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Difference between revisions of "Manuals/calci/TTESTEQUALVARIANCES"

(Created page with "<div id="6SpaceContent" class="zcontent" align="left"> '''TTESTTWOSAMPLESEQUALVARIANCES('''Array1, Array2, HypothesizeDiff, Alpha, NewTableFlag) where, '''Array1 '''...")
 
 
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<div style="font-size:30px">'''TTESTTWOSAMPLESEQUALVARIANCES(ar1,ar2,md,alpha,lv)'''</div><br/>
 +
*<math>ar1 </math> and <math> ar2 </math>  are set of values.
 +
*<math>md </math> is the  Hypothesized Mean Difference.
 +
*<math> alpha </math> is the significance level.
 +
*<math> lv </math> is the logical value.
  
−
'''TTESTTWOSAMPLESEQUALVARIANCES('''Array1, Array2, HypothesizeDiff, Alpha, NewTableFlag)
+
==Description==
 +
*This function calculating the two Sample for equal variances determines whether two sample means are equal.
 +
*We can use this test when both:
 +
*1.The two sample sizes  are equal;
 +
*2.It can be assumed that the two distributions have the same variance.
 +
*In <math>TTESTTWOSAMPLESEQUALVARIANCES(ar1,ar2,md,alpha,lv)</math>, <math>ar1 </math> and <math> ar2 </math> are two arrays of sample values. <math> md </math> is the Hypothesized Mean Difference .
 +
*Suppose md=0 which  indicates that sample means are hypothesized to be equal.
 +
*<math> alpha </math> is the significance level which ranges from 0 to 1.
 +
*<math> lv </math> is the logical value like TRUE or FALSE.
 +
*TRUE is indicating the result will display in new worksheet.Suppose we are omitted the lv value it will consider the value as FALSE.
 +
*The t statistic of this function calculated by:
 +
<math>t = \frac{\bar{x_1}-\bar{x_2}}{s_{x1}.s_{x2}.\sqrt{\frac{2}{n}}}</math>
 +
where <math>s_{x1}.s_{x2} = \sqrt{\frac{1}{2}(s_{x1}^2+s_{x2}^2)}</math>
 +
*Here <math>s_{x1}</math> and <math>s_{x2}</math> are unbiased estimators of the variances of two samples.<math>s_{x1}.s_{x2}</math> is the grand standard deviation data 1 and data2 and n is the data points of two data set. 
 +
*This function will give the result as error when
 +
  1.any one of the argument is non-numeric.
 +
  2.alpha>1
 +
  3.<math>ar1 </math> and <math> ar2 </math> are having different number of data points.
  
−
where,
+
==Examples==
 +
{| class="wikitable"
 +
|+Spreadsheet
 +
|-
 +
! !! A !! B !! C !! D!! E !! F
 +
|-
 +
! 1
 +
| 10 || 15 || 18 || 27 || 12 || 34
 +
|-
 +
! 2
 +
| 17 || 20 || 25 || 39 || 9 || 14
 +
|}
  
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'''Array1 '''- Input range should be one block.
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#=TTESTTWOSAMPLESEQUALVARIANCES(A1:F1,A2:F2,2,0.5)
  
−
'''Array2 '''- Input range should be one block.
+
{| class="wikitable"
−
 
+
|+Result
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'''HypothesizeDiff '''- represents the Hypothesized Mean Difference.A value 0 indicates that sample means are hypothesized to be equal.
+
|-
−
 
+
! !! Variable 1 !! Variable 2
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'''Alpha '''- represents the significance level and value in range 0 to 1.
+
|-
−
 
+
! Mean
−
''' ''''''NewTableFlag''' - is the TRUE or FALSE.If set as TRUE,the result in new sheet. If NewTableFlag is omitted, it assumed to be FALSE.</div>
+
| 19.333333333333332 || 20.666666666666668
−
----
+
|-
−
<div id="1SpaceContent" class="zcontent" align="left">T-Test: Two Sample for equal variances determines whether two sample means are equal.</div>
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! Variance
−
----
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| 87.06666666666666 || 109.86666666666667
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<div id="7SpaceContent" class="zcontent" align="left">
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|-
−
 
