Difference between revisions of "Manuals/calci/TTESTEQUALVARIANCES"

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*<math> alpha </math> is the significance level.
 
*<math> alpha </math> is the significance level.
 
*<math> lv </math> is the logical value.
 
*<math> lv </math> is the logical value.
−
 
  
 
==Description==
 
==Description==
 
*This function calculating the two Sample for equal variances determines whether two sample means are equal.  
 
*This function calculating the two Sample for equal variances determines whether two sample means are equal.  
 
*We can use this test when both:
 
*We can use this test when both:
−
*1.the two sample sizes  are equal;
+
*1.The two sample sizes  are equal;
−
*2.it can be assumed that the two distributions have the same variance.
+
*2.It can be assumed that the two distributions have the same variance.
−
*In TTESTTWOSAMPLESEQUALVARIANCES(ar1,ar2,md,alpha,lv), ar1 and ar2 are two arrays of sample values.md is the Hypothesized Mean Difference .
+
*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.
 
*Suppose md=0 which  indicates that sample means are hypothesized to be equal.
−
*alpha is the significance level which ranges from 0 to1.
+
*<math> alpha </math> is the significance level which ranges from 0 to 1.
−
*lv is the logical value like TRUE or FALSE.
+
*<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.
 
*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:
 
*The t statistic of this function calculated by:
−
  <math>t = \frac{\bar{x_1}-\bar{x_2}}{s_x_1.s_x_2.\sqrt\frac{2}{n}}</math> ,where <math>s_x_1.s_x_2 = \sqrt\frac{1}{2}(s_x_1^2+s_x_2^2)</math>.
+
  <math>t = \frac{\bar{x_1}-\bar{x_2}}{s_{x1}.s_{x2}.\sqrt{\frac{2}{n}}}</math>
−
*Here <math>s_x_1</math> and <math>s_x_2</math> are unbiased estimators of the variances of two samples.<math>s_x_1.s_x_2</math> is the grand standard deviation data 1 and data2 and n is the data points of two data set.   
+
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  
 
*This function will give the result as error when  
−
   1.any one of the argument is nonnumeric.
+
   1.any one of the argument is non-numeric.
 
   2.alpha>1
 
   2.alpha>1
−
   3.ar1 and ar2 are having different number of data points.
+
   3.<math>ar1 </math> and <math> ar2 </math> are having different number of data points.
−
 
 
  
 
==Examples==
 
==Examples==
Line 38: Line 37:
 
|}
 
|}
  
 +
#=TTESTTWOSAMPLESEQUALVARIANCES(A1:F1,A2:F2,2,0.5)
  
 +
{| class="wikitable"
 +
|+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
 +
|}
  
−
#=TTESTSAMPLESEQUALVARIANCE(A1:F1,A2:F2,0.5)
+
==Related Videos==
−
 
 
  
 +
{{#ev:youtube|OHHhzLHakKA|280|center|TTESTEQUALVARIANCES}}
  
 
==See Also==
 
==See Also==
Line 49: Line 87:
 
*[[Manuals/calci/TINV  | TINV ]]
 
*[[Manuals/calci/TINV  | TINV ]]
 
*[[Manuals/calci/TTESTUNEQUALVARIANCES  | TTESTUNEQUALVARIANCES ]]
 
*[[Manuals/calci/TTESTUNEQUALVARIANCES  | TTESTUNEQUALVARIANCES ]]
−
 
  
 
==References==
 
==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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