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<div id="6SpaceContent" class="zcontent" align="left">Analysis Of Variances(ANOVA) is a method of checking if there is a relationship between two ror more data sets.</div>
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=ANOVATWOFACTORWITHREPLICATION(Array, Alpha, NumberOfSamples, NewTableFlag)=
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<div id="1SpaceContent" class="zcontent" align="left">ANOVA :Two-Factor with replication performs an analysis of variances between two more data sets. And used when we have more than one sample from each data set.</div>
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<div id="7SpaceContent" class="zcontent" align="left">
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ANOVATWOFACTORWITHREPLICATION  returns #ERROR, if Alpha &lt;0 or Alpha &gt;1.
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*where, <math>Array</math> is an array of numbers or reference to cells containing array
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*<math>Alpha</math> represents a constant value between '0' and '1'
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*<math>NumberOfSamples</math> represents the number of samples in an array 
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*<math>NewTableFlag</math> that decides to display the output in the same worksheet or a new space cube.
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It returns the #ERROR, when length of Array != length of NumberofSample.
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ANOVATWOFACTORWITHREPLICATION() performs an analysis of variances between two or more data sets.
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</div>
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== Description ==
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<div id="12SpaceContent" class="zcontent" align="left"><div class="ZEditBox" align="left">
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ANOVA : TWO - FACTOR WITH REPLICATION
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ANOVATWOFACTORWITHREPLICATION(Array, Alpha, NumberOfSamples, NewTableFlag)
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</div></div>
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*Analysis Of Variances(ANOVA) is a method of checking relationship between two or more data sets.
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*<math>Alpha</math> should be in between '0' and '1'. Else Calci displays #N/A error message.
<div id="10SpaceContent" class="zcontent" align="left"><div class="ZEditBox" align="justify">what is ANOVA?</div><div class="ZEditBox"><center></center></div></div>
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*Data in an array can be divided in one or more groups. That is represented by <math>NumberOfSamples</math>.
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*<math>NewTableFlag</math> can be a logical value TRUE or FALSE. If omitted, Calci assumes it to be FALSE.
<div id="4SpaceContent" class="zcontent" align="left"><div class="ZEditBox" align="justify">Remarks </div></div>
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*If <math>NewTableFlag</math> is TRUE, the result is displayed on new zspace sheet.
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<div id="3SpaceContent" class="zcontent" align="left"><div class="ZEditBox" align="justify">Examples </div></div>
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<div id="11SpaceContent" class="zcontent" align="left"><div class="ZEditBox" align="justify">Description </div></div>
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<div id="9SpaceContent" class="zcontent" align="left"><div class="ZEditBox" align="justify">Syntax</div><div class="ZEditBox"><center></center></div></div>
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<div id="5SpaceContent" class="zcontent" align="left">
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<nowiki>=</nowiki>'''ANOVATWOFACTORWITHREPLICATION'''(Array, NumberofSample, Alpha, NewTableFlag)
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== Examples ==
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where,
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Consider the following table with Columns A and B as array inputs for ANOVATWOFACTORWITHREPLICATION() function.
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'''Array '''- Input range should be one or two blocks.
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'''Alpha '''- is the constant in between 0 and 1.
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'''NumberofSample''' - Input range should be one blocks.
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'''NewTableFlag''' - is the TRUE or FALSE.If set as TRUE, the result in new sheet.If NewTableFlag is omitted, it assumed to be false.
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</div>
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<div id="14SpaceContent" class="zcontent" align="left">
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Lets see an example in (Column3 , Row1)
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<nowiki>=ANOVATWOFACTORWITHREPLICATION(R1C1:R12C2, 2, 0.01, TRUE) </nowiki>
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ANOVATWOFACTORWITHREPLICATION  returns the result in new sheet(13Space).
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<nowiki>=ANOVATWOFACTORWITHREPLICATION(R1C1:R12C2 , 2,-0.05, FALSE)</nowiki>
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It returns the #ERROR(Alpha &gt;1 or Alpha&lt;0)
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</div>
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<div id="2SpaceContent" class="zcontent" align="left">
 
<div id="2SpaceContent" class="zcontent" align="left">
    
{| id="TABLE3" class="SpreadSheet blue"
 
{| id="TABLE3" class="SpreadSheet blue"
 
|- class="even"
 
|- class="even"
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| class="sshl_f" | 1
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| class=" " |3
 
| class=" " |
 
| class=" " |
| class="  " | Column1
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| class="  " | Column2
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| class="  " | Column3
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| Column4
   
|- class="odd"
 
|- class="odd"
| class=" " | Row1
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| class="sshl_f" | 2
| class=" " | 1
+
| class=" " |5
| class=" " | 3
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| class=" " |
| class="sshl_f" | 13Space
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| class="sshl_f" | 5
   
|- class="even"
 
|- class="even"
| class="sshl_f" | Row2
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| class="sshl_f" | 6
| class=" " | 2
+
| class=" " |41
| class=" " | 5
+
| class=" " |
| class="sshl_f  " |
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| class="sshl_f" | #ERROR
   
|- class="odd"
 