+
! Observations
−
Lets see an example in (Column3Row1)
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| 6 || 6
−
 
+
|-
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<nowiki>=TTESTTWOSAMPLESEQUALVARIANCES (R1C1:R6C1, R1C2:R6C2, 0, 0.05, TRUE)</nowiki>
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! Pooled Variance
−
 
+
| 98.46666666666667
−
TTESTTWOSAMPLESEQUALVARIANCES returns the result in new sheet(9Space).
+
|-
−
 
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! Hypothesized Mean Difference
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<nowiki>=TTESTTWOSAMPLESEQUALVARIANCES(R1C1:R4C1,R1C2:R6C2, 0, 0.055, TRUE)</nowiki>
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| 2
−
 
+
|-
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TTESTTWOSAMPLESEQUALVARIANCES returns the #ERROR(LengthofArray1 != LengthofArray2).
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! Degree Of Freedom
−
 
+
| 10
−
</div>
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|-
−
----
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! T- Statistics
−
<div id="12SpaceContent" class="zcontent" align="left"><div class="ZEditBox" align="left">
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| -0.5818281835787091
−
 
+
|-
−
T-TEST : TWO SAMPLE ASSUMING EQUAL VARIANCES
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! P(T<=t) One-tail
−
 
+
| 0.28678199670723614
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</div></div>
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|-
−
----
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! T Critical One-Tail
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<div id="10SpaceContent" class="zcontent" align="left"><div class="ZEditBox" align="justify">Syntax </div><div class="ZEditBox"><center></center></div></div>
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| 0
−
----
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|-
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<div id="4SpaceContent" class="zcontent" align="left"><div class="ZEditBox" align="justify">Remarks </div></div>
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! P(T<=t) Two-tail
−
----
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| 0.5735639934144723
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<div id="3SpaceContent" class="zcontent" align="left"><div class="ZEditBox" align="justify">Examples </div></div>
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|-
−
----
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! T Critical Two-Tail
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<div id="11SpaceContent" class="zcontent" align="left"><div class="ZEditBox" align="justify">Description </div></div>
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| 0.6998120613365443
−
----
+
|}
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<div id="8SpaceContent" class="zcontent" align="left">
 
−
 
 
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If the Alpha &lt; 0 or Alpha &gt;1, TTESTTWOSAMPLESEQUALVARIANCES returns the #ERROR.
 
−
 
 
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TTESTTWOSAMPLESEQUALVARIANCES returns the #ERROR, if Length of Array1 != Length of Array2.
 
  
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</div>
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==Related Videos==
−
----
 
−
<div id="2SpaceContent" class="zcontent" align="left">
 
  
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{| id="TABLE3" class="SpreadSheet blue"
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{{#ev:youtube|OHHhzLHakKA|280|center|TTESTEQUALVARIANCES}}
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|- class="even"
 
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| class=" " |
 
−
| Column1
 
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| Column2
 
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| class="  " | Column3
 
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| Column4
 
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|- class="odd"
 
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| class=" " | Row1
 
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| 10
 
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| 3
 
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| class="sshl_f" | 9Space
 
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| class=" " |
 
−
|- class="even"
 
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| class="  " | Row2
 
−
| 7
 
−
| 8
 
−
| class="    " |
 
−
| class=" " |
 
−
|- class="odd"
 
−
| Row3
 
−
| 12
 
−
| 8
 
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| class=" " |
 
−
| class=" " |
 
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|- class="even"
 
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| Row4
 
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| 17
 
−
| 18
 
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| class="sshl_f" | #ERROR
 
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| class=" " |
 
−
|- class="odd"
 
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| class=" " | Row5
 
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| class=" " | 46
 
−
| 34
 
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| class="          " |
 
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| class=" " |
 
−
|- class="even"
 
