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

Le test F vérifie si la différence entre deux variances est trop grande pour être expliquée par une erreur indéterminée. Il compare la variance d’un échantillon et celle d’une population ou les variances de deux échantillons.
Le test F est basé sur l’hypothèse nulle, qui stipule que les deux variances comparées sont égales.
La statistique de test F est évaluée comme le quotient de variances, où la variance est exprimée comme le carré de l’écart-type.
La variance avec une valeur plus grande est placée au numérateur, ce qui rend F toujours supérieur ou égal à un.
La valeur F doit être égale à un pour que l’hypothèse nulle soit vraie. Il devient supérieur à un en raison d’erreurs indéterminées et déterminées.
Dans le cas d’un test unilatéral, la valeur F obtenue est comparée à la valeur F tabulé à un niveau de confiance et à un degré de liberté choisis. L’hypothèse nulle est rejetée lorsque la valeur F obtenue est inférieure à la valeur F tabularisée dans un test unilatéral inférieur ou supérieure dans un test unilatéral supérieur.

identifier les différences statistiquement significatives : le test f

Le test F est utilisé pour comparer deux variances d'échantillon entre elles ou pour comparer la variance d'échantillon à la variance de population. Il est utilisé pour décider si une erreur indéterminée peut expliquer la différence de leurs valeurs. Les hypothèses sous-jacentes qui permettent l’utilisation du test F incluent que le ou les ensembles de données sont normalement distribués et que les ensembles de données sont indépendants les uns des autres. La statistique de test F est calculée en divisant une variance par une autre. En d’autres termes, le carré d’un écart type par le carré de l’autre. Pour obtenir une valeur égale ou supérieure à un comme résultat du quotient, la plus grande valeur est toujours divisée par la plus petite valeur.

L'hypothèse nulle du test F stipule que le rapport est égal à 1. Après avoir calculé la statistique du test, il est comparé aux valeurs F critiques tabulées à un niveau de confiance choisi et au degré de liberté approprié. L'hypothèse nulle est acceptée si la statistique de test F est inférieure à la valeur F tabulée. Dans ce cas, la différence par rapport à la valeur souhaitée de l’unité – le cas échéant – est justifiée par une erreur indéterminée, et nous affirmons que les variations ne sont pas significativement différentes.

Identifier les différences statistiquement significatives : le test F

Le test F vérifie si la différence entre deux variances est trop grande pour être expliquée par une erreur indéterminée. Il compare la variance d’un échantillon et ...

Education

Enseignement

JoVE Core

Analytical Chemistry

Chimie analytique

Unit 1

Unité 1

Chemical Applications of Statistical Analyses

Applications chimiques des analyses statistiques

chemical-applications-of-statistical-analyses

KEY TERMS AND CONCEPTS

TERMES ET CONCEPTS CLÉS

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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Learn how the F-test compares variances, checks normality and independence, and uses critical F values to judge whether differences are significant.

Comparing Variance with the F-Test | JoVE K12

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Comparing Variance with the F-Test

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