Name: comparing variance with the f-test
Uploaded: 2024-04-04T10:51:12.000Z
Duration: 1 min 14 s
Channel: JoVE

K12 Standards

Texas Essential Knowledge and Skills

High School

Chemistry

CHEM.2

CHEM.2.C

identifying-statistically-significant-differences-the-f-test

Identifying Statistically Significant Differences: The F-Test

Der F-Test prüft, ob die Differenz zwischen zwei Varianzen zu groß ist, um durch einen unbestimmten Fehler erklärt zu werden. Er vergleicht die Varianz einer Stichprobe mit der einer Grundgesamtheit oder die Varianzen zweier Stichproben.
Der F-Test basiert auf der Nullhypothese, die besagt, dass die beiden verglichenen Varianzen gleich sind.
Die Teststatistik F wird als Quotient der Varianzen ausgewertet, wobei die Varianz als Quadrat der Standardabweichung ausgedrückt wird.
Die Varianz mit einem größeren Wert wird in den Zähler eingefügt, sodass F immer größer oder gleich eins ist.
Der F-Wert sollte eins sein, damit die Nullhypothese wahr ist. Sie wird aufgrund von unbestimmten und bestimmten Fehlern größer als eins.
Bei einem einseitigen Test wird der erhaltene F-Wert mit dem tabellarischen F-Wert bei einem gewählten Konfidenzniveau und Freiheitsgrad verglichen. Die Nullhypothese wird verworfen, wenn der ermittelte F-Wert niedriger als der tabellarische F-Wert in einem unteren einseitigen Test oder größer in einem oberen einseitigen Test ist.

statistisch signifikante unterschiede identifizieren: der f-test

Der F-Test wird verwendet, um zwei Stichprobenvarianzen miteinander zu vergleichen oder die Stichprobenvarianz mit der Populationsvarianz zu vergleichen. Es wird verwendet, um zu entscheiden, ob ein unbestimmter Fehler den Unterschied in ihren Werten erklären kann. Zu den zugrunde liegenden Annahmen, die die Verwendung des F-Tests ermöglichen, gehört, dass der oder die Datensätze normalverteilt sind und die Datensätze unabhängig voneinander sind. Die Teststatistik F wird berechnet, indem eine Varianz durch eine andere dividiert wird. Mit anderen Worten, das Quadrat einer Standardabweichung durch das Quadrat der anderen. Um als Ergebnis des Quotienten einen Wert von eins oder größer eins zu erhalten, wird immer der größere Wert durch den kleineren Wert dividiert.

Die Nullhypothese des F-Tests besagt, dass das Verhältnis gleich 1 ist. Nach der Berechnung der Teststatistik wird diese mit den tabellierten kritischen F-Werten bei einem gewählten Konfidenzniveau und dem entsprechenden Freiheitsgrad verglichen. Die Nullhypothese wird akzeptiert, wenn die Teststatistik F kleiner als der tabellierte F-Wert ist. In diesem Fall ist der Unterschied zum gewünschten Wert der Einheit – falls vorhanden – durch einen unbestimmten Fehler gerechtfertigt, und wir geben an, dass die Variationen nicht signifikant unterschiedlich sind.

Statistisch signifikante Unterschiede identifizieren: Der F-Test

Der F-Test prüft, ob die Differenz zwischen zwei Varianzen zu groß ist, um durch einen unbestimmten Fehler erklärt zu werden. Es vergleicht die Varianz einer Stichprobe und ...

Education

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JoVE Core

Analytical Chemistry

Analytische Chemie

Unit 1

Einheit 1

Chemical Applications of Statistical Analyses

Chemische Anwendungen statistischer Analysen

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KEY TERMS AND CONCEPTS

WICHTIGE BEGRIFFE UND KONZEPTE

comparing variance with the f-test

The F-test compares variance in two data sets or compares a sample variance with a population variance. It helps decide whether an indeterminate error can explain a difference in the values. In statistics, variance shows how spread out the data are.

The test assumes that the data set or sets are normally distributed. It also assumes that the data sets are independent of each other. These conditions must be met before the F-test is used.

The F test statistic is found by dividing one variance by another. That means one standard deviation is squared and divided by the square of the other standard deviation. To get a value of one or greater than one, the larger variance is always divided by the smaller variance.

The null hypothesis for the F-test states that the ratio is equal to 1. After the test statistic is calculated, it is compared with tabulated critical F values at a chosen confidence level and the correct degree of freedom. If the test statistic F is smaller than the tabulated F value, the null hypothesis is rejected. In that case, any difference from unity is explained by indeterminate error, and the variations are not considered significantly different.

Comparing Variance with the F-Test

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The F-test compares variance in two data sets or compares a sample variance with a population variance. It helps decide whether an indeterminate error can explain a difference in the values. In statistics, variance shows how spread out the data are. The test assumes that the data set or sets are normally distributed. It also assumes that the data sets are independent of each other. These conditions must be met before the F-test is used. The F test statistic is found by dividing one variance...

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Comparing Variance with the F-Test | JoVE K12

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Comparing Variance with the F-Test

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