8.15
The F test, named after the renowned statistician Sir Ronald Fisher, compares the difference between population variances of two normally distributed populations.
The F test uses the F statistic, which is the ratio of the sample variances and, thus, is never negative.
Generally, for ease of calculations, the numerator represents the higher sample variance while the denominator denotes the smaller sample variance.
As the difference between the sample variances reduces, the F statistic gets closer to unity.
Computing the F statistic for several random samples of two independent normally distributed populations, and plotting the F statistic yields the F distribution curve, an asymmetric curve, similar to the chi-square distribution curve.
However, unlike the chi-square-based tests, the F distribution has two sets of degrees of freedom, one for the numerator and another for the denominator. The exact shape of the F distribution curve depends on these two degrees of freedom.
This distribution is helpful in the F test and methods involving the comparison of variances, such as ANOVA.
De F-verdeling is vernoemd naar Sir Ronald Fisher, een Engelse statisticus. De F-statistiek is een verhouding (een breuk) met twee vrijheidsgraden; één voor de teller en één voor de noemer. De F-verdeling is afgeleid van de Student's t-verdeling. De waarden van de F-verdeling zijn de kwadraten van de overeenkomstige waarden van de t-verdeling. One-Way ANOVA breidt de t-toets uit voor het vergelijken van meer dan twee groepen. De afleiding hiervan valt buiten de scope van deze cursus. Het verdient de voorkeur om ANOVA te gebruiken wanneer er meer dan twee groepen zijn, in plaats van meerdere paarsgewijze t-toetsen uit te voeren, omdat dit de kans vergroot op het maken van een Type 1-fout.
Om de F-ratio te berekenen, worden twee schattingen van de variantie gemaakt:
SSbetween = de som van de kwadraten die de variantie tussen de verschillende steekproeven weergeeft.
SSwithin = de som van de kwadraten die de variantie binnen de steekproeven weergeeft als gevolg van toevallige variatie.
Deze tekst is een bewerking van Openstax, Inleidende statistieken, sectie 13.2 De F-verdeling en de F-ratio
The F test, named after the renowned statistician Sir Ronald Fisher, compares the difference between population variances of two normally distributed populations.
The F test uses the F statistic, which is the ratio of the sample variances and, thus, is never negative.
Generally, for ease of calculations, the numerator represents the higher sample variance while the denominator denotes the smaller sample variance.
As the difference between the sample variances reduces, the F statistic gets closer to unity.
Computing the F statistic for several random samples of two independent normally distributed populations, and plotting the F statistic yields the F distribution curve, an asymmetric curve, similar to the chi-square distribution curve.
However, unlike the chi-square-based tests, the F distribution has two sets of degrees of freedom, one for the numerator and another for the denominator. The exact shape of the F distribution curve depends on these two degrees of freedom.
This distribution is helpful in the F test and methods involving the comparison of variances, such as ANOVA.
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