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Hypothesis Test

H0 :σx2 = σy2 versus H1 :σx2 != σy2

Sx2/Sy2 ∼ Fn−1,m−1

PH0 {F1−α/2,n−1,m−1 ≤ Sx2/Sy2 ≤ Fα/2,n−1,m−1} = 1 − α

Thus, a significance level α test of H0 against H1 is to

accept H0 if F1−α/2,n−1,m−1 < Sx2/Sy2 < Fα/2,n−1,m−1

reject H0 otherwise

Significance level α = 5 %

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The Levene test tests the null hypothesis that all input samples are from populations with equal variances.

=> Result here does not rejct H0 since p-value is above significance level of 5%

It can not be infered that there is a difference between the variances in the population.

ANOVA is used to compare the means of three or more samples

An ANOVA will provide an F-statistic which can, along with degrees of freedom, be used to calculate a p value.

ANOVAs assume independence of observations, homogeneity of variances and normally distributed observations within groups.

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=> Result here does not rejct H0 since p-value is way above significance level of 5%

-> under H0 we obtain the test statistic from this sample with 99.9 %

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=> Result here does reject H0 since p-value is below significance level of 5%

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Ambiguous results -> small dataset: ANOVA is very sensitive to distributional assumptions => less robust than Levene