Difference between revisions of "Manuals/calci/TTESTUNEQUALVARIANCES"

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(Created page with "<div id="6SpaceContent" class="zcontent" align="left"> '''TTESTTWOSAMPLESUNEQUALVARIANCES('''Array1, Array2, HypothesizeDiff, Alpha, NewTableFlag) where, '''Array1 '...")
 
 
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<div style="font-size:30px">'''TTESTTWOSAMPLESUNEQUALVARIANCES(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.
  
−
'''TTESTTWOSAMPLESUNEQUALVARIANCES('''Array1, Array2, HypothesizeDiff, Alpha, NewTableFlag)
+
==Description==
 +
*This function calculating the two Sample for unequal variances determines whether two sample means also distinct.
 +
*We can use this test when both:
 +
*1.the two sample sizes  are may are may not be equal;
 +
*2. The means and variances are distinct .
 +
*In <math>TTESTTWOSAMPLESUNEQUALVARIANCES(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 <math>lv</math> 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_{\bar{x_1}-\bar{x_2}}}</math>
 +
where <math>s_{\bar{x_1}-\bar{x_2}}= \sqrt{\frac{s_1^2}{n_1}+\frac{s_2^2}{n_2}} </math>
 +
*Here <math> s_1^2</math> and <math> s_2^2</math> are unbiased estimators of the variances of two samples. <math> n_1</math> and <math> n_2</math> are the number of data points in two arrays. <math>s_{\bar{x_1}-\bar{x_2}}</math> is not a pooled variance.
 +
*This function will give the result as error when
 +
      1. any one of the argument is non-numeric.
 +
      2.alpha>1
  
−
where,
+
==Examples==
 +
{| class="wikitable"
 +
|+Spreadsheet
 +
|-
 +
! !! A !! B !! C !! D!! E !! F !! G
 +
|-
 +
! 1
 +
| 12 || 21 || 9 || 18 || 27 || 37 ||41
 +
|-
 +
! 2
 +
| 19 || 8 || 45 || 29 || 14 || 10 || 11
 +
|}
  
−
'''Array1 '''- Input range should be one block.
 
  
−
'''Array2 '''- Input range should be one block.
 
  
−
'''HypothesizeDiff '''- represents the Hypothesized Mean Difference.A value 0 indicates that sample means are hypothesized to be equal.
+
#=TTESTTWOSAMPLESUNEQUALVARIANCES(A1:F1,A2:F2,3,0.5)
−
 
+
{| class="wikitable"
−
'''Alpha '''- represents the significance level and value in range 0 to 1.
+
|+Result
−
 
+
|-
−
''' ''''''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>
+
! !! Variable 1 !! Variable 2
−
----
+
|-
−
<div id="1SpaceContent" class="zcontent" align="left">T-Test: Two Sample for unequal variances determines whether two sample means are distinct.</div>
+
! Mean
−
----
+
| 20.666666666666668 || 20.833333333333332
−
<div id="7SpaceContent" class="zcontent" align="left">
+
|-
−
 
+
! Variance
−
Lets see an example in (Column3Row1)
+
| 105.06666666666665 || 196.56666666666666
−
 
+
|-
−
<nowiki>=TTESTTWOSAMPLESUNEQUALVARIANCES (R1C1:R6C1, R1C2:R5C2, 0, 0.05, TRUE)</nowiki>
+
! Observations
−
 
+
| 6 || 6
−
TTESTTWOSAMPLESUNEQUALVARIANCES returns the result in new sheet(9Space).
+
|-
−
 
+
! Hypothesized Mean Difference
−
<nowiki>=TTESTTWOSAMPLESUNEQUALVARIANCES(R1C1:R4C1,R1C2:R6C2, 0,- 0.055, TRUE)</nowiki>
+
| 3
−
 
+
|-
−
TTESTTWOSAMPLESUNEQUALVARIANCES returns the #ERROR(Alpha = -0.055).
+
! Degree Of Freedom
 +
| 9
 +
|-
 +
! T- Statistics
 +
| -0.4466201458140038
 +
|-
 +
! P(T<=t) One-tail
 +
| 0.3328511748583461
 +
|-
 +
! T Critical One-Tail
 +
| 0
 +
|-
 +
! P(T<=t) Two-tail
 +
| 0.6657023497166922
 +
|-
 +
! T Critical Two-Tail
 +
| 0.7027221467691982
 +
|}
  
−
</div>
+
==Related Videos==
−
----
 
−
<div id="12SpaceContent" class="zcontent" align="left"><div class="ZEditBox" align="left">
 
  
−
T-TEST : TWO SAMPLE ASSUMING UNEQUAL VARIANCES
+
{{#ev:youtube|L-jfenou5hI|280|center|TTESTUNEQUALVARIANCES}}
  
