How to prove that $mathbbE[mathrmMSA]=sigma^2+fracna-1sum_i=1^a(mu_i−mu)^2$.

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I need to prove that the expected value of MSA is equal to the expression to the right. Where MSA is the mean square of a factor a. The equations are easier to understand in the link of the images.



$$ mathrmMSA = fracmathrmSSAmathrmgla, qquad mathrmSSA = sum_i (barY_i - bary)^2 $$



$$ mu = frac1asum_i=1^a mu_i, $$



$$ mathbbE[mathrmMSA]=sigma^2+fracna-1sum_i=1^a(mu_i−mu)^2. $$
asume the experiment is balanced.










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  • 2




    Please write the complete question (defining your expressions) and try to include your thoughts on the problem.
    – StubbornAtom
    Sep 10 at 19:25










  • I edited your question so that formulas are more readable. Hope this is to your liking.
    – Sangchul Lee
    Sep 10 at 19:44










  • Sangchul Lee thanks.
    – Esteban Martinez
    Sep 10 at 19:59










  • Please show your work. Presumably you are working with a linear model, in which case what is your model exactly?
    – StubbornAtom
    Sep 10 at 20:06










  • what is the MSA expression, what is SSA and what is gla ?
    – Ahmad Bazzi
    Sep 10 at 21:27














up vote
0
down vote

favorite












I need to prove that the expected value of MSA is equal to the expression to the right. Where MSA is the mean square of a factor a. The equations are easier to understand in the link of the images.



$$ mathrmMSA = fracmathrmSSAmathrmgla, qquad mathrmSSA = sum_i (barY_i - bary)^2 $$



$$ mu = frac1asum_i=1^a mu_i, $$



$$ mathbbE[mathrmMSA]=sigma^2+fracna-1sum_i=1^a(mu_i−mu)^2. $$
asume the experiment is balanced.










share|cite|improve this question



















  • 2




    Please write the complete question (defining your expressions) and try to include your thoughts on the problem.
    – StubbornAtom
    Sep 10 at 19:25










  • I edited your question so that formulas are more readable. Hope this is to your liking.
    – Sangchul Lee
    Sep 10 at 19:44










  • Sangchul Lee thanks.
    – Esteban Martinez
    Sep 10 at 19:59










  • Please show your work. Presumably you are working with a linear model, in which case what is your model exactly?
    – StubbornAtom
    Sep 10 at 20:06










  • what is the MSA expression, what is SSA and what is gla ?
    – Ahmad Bazzi
    Sep 10 at 21:27












up vote
0
down vote

favorite









up vote
0
down vote

favorite











I need to prove that the expected value of MSA is equal to the expression to the right. Where MSA is the mean square of a factor a. The equations are easier to understand in the link of the images.



$$ mathrmMSA = fracmathrmSSAmathrmgla, qquad mathrmSSA = sum_i (barY_i - bary)^2 $$



$$ mu = frac1asum_i=1^a mu_i, $$



$$ mathbbE[mathrmMSA]=sigma^2+fracna-1sum_i=1^a(mu_i−mu)^2. $$
asume the experiment is balanced.










share|cite|improve this question















I need to prove that the expected value of MSA is equal to the expression to the right. Where MSA is the mean square of a factor a. The equations are easier to understand in the link of the images.



$$ mathrmMSA = fracmathrmSSAmathrmgla, qquad mathrmSSA = sum_i (barY_i - bary)^2 $$



$$ mu = frac1asum_i=1^a mu_i, $$



$$ mathbbE[mathrmMSA]=sigma^2+fracna-1sum_i=1^a(mu_i−mu)^2. $$
asume the experiment is balanced.







statistics expected-value






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edited Sep 10 at 20:30

























asked Sep 10 at 19:20









Esteban Martinez

12




12







  • 2




    Please write the complete question (defining your expressions) and try to include your thoughts on the problem.
    – StubbornAtom
    Sep 10 at 19:25










  • I edited your question so that formulas are more readable. Hope this is to your liking.
    – Sangchul Lee
    Sep 10 at 19:44










  • Sangchul Lee thanks.
    – Esteban Martinez
    Sep 10 at 19:59










  • Please show your work. Presumably you are working with a linear model, in which case what is your model exactly?
    – StubbornAtom
    Sep 10 at 20:06










  • what is the MSA expression, what is SSA and what is gla ?
    – Ahmad Bazzi
    Sep 10 at 21:27












  • 2




    Please write the complete question (defining your expressions) and try to include your thoughts on the problem.
    – StubbornAtom
    Sep 10 at 19:25










  • I edited your question so that formulas are more readable. Hope this is to your liking.
    – Sangchul Lee
    Sep 10 at 19:44










  • Sangchul Lee thanks.
    – Esteban Martinez
    Sep 10 at 19:59










  • Please show your work. Presumably you are working with a linear model, in which case what is your model exactly?
    – StubbornAtom
    Sep 10 at 20:06










  • what is the MSA expression, what is SSA and what is gla ?
    – Ahmad Bazzi
    Sep 10 at 21:27







2




2




Please write the complete question (defining your expressions) and try to include your thoughts on the problem.
– StubbornAtom
Sep 10 at 19:25




Please write the complete question (defining your expressions) and try to include your thoughts on the problem.
– StubbornAtom
Sep 10 at 19:25












I edited your question so that formulas are more readable. Hope this is to your liking.
– Sangchul Lee
Sep 10 at 19:44




I edited your question so that formulas are more readable. Hope this is to your liking.
– Sangchul Lee
Sep 10 at 19:44












Sangchul Lee thanks.
– Esteban Martinez
Sep 10 at 19:59




Sangchul Lee thanks.
– Esteban Martinez
Sep 10 at 19:59












Please show your work. Presumably you are working with a linear model, in which case what is your model exactly?
– StubbornAtom
Sep 10 at 20:06




Please show your work. Presumably you are working with a linear model, in which case what is your model exactly?
– StubbornAtom
Sep 10 at 20:06












what is the MSA expression, what is SSA and what is gla ?
– Ahmad Bazzi
Sep 10 at 21:27




what is the MSA expression, what is SSA and what is gla ?
– Ahmad Bazzi
Sep 10 at 21:27















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