Difference between revisions of "Manuals/calci/TTESTTWOSAMPLESEQUALVARIANCES"

Revision as of 15:34, 22 December 2016

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

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 $TTESTTWOSAMPLESEQUALVARIANCES(Array1,Array2,HypothesizedMeanDifference,Alpha,NewTableFlag)$ , $Array1$ and $Array2$ are two arrays of sample values. $HypothesizedMeanDifference$ is the Hypothesized Mean Difference .
Suppose HypothesizedMeanDifference=0 which indicates that sample means are hypothesized to be equal.
$Alpha$ is the significance level which ranges from 0 to 1.
$NewTableFlag$ 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:

 $t={\frac {{\bar {x_{1}}}-{\bar {x_{2}}}}{s_{x1}.s_{x2}.{\sqrt {\frac {2}{n}}}}}$

where $s_{x1}.s_{x2}={\sqrt {{\frac {1}{2}}(s_{x1}^{2}+s_{x2}^{2})}}$

Here $s_{x1}$ and $s_{x2}$ are unbiased estimators of the variances of two samples. $s_{x1}.s_{x2}$ 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. $Array1$  and  $Array2$  are having different number of data points.

Spreadsheet
	A	B	C	D	E	F
1	10	15	18	27	12	34
2	17	20	25	39	9	14

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

@@ Line 38: / Line 38: @@
 |}
-#=TTESTTWOSAMPLESEQUALVARIANCES(A1:F1,A2:F2,2,0.5,1)
+#=TTESTTWOSAMPLESEQUALVARIANCES(A1:F1,A2:F2,2,0.5,0)
+{| class="wikitable"
+|+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
+|}
 ==See Also==