What Does Rejecting the Null in ANOVA but Not Hartley's FMAX Mean?

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SUMMARY

Rejecting the null hypothesis in ANOVA indicates that at least one group mean differs from the others, while failing to reject the null in Hartley's FMAX suggests that the variances among the groups are similar. ANOVA is utilized to compare means across multiple groups, whereas Hartley's test focuses on variance similarity. Additionally, a t-test is specifically designed to compare the means of two groups, functioning as a specialized form of ANOVA for two-group comparisons.

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melissahalliwel
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What does it mean when I reject the null in an ANOVA but fail to reject the null when doing something such as Hartleys FMAX?

Also, what's the difference between ANOVA AND T-TEST?
 
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melissahalliwel said:
What does it mean when I reject the null in an ANOVA but fail to reject the null when doing something such as Hartleys FMAX?

Hi melissahalliwel, welcome to MHB!

ANOVA and Hartley test for different things.
The ANOVA tests whether the means of several groups are the same.
Hartley tests if the variances of the groups are similar.

Rejecting the null in ANOVA means there is a group with a different mean.
Failing to reject Hartley means that the variances of the groups are assumed to be similar (even if their means are not).

melissahalliwel said:
Also, what's the difference between ANOVA AND T-TEST?

A textbook will list a whole set of characteristics for each of them.
Anyway, let me try to put some of it in just a couple sentences.

A t-test compares two means.
An ANOVA compares variances. ANOVA is also considered a generalized t-test, as we use it when we have more than 2 groups.

A t-test compares the means directly using a t-distribution.
An ANOVA is an ANalysis of VAriances, meaning it compares variances using an F-distribution.
 

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