−
</div></div>
+
==See Also==
−
----
+
*[[Manuals/calci/TTEST  | TTEST ]]
−
<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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*[[Manuals/calci/TDIST  | TDIST ]]
−
----
+
*[[Manuals/calci/TINV | TINV ]]
−
<div id="4SpaceContent" class="zcontent" align="left"><div class="ZEditBox" align="justify">Remarks </div></div>
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*[[Manuals/calci/TTESTEQUALVARIANCES  | TTESTEQUALVARIANCES ]]
−
----
 
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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>
 
−
----
 
−
<div id="8SpaceContent" class="zcontent" align="left">
 
−
 
 
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If the Alpha &lt; 0 or Alpha &gt;1, TTESTTWOSAMPLESUNEQUALVARIANCES returns the #ERROR.
 
−
 
 
−
</div>
 
−
----
 
−
<div id="2SpaceContent" class="zcontent" align="left">
 
−
 
 
−
{| id="TABLE3" class="SpreadSheet blue"
 
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|- class="even"
 
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| class=" " |
 
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| 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
 
−
| 3
 
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| class="sshl_f" | 5Space
 
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| class=" " |
 
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|- class="even"
 
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| class=" " | Row2
 
−
| 7
 
−
| 8
 
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| class="      " |
 
−
| class=" " |
 
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|- class="odd"
 
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| Row3
 
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| 12
 
−
| 8
 
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| class=" " |
 
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| 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
 
−
| class=" " | 46
 
−
| 34
 
−
| class="          SelectTD1 ChangeBGColor SelectTD1" |
 
−
<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=" " |
 
−
|- class="even"
 
−
| Row6
 
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| class=" " | 6
 
−
| 7
 
−
| class=" " |
 
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| class=" " |
 
−
|}
 
−
 
 
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<div align="left">[[Image:calci1.gif]]</div></div>
 
−
----
 
−
<div id="5SpaceContent" class="zcontent" align="left">
 
−
 
 
−
{| class="SpreadSheet blue"
 
−
|+ t-Test: Two-Sample Assuming Unequal Variances<br />
 
−
|- class="even"
 
−
!
 
−
! Variable1
 
−
! Variable2
 
−
|- class="odd"
 
−
| Mean
 
−
| 16.333333333333332
 
−
| 14.2
 
−
|- class="even"
 
−
| Variance
 
−
| 226.66666666666668
 
−
| 152.2
 
−
|- class="odd"
 
−
| Observations
 
−
| 6
 
−
| 5
 
−
|- class="even"
 
−
| Hypothesized Mean Difference
 
−
| 0
 
−
|- class="odd"
 
−
| Degree Of Freedom
 
−
| 9
 
−
|- class="even"
 
−
| T Statistics
 
−
| 0.2582913934642728
 
−
|- class="odd"
 
−
| P(T&lt;=t) One-tail
 
−
| 0.4009958484338277
 
−
|- class="even"
 
−
| T Critical One-tail
 
−
| 1.833112928058645
 
−
|- class="odd"
 
−
| P(T&lt;=t) Two-tail
 
−
| 0.8019916968676554
 
−
|- class="even"
 
−
| T Critical Two-tail
 
−
| 2.262157150957689
 
−
|}
 
  
−
</div>
+
==References==
−
----
+
*[http://en.wikipedia.org/wiki/Student%27s_t-test Student's t-test]

Latest revision as of 13:04, 2 July 2015

TTESTTWOSAMPLESUNEQUALVARIANCES(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 unequal variances determines whether two sample means also distinct.
  • We can use this test when both:
  • 1.the two sample sizes are may are may not be equal;
  • 2. The means and variances are distinct .
  • 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 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. and are the number of data points in two arrays. is not a pooled variance.
  • This function will give the result as error when
     1. any one of the argument is non-numeric.
     2.alpha>1

Examples

Spreadsheet
A B C D E F G
1 12 21 9 18 27 37 41
2 19 8 45 29 14 10 11


  1. =TTESTTWOSAMPLESUNEQUALVARIANCES(A1:F1,A2:F2,3,0.5)
Result
Variable 1 Variable 2
Mean 20.666666666666668 20.833333333333332
Variance 105.06666666666665 196.56666666666666
Observations 6 6
Hypothesized Mean Difference 3
Degree Of Freedom 9
T- Statistics -0.4466201458140038
P(T<=t) One-tail 0.3328511748583461
T Critical One-Tail 0
P(T<=t) Two-tail 0.6657023497166922
T Critical Two-Tail 0.7027221467691982

Related Videos

TTESTUNEQUALVARIANCES

See Also

References

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