Manuals/calci/TTESTTWOSAMPLESEQUALVARIANCES

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

• $Array1$ and $Array2$ are set of values.
• $HypothesizedMeanDifference$ is the Hypothesized Mean Difference.
• $Alpha$ is the significance level.
• $NewTableFlag$ is either 0 or 1.

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

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

See Also

• TTEST
• TDIST
• TINV
• TTESTTWOSAMPLESUNEQUALVARIANCES

References

• Student's t-distribution

• List of Main Z Functions

• Z3 home