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# Anova

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### Anova

1. 1. ANOVA is a method of analyzing data fromdesigned experiments whose objective is tocompare two or more group means.Factorial ANOVA has two independentvariables which are crossed with each other.That means each value of one variable ispaired with every value of other variable.
2. 2. ONE WAY ANOVATYPES OF ANOVA TWO WAY ANOVA
3. 3. ANOVA One-Way ANOVA Two way ANOVA•One independent variable •Two or more independent variables•One dependent variable •Two dependent variablesFor Example,Only temperature as For Example,independent variable Both Temperature and Concentration as independent variable
4. 4. Concentration Pure Methanol 50% Methanol Room 108 120Temperature 98 130 600 194 144Temperature 202 140
5. 5. concentration Main Effect A 50% Pure Methanol Methanol Sum Square Sum of Squares SS/4 (SS/4)-CT Room 108 120 456 207936Temperature 98 130 670336 167584 6272 60 C 194 144 680 462400Temperature 202 140 Sum 602 534 1136 It is square of sum of grand total of all the observations divided Square 362404 285156 1290496 by number of observations SS 647560 161312 CT It is sum of squares of grand total of the SS/4 161890 observations (in column) divided by product of number of rows and replicationMain Effect which is subtracted by CT B 578
6. 6. concentration Interaction term AB Pure 50% Square Square of Sum of Methanol Methanol Sum Sum of sum sum Squares SS/2 MS-A-B-CTRoom 108 120 206 250 42436 62500temp. 98 130 342408 171204 3042 194 144 396 284 156816 8065660 C 202 140
7. 7. TOTAL Sum of Pure Methanol 50% Methanol Square Square squares SS-CTRoom 108 120 11664 14400temp. 98 130 9604 16900 171344 10032 194 144 37636 2073660 C 202 140 40804 19600
8. 8. Residual = Total (10032) – Main effect A(578) – Main effect B (6272) –Interactionterm AB (3042) = 140
9. 9.  Main effect A= (∑ Cj2)/Rr - CT Main effect B= (∑ Ri2 ) /Rr – CT Cj= Sum of observations in column j Ri= Sum of observations in row i R= number of rows r= number of replicates per cell CT= Correction term Interaction term AB= ∑ Cij2/2 – A – B - CT Total= ∑ X2 - CT X = All Observations in each column and row
10. 10. Source of Variation DF SS MS F PMain Effect A 1 6272 6272 179.2 <0.001Main Effect B 1 578 578 16.514 0.015Interaction Term AB 1 3042 3042 86.914 <0.001Residual 4 140 35Total 7 10032 1433.143
11. 11. ANOVA Df SS MS F Significance F Regression 3 9892 3297.333 94.20952 0.000363456 Residual 4 140 35 Total 7 10032
12. 12. Sigma stat plot Multiple linear regressionSource of Variation DF SS DF SSMain Effect A 1 6272 Regression 3 9892Main Effect B 1 578 Residual 4 140Interaction Term AB 1 3042Residual 4 140While in both the case RESIDUAL will be same
13. 13. Sigma stat plot is one of the software to carry out ANOVA.Over here we get individual sum of squares which is an advantage over multiple linear regression analysis.While any of the independent variable has a significanteffect on the dependent variable can be easily known from multiple linear regression analysis.