Difference between revisions of "Manuals/calci/TTESTTWOSAMPLESEQUALVARIANCES"

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<div style="font-size:25px">'''TTESTTWOSAMPLESEQUALVARIANCES (Array1,Array2,HypothesizedMeanDifference,Alpha,NewTableFlag)'''</div><br/>
 +
*<math>Array1 </math> and <math> Array2 </math>  are set of values.
 +
*<math>HypothesizedMeanDifference </math> is the  Hypothesized Mean Difference.
 +
*<math> Alpha </math> is the significance level.
 +
*<math> NewTableFlag </math> is either 0 or 1.
 +
**TTESTTWOSAMPLESEQUALVARIANCES(), determines whether two sample means are equal.
 +
 
 +
==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 (Array1,Array2,HypothesizedMeanDifference,Alpha,NewTableFlag)</math>, <math>Array1 </math> and <math> Array2 </math> are two arrays of sample values. <math> HypothesizedMeanDifference </math> is the Hypothesized Mean Difference .
 +
*Suppose HypothesizedMeanDifference=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> NewTableFlag </math> is either 0 or 1.
 +
*"1" is indicating the result will display in new worksheet.Suppose we are omitted the NewTableFlag value it will consider the value as "0".
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*The t statistic of this function calculated by:
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<math>t = \frac{\bar{x_1}-\bar{x_2}}{s_{x1}.s_{x2}.\sqrt{\frac{2}{n}}}</math>
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where <math>s_{x1}.s_{x2} = \sqrt{\frac{1}{2}(s_{x1}^2+s_{x2}^2)}</math>
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*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. 
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*This function will give the result as error when
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  1.any one of the argument is non-numeric.
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  2.Alpha>1
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  3.<math>Array1 </math> and <math> Array2 </math> are having different number of data points.
 +
 
 +
==Examples==
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{| class="wikitable"
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|+Spreadsheet
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|-
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! !! A !! B !! C !! D!! E !! F
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|-
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! 1
 +
| 10 || 15 || 18 || 27 || 12 || 34
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|-
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! 2
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| 17 || 20 || 25 || 39 || 9 || 14
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|}
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#=TTESTTWOSAMPLESEQUALVARIANCES(A1:F1,A2:F2,2,0.5,0)
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{| class="wikitable"
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|+t-Test: Two-Sample Assuming Equal Variances
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|-
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! !! Variable 1 !! Variable 2
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|-
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! Mean
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| 19.333333333333332 || 20.666666666666668
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|-
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! Variance
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| 87.06666666666666 || 109.86666666666667
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|-
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! Observations
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| 6 || 6
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|-
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! Pooled Variance
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| 98.46666666666667
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|-
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! Hypothesized Mean Difference
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| 2
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|-
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! Degree Of Freedom
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| 10
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|-
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! T- Statistics
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| -0.5818281835787091
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|-
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! P(T<=t) One-tail
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| 0.28678199670723614
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|-
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! T Critical One-Tail
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| 0
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|-
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! P(T<=t) Two-tail
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| 0.5735639934144723
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|-
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! T Critical Two-Tail
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| 0.6998120613365443
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|}
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==Related Videos==
 +
 
 +
{{#ev:youtube|v=-pTbC_tBy6w|280|center|T Test two sample Equal variances}}
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==See Also==
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*[[Manuals/calci/TTEST  | TTEST ]]
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*[[Manuals/calci/TDIST  | TDIST ]]
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*[[Manuals/calci/TINV  | TINV ]]
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*[[Manuals/calci/TTESTTWOSAMPLESUNEQUALVARIANCES  | TTESTTWOSAMPLESUNEQUALVARIANCES ]]
 +
 
 +
==References==
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*[http://en.wikipedia.org/wiki/Student%27s_t-test Student's t-distribution]
 +
 
 +
 
 +
 
 +
*[[Z_API_Functions | List of Main Z Functions]]
 +
 
 +
*[[ Z3 |  Z3 home ]]

Latest revision as of 15:48, 6 December 2018

TTESTTWOSAMPLESEQUALVARIANCES (Array1,Array2,HypothesizedMeanDifference,Alpha,NewTableFlag)


  • and are set of values.
  • is the Hypothesized Mean Difference.
  • is the significance level.
  • is either 0 or 1.
    • TTESTTWOSAMPLESEQUALVARIANCES(), determines whether two sample means are equal.

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 HypothesizedMeanDifference=0 which indicates that sample means are hypothesized to be equal.
  • is the significance level which ranges from 0 to 1.
  • is either 0 or 1.
  • "1" is indicating the result will display in new worksheet.Suppose we are omitted the NewTableFlag value it will consider the value as "0".
  • 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:F2,2,0.5,0)
t-Test: Two-Sample Assuming Equal Variances
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

T Test two sample Equal variances

See Also

References


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