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| Row6
 
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| class="SelectTD1" | 6
 
−
| 7
 
−
| class=" " |
 
−
| class=" " |
 
−
|}
 
  
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<div align="left">[[Image:calci1.gif]]</div></div>
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==See Also==
−
----
+
*[[Manuals/calci/TTEST  | TTEST ]]
−
<div id="9SpaceContent" class="zcontent" align="left">
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*[[Manuals/calci/TDIST  | TDIST ]]
−
 
+
*[[Manuals/calci/TINV  | TINV ]]
−
{| class="SpreadSheet blue"
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*[[Manuals/calci/TTESTUNEQUALVARIANCES  | TTESTUNEQUALVARIANCES ]]
−
|+ t-Test: Two-Sample Assuming Equal Variances<br />
 
−
|- class="even"
 
−
!
 
−
! Variable1
 
−
! Variable2
 
−
|- class="odd"
 
−
| Mean
 
−
| 16.333333333333332
 
−
| 13
 
−
|- class="even"
 
−
| Variance
 
−
| 226.66666666666668
 
−
| 130.4
 
−
|- class="odd"
 
−
| Observations
 
−
| 6
 
−
| 6
 
−
|- class="even"
 
−
| Pooled Variance
 
−
| 178.53333333333336
 
−
|- class="odd"
 
−
| Hypothesized Mean Difference
 
−
| 0
 
−
|- class="even"
 
−
| Degree Of Freedom
 
−
| 10
 
−
|- class="odd"
 
−
| T Statistics
 
−
| 0.4320954725359997
 
−
|- class="even"
 
−
| P(T&lt;=t) One-tail
 
−
| 0.3374203531947199
 
−
|- class="odd"
 
−
| T Critical One-tail
 
−
| 1.8124611201453893
 
−
|- class="even"
 
−
| P(T&lt;=t) Two-tail
 
−
| 0.6748407063894398
 
−
|- class="odd"
 
−
| T Critical Two-tail
 
−
| 2.2281388448257084
 
−
|}
 
  
−
</div>
+
==References==
−
----
+
*[http://en.wikipedia.org/wiki/Student%27s_t-test Student's t-distribution]

Latest revision as of 13:03, 2 July 2015

TTESTTWOSAMPLESEQUALVARIANCES(ar1,ar2,md,alpha,lv)


  • and are set of values.
  • is the Hypothesized Mean Difference.
  • is the significance level.
  • is the logical value.

Description

  • This function calculating the two Sample for equal variances determines whether two sample means are equal.
  • We can use this test when both:
  • 1.The two sample sizes are equal;
  • 2.It can be assumed that the two distributions have the same variance.
  • In  ,   and   are two arrays of sample values.   is the Hypothesized Mean Difference .
  • Suppose md=0 which indicates that sample means are hypothesized to be equal.
  •   is the significance level which ranges from 0 to 1.
  •   is the logical value like TRUE or FALSE.
  • TRUE is indicating the result will display in new worksheet.Suppose we are omitted the lv value it will consider the value as FALSE.
  • The t statistic of this function calculated by:
 

where  

  • Here   and   are unbiased estimators of the variances of two samples.  is the grand standard deviation data 1 and data2 and n is the data points of two data set.
  • This function will give the result as error when
  1.any one of the argument is non-numeric.
  2.alpha>1
  3.  and   are having different number of data points.

Examples

Spreadsheet
A B C D E F
1 10 15 18 27 12 34
2 17 20 25 39 9 14
  1. =TTESTTWOSAMPLESEQUALVARIANCES(A1:F1,A2:F2,2,0.5)
Result
Variable 1 Variable 2
Mean 19.333333333333332 20.666666666666668
Variance 87.06666666666666 109.86666666666667
Observations 6 6
Pooled Variance 98.46666666666667
Hypothesized Mean Difference 2
Degree Of Freedom 10
T- Statistics -0.5818281835787091
P(T<=t) One-tail 0.28678199670723614
T Critical One-Tail 0
P(T<=t) Two-tail 0.5735639934144723
T Critical Two-Tail 0.6998120613365443

Related Videos

TTESTEQUALVARIANCES

See Also

References

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