|- class="odd"
| class="sshl_f" | Row3
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| class="sshl_f" | 8
| class=" " | 6
+
| class=" " |45
| class=" " | 41
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| class=" " |
| class="sshl_f" |
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| class="sshl_f SelectTD1 ChangeBGColor SelectTD1" |
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<div id="2Space_Handle" class="zhandles" title="Click and Drag to resize CALCI Column/Row/Cell. It is EZ!"></div><div id="2Space_Copy" class="zhandles" title="Click and Drag over to AutoFill other cells."></div><div id="2Space_Drag" class="zhandles" title="Click and Drag to Move/Copy Area.">[[Image:copy-cube.gif]]  </div>
   
|- class="even"
 
|- class="even"
| class="sshl_f" | Row4
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| class="sshl_f" | 9
| class=" " | 8
+
| class=" " |56
| class=" " | 45
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| class=" " |
| class="sshl_f" |
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| class="sshl_f" |
   
|- class="odd"
 
|- class="odd"
| class="sshl_f" | Row5
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| class="sshl_f" | 10
| class=" " | 9
+
| class=" " |8
| class=" " | 56
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| class=" " |
| class="sshl_f" |
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| class="sshl_f" |
   
|- class="even"
 
|- class="even"
| class="sshl_f" | Row6
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| class="sshl_f" | 7
| class=" " | 10
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| class=" " |8
| class=" " | 8
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| class=" " |
| class="sshl_f" |
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| class="sshl_f" |
   
|- class="odd"
 
|- class="odd"
| class="sshl_f" | Row7
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| class="sshl_f" | 12
| class=" " | 7
+
| class=" " |5
| class=" " | 8
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| class=" " |
| 9
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| class="sshl_f" | 128
   
|- class="even"
 
|- class="even"
| class="sshl_f" | Row8
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| class="sshl_f" | 17
| class=" " | 12
+
| class=" " |18
| class=" " | 5
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| class=" " |
| 14
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| class="sshl_f    " | 15
   
|- class="odd"
 
|- class="odd"
| class="sshl_f" | Row9
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| class="sshl_f" | 72
| class=" " | 17
+
| class=" " |31
| class=" " | 18
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| class=" " |
| class="sshl_f" | 10000
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| class="  " | 20
   
|- class="even"
 
|- class="even"
| class="sshl_f" | Row10
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| class="sshl_f" | 6
| class=" " | 72
+
| class=" " |3
| class=" " | 31
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| class=" " |
| 23
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| 40
   
|- class="odd"
 
|- class="odd"
| class="sshl_f" | Row11
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| class="sshl_f" | 2
| class=" " | 6
+
| class=" " |7
| class=" " | 3
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| class=" " |
| 1.619775
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| 0.525322
   
|- class="even"
 
|- class="even"
| class="sshl_f" | Row12
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| class="sshl_f" |  
| class=" " | 2
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| class=" " |
| class=" " | 7
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| class=" " |
| class="sshl_f" |
  −
| class="sshl_f" |
   
|}
 
|}
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<div align="left">[[Image:calci1.gif]]</div></div>
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=ANOVATWOFACTORWITHREPLICATION(A1:B12, 0.01, 2, TRUE) returns the result in new Zspace cube.
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<div id="8SpaceContent" class="zcontent" align="left">
 
<div id="8SpaceContent" class="zcontent" align="left">
   Line 158: Line 109:  
| 152
 
| 152
 
| 12.666666666666666
 
| 12.666666666666666
| 369.69696969696974
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| 369.69696969696975
 
|- class="even"
 
|- class="even"
 
| Array2
 
| Array2
Line 182: Line 133:  
| 5
 
| 5
 
| 654.0666666666668
 
| 654.0666666666668
| 2.8081574239713784
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| 2.8081574239713785
 
| 0.06629115945265437
 
| 0.06629115945265437
| 5.061984369714618
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| 5.064312767657053
 
|- class="even"
 
|- class="even"
 
| Columns:
 
| Columns:
Line 192: Line 143:  
| 1.0883720930232565
 
| 1.0883720930232565
 
| 0.36437615127626016
 
| 0.36437615127626016
| 9.332898584189282
+
| 9.330229140735954
 
|- class="odd"
 
|- class="odd"
 
| Interaction:
 
| Interaction:
Line 200: Line 151:  
| 1.6872987477638656
 
| 1.6872987477638656
 
| 0.2120282015971952
 
| 0.2120282015971952
| 5.061984369714618
+
| 5.0650509516310676
 
|- class="even"
 
|- class="even"
 
| Within:
 
| Within:
Line 208: Line 159:  
|- class="odd"
 
|- class="odd"
 
| Total:
 
| Total:
| 8283.833333333335
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| 8283.833333333336
 
| 23
 
| 23
 
|}
 
|}
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</div>
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== See Also ==
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*[[Manuals/calci/ANOVATWOFACTORWITHOUTREPLICATION | ANOVATWOFACTORWITHOUTREPLICATION]]
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*[[Manuals/calci/ANOVASINGLEFACTOR | ANOVASINGLEFACTOR]]
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== References ==
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*[http://en.wikipedia.org/wiki/Analysis_of_variance ANOVA]
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*[http://en.wikipedia.org/wiki/Analysis_of_variance#ANOVA_for_multiple_factors Anova Multiple Factors]
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