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

The name of the pictureThe name of the pictureThe name of the pictureClash Royale CLAN TAG#URR8PPP











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.






statistics expected-value







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












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







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.






statistics expected-value







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




statistics expected-value






share|cite|improve this question















share|cite|improve this question













share|cite|improve this question




share|cite|improve this question








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















active

oldest

votes











Your Answer




StackExchange.ifUsing("editor", function ()
return StackExchange.using("mathjaxEditing", function ()
StackExchange.MarkdownEditor.creationCallbacks.add(function (editor, postfix)
StackExchange.mathjaxEditing.prepareWmdForMathJax(editor, postfix, [["$", "$"], ["\\(","\\)"]]);
);
);
, "mathjax-editing");

StackExchange.ready(function()
var channelOptions =
tags: "".split(" "),
id: "69"
;
initTagRenderer("".split(" "), "".split(" "), channelOptions);

StackExchange.using("externalEditor", function()
// Have to fire editor after snippets, if snippets enabled
if (StackExchange.settings.snippets.snippetsEnabled)
StackExchange.using("snippets", function()
createEditor();
);

else
createEditor();

);

function createEditor()
StackExchange.prepareEditor(
heartbeatType: 'answer',
convertImagesToLinks: true,
noModals: false,
showLowRepImageUploadWarning: true,
reputationToPostImages: 10,
bindNavPrevention: true,
postfix: "",
noCode: true, onDemand: true,
discardSelector: ".discard-answer"
,immediatelyShowMarkdownHelp:true
);



);













 

draft saved


draft discarded


















StackExchange.ready(
function ()
StackExchange.openid.initPostLogin('.new-post-login', 'https%3a%2f%2fmath.stackexchange.com%2fquestions%2f2912253%2fhow-to-prove-that-mathbbe-mathrmmsa-sigma2-fracna-1-sum-i-1a%23new-answer', 'question_page');

);

Post as a guest






















active

oldest

votes













active

oldest

votes









active

oldest

votes






active

oldest

votes















 

draft saved


draft discarded















































 


draft saved


draft discarded














StackExchange.ready(
function ()
StackExchange.openid.initPostLogin('.new-post-login', 'https%3a%2f%2fmath.stackexchange.com%2fquestions%2f2912253%2fhow-to-prove-that-mathbbe-mathrmmsa-sigma2-fracna-1-sum-i-1a%23new-answer', 'question_page');

);

Post as a guest
































































-

這個網誌中的熱門文章

How to combine Bézier curves to a surface?

圖片
Clash Royale CLAN TAG #URR8PPP up vote 2 down vote favorite My aim is to smooth the terrain in a video game. Therefore I contrived an algorithm that makes use of Bézier curves of different orders. But this algorithm is defined in a two dimensional space for now. To shift it into the third dimension I need to somehow combine the Bézier curves. Given two curves in each two dimensions, how can I combine them to build a surface? I thought about something like a curve of a curve. Or maybe I could multiply them somehow. How can I combine them to cause the wanted behavior? Is there a common approach? In the image you can see the input, on the left, and the output, on the right, of the algorithm that works in a two dimensional space. For the real application there is a three dimensional input. The algorithm relays only on the adjacent tiles. Given these it will define the control points of the mentioned Bézier curve. Additionally it marks one side of the curve as inside t
閱讀完整內容

Why am i infinitely getting the same tweet with the Twitter Search API?

圖片
up vote 0 down vote favorite My code workes perfectly for other queries, but for one query I am infinitely getting the same tweet. I can't understand what the problem is. API call: query='Allergic asthma OR Nonallergic asthma OR Occupational asthma OR EIB OR Exercise-induced bronchoconstriction OR Nocturnal asthma OR Cough-variant asthma' new_tweets = api.search(q=searchQuery, count=100, since_id=since_id, lang='en',tweet_mode='extended') if not new_tweets: print("No more tweets found") break for tweet in new_tweets: if True: print(jsonpickle.encode(tweet._json, unpicklable=False)) my_file = open('searchTweets.txt','a') my_file.write(jsonpickle.encode(tweet._json, unpicklable=False)+'n') my_file.close() else: continue Output in file: https://pastebin.com/JmRCsTeE These are the JSONs of the same Tweet. Other queries that work: Breast cancer OR Prostate cancer OR Colon cancer OR Lung cancer Type 2 dia
閱讀完整內容

Carbon dioxide

圖片
"CO2" redirects here. For other uses, see CO2 (disambiguation). Carbon dioxide Names Other names Carbonic acid gas Carbonic anhydride Carbonic oxide Carbon oxide Carbon(IV) oxide Dry ice (solid phase) Identifiers CAS Number 124-38-9   Y 3D model (JSmol) Interactive image Interactive image 3DMet B01131 Beilstein Reference 1900390 ChEBI CHEBI:16526   Y ChEMBL ChEMBL1231871   N ChemSpider 274   Y ECHA InfoCard 100.004.271 EC Number 204-696-9 E number E290 (preservatives) Gmelin Reference 989 KEGG D00004   Y MeSH Carbon+dioxide PubChem CID 280 RTECS number FF6400000 UNII 142M471B3J   Y UN number 1013 (gas), 1845 (solid) InChI InChI=1S/CO2/c2-1-3   Y Key: CURLTUGMZLYLDI-UHFFFAOYSA-N   Y InChI=1/CO2/c2-1-3 Key: CURLTUGMZLYLDI-UHFFFAOYAO SMILES O=C=O C(=O)=O Properties Chemical formula C O 2 Molar mass 44.01 g·mol −1 Appearance Colorless gas Odor Low concentrations: none High concentrations: sharp; acidic [1] Density 1562 kg/m 3 (solid at 1 atm and −78.5 °C) 1101 kg/m 3 (liquid at
閱讀完整內容