Name: significance testing in analytical chemistry
Uploaded: 2024-04-04T10:51:12.000Z
Duration: 1 min 4 s
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Chemistry

CHEM.2

CHEM.2.C

Significance Testing: Overview

Ist die Differenz zwischen den beiden Werten auf einen unerklärlichen Zufallsfehler zurückzuführen oder auf einen systematischen Fehler, der durch ein hypothetisches Modell rationalisiert werden kann?
Der Signifikanztest ist eine statistische Analyse, mit der validiert wird, ob die Differenz zwischen zwei Werten durch unbestimmte Fehler erklärt werden kann oder nicht.
Die Nullhypothese geht davon aus, dass die verglichenen Werte identisch sind und jeder Unterschied auf unbestimmte Fehler zurückzuführen ist. Die alternative Hypothese besagt, dass die Differenz real sein muss und nicht durch unbestimmte Fehler erklärt werden kann.
Ein Signifikanzniveau, das durch α bezeichnet wird, legt eine Konfidenzniveaubedingung für die Gültigkeit der Nullhypothese fest. Die Nullhypothese wird verworfen, wenn Werte jenseits des Konfidenzniveaus vorhanden sind.
Der Signifikanztest wird als einseitig bezeichnet, wenn Werte nur an einem Ende der Normalverteilungskurve abgelehnt werden. Bei zweiseitigen Signifikanztests kann die Ablehnung bei Werten auftreten, die an beiden Enden der Normalverteilungskurve liegen.

signifikanztests: Überblick

Signifikanztests sind eine Reihe statistischer Methoden, mit denen getestet wird, ob eine Aussage zu einem Parameter gültig ist. In der analytischen Chemie werden Signifikanztests hauptsächlich verwendet, um festzustellen, ob der Unterschied zwischen zwei Werten auf bestimmten oder zufälligen Fehlern beruht. Die Auswirkung einer bestimmten Änderung des Messprotokolls, des Analysten oder der Probe selbst kann zu einer Abweichung vom erwarteten Ergebnis führen. Im Falle einer vermuteten Abweichung/Ausreißer müssen wir mathematisch bestätigen können, dass die Abweichung von einer bestimmten Quelle stammt und dass die Beobachtung mit der Abweichung logischerweise aus der Analyse weggelassen werden kann.

Als Kriterien für die Signifikanzprüfung werden zwei Hypothesen verwendet. Die Nullhypothese (H0) besagt, dass sich die verglichenen Werte nicht wesentlich voneinander unterscheiden. Mit anderen Worten: Wenn zwischen zwei Werten ein Unterschied besteht, wird dieser einem unbestimmten Fehler zugeschrieben. Die Alternativhypothese (HA) besagt, dass die verglichenen Werte nicht gleich sind und der Unterschied signifikanter ist, als durch einen unbestimmten Fehler erklärt werden kann.

Bevor der Test durchgeführt wird, müssen die Hypothesen aufgestellt und ein Signifikanzniveau (α) festgelegt werden. Anschließend wird die Teststatistik basierend auf dem Stichprobenmittelwert und der Standardabweichung berechnet und mit den tabellierten Werten verglichen, die auf bestimmte Signifikanzniveaus festgelegt und als ein- oder zweiseitig definiert sind. Wenn die berechnete Teststatistik die kritischen Werte überschreitet (Tabellenstatistik), wird die Nullhypothese verworfen und wir stellen fest, dass die Differenz zwischen den beiden Werten nicht durch einen zufälligen, unbestimmten Fehler erklärt werden kann.

Beim einseitigen Signifikanztest kann die Alternativhypothese angeben, dass der beobachtete Wert entweder höher oder niedriger als der erwartete Wert ist, aber nicht beides. Beim zweiseitigen Signifikanztest kann die Alternativhypothese aussagen, dass der beobachtete Wert nicht dem erwarteten Wert entspricht, unabhängig von der Richtung.

Signifikanztests können für verschiedene statistische Parameter eines oder mehrerer Datensätze verwendet werden. Tests erhalten je nach Parameter oder Zweck unterschiedliche Namen. Signifikanztests werden häufig angewendet, um einen beobachteten Wert mit dem Mittelwert zu vergleichen oder zwei Mittelwerte aus zwei verschiedenen Datensätzen zu vergleichen. Diese Tests werden als t-Tests bezeichnet. Signifikanztests können auch für die Varianz zweier Datensätze durchgeführt werden. In diesem Fall wird der Test als F-Test bezeichnet. Wenn ein Signifikanztest zur Identifizierung von Ausreißern verwendet wird, wird der Test als Q-Test bezeichnet.

Signifikanztests: Überblick

Ist die Differenz zwischen den beiden Werten auf einen unerklärlichen Zufallsfehler zurückzuführen oder auf einen systematischen Fehler, der durch ein hypothetisches Modell rationalisiert werden kann?
Das...

Education

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JoVE Core

Analytical Chemistry

Analytische Chemie

Unit 1

Einheit 1

Chemical Applications of Statistical Analyses

Chemische Anwendungen statistischer Analysen

chemical-applications-of-statistical-analyses

KEY TERMS AND CONCEPTS

WICHTIGE BEGRIFFE UND KONZEPTE

significance testing in analytical chemistry

Significance testing helps analytical chemists decide whether a difference is meaningful or just caused by random error. It is used to test whether a claim about a parameter is valid. In analytical chemistry, it mainly helps determine whether a change between two values comes from determinate error or indeterminate error.

A determinate error has a clear source. It may come from a change in the measurement protocol, the analyst, or the sample itself. These changes can create a deviation from the expected result. If a value looks like an outlier, significance testing can help show mathematically that the deviation comes from a determinate source and that the value can be logically left out of the analysis.

Significance testing begins with two hypotheses. The null hypothesis, H0, says the values being compared do not differ significantly. If any difference exists, it is treated as an indeterminate error. The alternate hypothesis, HA, says the values are not equal and that the difference is too large to be explained by indeterminate error.

Before the test is performed, the hypotheses must be stated and a significance level, α, must be set. The test statistic is then calculated from the sample mean and standard deviation. This value is compared with tabulated critical values, which are defined at specific significance levels and can be one-tailed or two-tailed. If the calculated test statistic is greater than the critical value, the null hypothesis is rejected.

A rejected null hypothesis means the difference cannot be explained by random, indeterminate error. In one-tailed significance testing, the alternative hypothesis says the observed value is either higher or lower than expected, but not both. In two-tailed testing, the alternative hypothesis only says the observed value is not equal to the expected value, without naming a direction.

Significance testing can be used on different statistical parameters from one or more data sets. When it compares an observed value with a mean or compares two means, it is called a t-test. When it compares the variance of two data sets, it is called an F-test. When it is used to identify outliers, it is called a Q-test.

Significance Testing in Analytical Chemistry

significance-testing-in-analytical-chemistry

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significance testing: overview

Significance testing helps analytical chemists decide whether a difference is meaningful or just caused by random error. It is used to test whether a claim about a parameter is valid. In analytical chemistry, it mainly helps determine whether a change between two values comes from determinate error or indeterminate error. A determinate error has a clear source. It may come from a change in the measurement protocol, the analyst, or the sample itself. These changes can create a deviation from...

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key terms and concepts

Learn how significance testing helps identify random versus determinate error, set hypotheses, and choose t-tests, F-tests, or Q-tests in chemistry.

Significance Testing in Analytical Chemistry | JoVE K12

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Significance Testing in Analytical Chemistry

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