Graduate Extended version of Cochran's Theorem

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Cochran's Theorem may potentially be extended to many-factor ANOVA to analyze the distribution of statistics involved. Participants are exploring whether similar results from Cochran's Theorem can apply to multifactor ANOVA scenarios. The discussion highlights the need for clarity on how these statistical principles interact in complex designs. There is interest in identifying relevant statistics that could be derived from such extensions. Further research and examples are encouraged to solidify understanding in this area.
WWGD
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Hi,
Anyone know if Cochran's Theorem can be extended to many-factor Anova, to determine the distribution of statistics used therein? Maybe similar other results can be used for determining relevant stats in use in multifactor Anova?
 

Thread 'How do E[X] and E[|X|] relate?'

Greetings, I am studying probability theory [non-measure theory] from a textbook. I stumbled to the topic stating that Cauchy Distribution has no moments. It was not proved, and I tried working it via direct calculation of the improper integral of E[X^n] for the case n=1. Anyhow, I wanted to generalize this without success. I stumbled upon this thread here: https://www.physicsforums.com/threads/how-to-prove-the-cauchy-distribution-has-no-moments.992416/ I really enjoyed the proof...
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