fehlern: Erkennung und Minimierung
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 ...
Systematischer Fehler: Methoden- und Stichprobenfehler
Systematischer Fehler: Methoden- und Stichprobenfehler
Systematic errors, depending on their source, are of four types – sampling, instrumental, method, and personal errors. Sampling errors occur due to ...
Zufälliger Fehler
Zufälliger Fehler
Indeterminate or random errors arise from several uncontrollable variables in successive measurements. Since these errors can neither be predicted nor ...
Standardabweichung der berechneten Ergebnisse
Standardabweichung der berechneten Ergebnisse
A plot of relative deviation from the mean and its frequency of occurrence appears as a Gaussian curve. This probability distribution curve of a ...
Einführung <em>in die</em> z-Scores
Einführung in die 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 ...
Unsicherheit: Überblick
Unsicherheit: Überblick
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 ...
Ausbreitung der Unsicherheit durch Zufallsfehler
Ausbreitung der Unsicherheit durch Zufallsfehler
In an experiment, multiple arithmetic operations are often required. Here, the uncertainty associated with the first measurement propagates to the next in ...
Ausbreitung von Unsicherheit durch systematischen Fehler
Ausbreitung von Unsicherheit durch systematischen Fehler
The atomic mass of an element obtained from different sources changes slightly due to the variation in relative isotope concentration from one source to ...
Unsicherheit: Konfidenzintervalle
Unsicherheit: Konfidenzintervalle
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 ...
Signifikanzprüfung: Überblick
Signifikanzprüfung: Überblick
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 ...
Statistisch signifikante Unterschiede erkennen: Der <em>F-Test</em>
Statistisch signifikante Unterschiede erkennen: Der 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 ...
Vergleich experimenteller Ergebnisse: <em>Student's t-Test</em>
Vergleich experimenteller Ergebnisse: 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 ...
Erkennung von groben Fehlern: Der <em>Q-Test</em>
Erkennung von groben Fehlern: Der 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 ...
Kalibrierungskurven: Lineare kleinste Quadrate
Kalibrierungskurven: Lineare kleinste Quadrate
A calibration curve is a mathematical relationship between the instrument's signal and known analyte concentrations. This curve equation predicts the ...
Kalibrierkurven: Korrelationskoeffizient
Kalibrierkurven: Korrelationskoeffizient
A correlation coefficient is a statistical test to evaluate the degree and the direction of linear correlation between two variables. The Pearson ...
Korrelation und Regression
Korrelation und Regression
Regression and correlation are statistical techniques that examine the relationship between two variables.  While regression is used to understand ...
Unterschied zum Hintergrund: Nachweisgrenze
Unterschied zum Hintergrund: Nachweisgrenze
Background noise is intrinsic to any measurement interfering with the detection of the analyte signal. To analyze if the measured signal is from the ...
Quantifizierung und Ablehnung von Ausreißern: Der Grubbs-Test
Quantifizierung und Ablehnung von Ausreißern: Der 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 ...
Was ist ANOVA?
Was ist 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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