TTESTTWOSAMPLESUNEQUALVARIANCES

TTESTTWOSAMPLESUNEQUALVARIANCES (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 unequal variances determines whether two sample means also distinct.
• We can use this test when both:

* The two sample sizes  are may are may not be equal;
* The means and variances are distinct .

In TTESTTWOSAMPLESUNEQUALVARIANCES (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:

$t={\frac {{\bar {x_{1}}}-{\bar {x_{2}}}}{s_{{\bar {x_{1}}}-{\bar {x_{2}}}}}}$ where $s_{{\bar {x_{1}}}-{\bar {x_{2}}}}={\sqrt {{\frac {s_{1}^{2}}{n_{1}}}+{\frac {s_{2}^{2}}{n_{2}}}}}$

• Here $s_{1}^{2}$ and $s_{2}^{2}$ are unbiased estimators of the variances of two samples. $n_{1}$ and $n_{2}$ are the number of data points in two arrays. $s_{{\bar {x_{1}}}-{\bar {x_{2}}}}$ is not a pooled variance.
• This function will give the result as error when

* Any one of the argument is non-numeric.
* 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

=TTESTTWOSAMPLESUNEQUALVARIANCES(A1:F1,A2:F2,3,0.5,0)

t-Test: Two-Sample Assuming Unequal Variances

	Variable 1	Variable 2
Mean	23.571428571428573	19.428571428571427
Variance	146.61904761904762	177.6190476190476
Observations	7	7
Hypothesized Mean Difference	3
Degree Of Freedom	12
T- Statistics	0.1679225216302784
P(T<=t) One-tail	0.43472054489717515
T Critical One-Tail	0
P(T<=t) Two-tail	0.8694410897943503
T Critical Two-Tail	0.6954828655202375

Excel Results

See Also

• TTEST
• TDIST
• TINV
• TTESTTWOSAMPLESEQUALVARIANCES

References

• Student's t-test

• List of Main Z Functions

• Z3 home