Manuals/calci/FTESTANALYSIS

FTESTANALYSIS(ar1,ar2,alpha,newtableflag)

• $ar1$ and $ar2$ are array of data.
• $alpha$ is the significance level.
• $newtableflag$ is the logical value.

Description

• This function gives the analysis of variance.
• This statistics used to determine the significant difference of three or more variables or multivariate collected from experimental

research.

• So this analysis is depending on the hypothesis.
• The hypotheses for this test are

$H_{0}:\sigma _{1}=\sigma _{2}$  (null hypothesis, variances are equal)
$H_{0}:\sigma _{1}\neq \sigma _{2}$  (alternative hypothesis, variances are not equal)

• For example, the comparison of SCORES across GROUPS,where there are two groups.
• The purpose is to determine if the mean SCORE on a test is different for the two groups tested (i.e., control and treatment groups)
• In FTESTANALYSIS(ar1,ar2,alpha,newtableflag) where $ar1$ is the data of first array, $ar2$ is the data of second array.
• $alpha$ is the significance level which ranges from 0 to 1.
• $newtableflag$ 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 F statistic of this function calculated by:

${\frac {Sx^{2}}{Sy^{2}}}$ has an F-distribution with Failed to parse (MathML with SVG or PNG fallback (recommended for modern browsers and accessibility tools): Invalid response ("Math extension cannot connect to Restbase.") from server "https://wikimedia.org/api/rest_v1/":): {\displaystyle n−1} and Failed to parse (syntax error): {\displaystyle m−1} degrees of freedom.

• Also $Sx^{2}$ is the sample variance of first set of values.
• And $Sy^{2}$ is the sample variance of second set of values.
• If the f-value from the test is higher than the f-critical value then the null hypothesis should be rejected and the variances are unequal.
• So the following cases will occur:
• If the variances are assumed to NOT be equal, proceed with the t-test that assumes non-equal variances.
• If the variances are assumed to be equal, proceed with the t-test that assumes equal variances.
• In this function the array may be any numbers, names, or references that contains numbers.
• values are not considered if the array contains any text, logical values or empty cells.

When the $ar1$ or $ar2$ is less than 2 or the variance of the array value is zero, then this function will return the result as error.

Examples

1.

Spreadsheet

	A	B
1	15	21
2	27	12
3	19	30
4	32	11

=FTESTANALYSIS(A1:A4,B1:B4,0.5,TRUE)

	Variable1	Variable2
Mean	23.25	18.5
Variance	58.916666666666664	79
Observations	4	4
Degree Of Freedom	3	3
F-Value	0.7457805907172995
P(F<=f) one-tail	0.407624533735915
F Critical one-tail	1

2.

Spreadsheet

	A	B
1	5	10
2	8	20
3	12	30
4	45	40
5	23	50

=FTEST(A1:A5,B1:B5,0.30,false)

	Variable1	Variable2
Mean	18.6	30
Variance	264.29999999999995	250
Observations	5	5
Degree Of Freedom	4	4
F-Value	1.0572
P(F<=f) one-tail	0.4791517866106137
F Critical one-tail	1.7528541706121352

See Also

• FDIST
• FINV

References

F Test