 student, in Manova, we need the sum of square of deviation from mean. So we need to partitioning the observation in terms of deviation from mean. So here is the example of Manova partitioning of observation. So in this example, we have considered the following independent sample. So we have three independent sample, sample 1, sample 2 and the sample 3. For above example, this is the above example. Now the x bar 1, x bar 1 kaansa aega sample 1 se? So x bar 2 sample 2 ka? And the x bar 3 sample 3 se? Overall mean, this is called the x bar and find x3 1. So particular hum ne lena hai, x3 1 ke liye hum isko find karin. x3 1 means third sample ki first observation. Hum ne iske according liya, x3 1 kya hai aap ke paas x3 1? First third sample ki humare paas first observation, this is the 3. So here is the 3 which is equals to x3 1. Hum ne kya kya karin hai basically? Sum of square of deviation from mean ne kaal ne. So yaha pe hum deviation from mean ke according karin hai, x3 1. x3 1 basically kya se banega? Hum ne yaha pe kya kya? Which is equals to hum ne ni? Jo journal humare paas case hai. Journal humare paas case kya hai. xij which is equals to x bar plus x bar i minus x bar plus x bar j ij minus x bar i. Aap agar aap idar dekho isko open karenge to humare paas kya hojega? This value minus value cancel out hojegi humare paas plus value ke saath. Minus x bar cancel out hojegiya. Plus x bar se. So kya rege aap ke paas value? xij rege na? Similarly humare paas kya hai x3 1. Third sample ki first observation kya which is equals to 3. Abhi aap ne kya kya? x bar as it is jaisi hum ne aap pe xij ki x bar liya tha? x bar 3 minus x bar total mean se hum ne minus kya liya. Sum of deviation from mean kya leh re hum aap pe sum of deviation from mean? Deviation from mean kya? x3 1 minus x bar 3. Aap yaha pe aap me aasko cancel out karun to humare paas easily kya se cancel out hojega? Ye factor because this is the minus plus x bar x bar se cancel hojegiya to kya hojega? Aap ke paas x3 1 hi rege aap. So iss ke according ab hum isko zara solve kar ke dikte. So xij aap me aap pe leh jo hi aap pe aap me supose kya hum ke this is the xij minus x bar yaap ke paas equality ke dar aagya? This is the minus x bar and which is equals to this So you can say that this is the corrected total and this is the corrected between values there. This is the corrected between, this is the corrected error or within term. Aap fardar hum kya karte iss ka sum leheti hain, square leheti hain aur hum usse kyaenge corrected total sum of square. Corrected between sum of squares and the corrected within sum of square. Aap fardar usse kya, abhi hum maini me jaari hu ki hum fardar iss me kya dekhre hain hum ne aap iss ka manoa banana hain. Manoa kaise leki aap hain. So you know that the solution you know that kirtne total variables hain. So we have three variables, three samples First, ter di naal and alternative hypothesis. Hypothesis mu1 equals to mu2 equals to mu3 all three means are equal. Alternative hypothesis all three means are not equal. Level of significance alpha 0.10, 10% pe hum ne significance level liya and the test statistics you know that the manoa ka test statistics kya mean square between over mean square error and these are the degree of freedom. This is the degree of freedom for the equal in size. So this example is the unequal in size. Okay. So repeating the observation for each observation we obtain. Now look at this. Ye aap ke paas kya tha? Yaha pe amare paas x ij. Total x ij. So x ij jho hume given hai values hum ne wo likhne hai. This is the x bar. So x bar kya tha maare paas 4. So 4, 4, 4 plus. Now next humare paas kya tam thi? Next humare paas tam kya rey hum final hum. X ij ke according dekhne. X bar hoge. X bar 3 minus X bar. Journal kya hoge? X bar i minus X bar. So X bar i means ki agar mai first leh rin ho. So first leh paas kya hai. X bar i mean 8. Aur yaha pe aap ke paas kya? 4. So 8 minus 4, 4, 4, 4. Okay. Got it? Now next humare paas mean kya ho jah rey? X bar 2, 1 aur X bar kya hai. Mere paas 4. So 1 minus 4, minus 3, minus. Further? So this is the degree of freedom X bar i. Aap ke paas X bar 3, 2, 2 minus 4. 2 minus 4 mere paas kya aag kya? Minus 2, minus 2, minus 2. Tkya humne kya kar diya? Sum of deviation ke saath isko solf kar rey. Now the last is X ij minus X bar i. X ij means yeh value. Aap ke paas tehariye. X ij. First value kya 9. Minus its mean. X bar i. Uska mean kya ho kya aap ke paas 8? So 9 minus 8, 6 minus 8, 9 minus 8. 9 minus 8, 1. 6 minus 8, minus 2. Again 9 minus 8, 1. Tkya humne mean adjust kya hain aap ke. So further humare paas kya hain? Sum of scare of the observation. Aap haas kaye humne sum of scare of the observation karin? Observation kya ati aam hain, aap haas? X ij uska humne scare kya 9 plus, 9 square plus, 6 square plus, 9 square plus 0 square plus, two square like this. So total SS observations aamari Paas uska sum a monia hai. 2, 1, 6. Similarly sum of scare of mean, mean aapko baat hush total aamari paas psa. 4, 4, 4 saa So, sum of scare of the treatment, so this is the sum of scare of the treatment and this is the within or residual or you can say that the error, so here is the sum of scare of the treatment. And the last column is the sum of scare of the residual which is equals to the 10. The sum of scare satisfies the same decomposition and the observation, Decomposition only, basically, we are decomposing. Same decomposition as observation, so SS observation, SS mean plus SS treatment plus SS residue. So, the results are summarized in the ANOVA table, so this is the ANOVA. We have the source of variation, degree of freedom, sum of scare and the F. So, between treatment, total number of groups, we have three number of groups or we have three different sample number, so N minus one or group minus one which is equals to 2. Total observations, total observation, 8 minus one, 7. So, 7 minus 2, 5. Sum of scare of the treatment, previous time we have seen the sum of scare of the treatment which is equals to 78. and some of the care of the residual or we can say that the sum of care within treatment. So, this is the 10. Now, you know that this is the sum of care of treatment and between we also call it sum of care of residual and we also call it within. In ANOVA, we have written between and within. Basically, we have written between and within in ANOVA. So, I am telling you that we are calling residual as within and we have called treatment as between. So, this is the within treatment and the between treatment, the value of sum of care of the treatment. Next, we have mean square error. So, you know that the mean square error which is equal to the 78 divided by 2, 78 divided by 2 and the mean square error, 10 divided by its degree of freedom, which is equals to this. Or F, how do we compute it? First, mean square between divided by mean square treatment and the final F value calculated F value which is equals to 19.5. So, we have the calculated F value is 19.5. After that, the fifth step is the critical region and the critical region is the calculated F is greater than the table value. So, we reject H naught. So, F which is equals to 19.5 and F which is equals to alpha by 2, alpha Gata 10 percent, alpha by 2, 0.05 and the degree of freedom 2 and 5 further have net table may check here. Here is the 2 and here is the 5. The value of table value is 5.79. So, this is the 5.79 and the calculated F is 19.5. So, the final conclusion is since our calculated value F do not fall in the rejection region will reject H naught because calculated F is greater than the table value. It may conclude that all means are not equal. This particular example we have checked here, we have the hypothesis all means are equal because we have the three sample values all means are equal and the alternative hypothesis all means are not equal. So, in particular example, so we reject the null hypothesis and the reject the null hypothesis. So, we can say that the all means are not equal because this is the unequal case. According to the unequal case, we have performed it here.