# Manuals/calci/FTESTANALYSIS

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FTESTANALYSIS (Array1,Array2,Alpha,NewTableFlag)

• and are array of data.
• is the significance level.
• is the logical value.
• FTESTANALYSIS(), compares the variances between two group of data.

## 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
   (null hypothesis, variances are equal)
(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 (Array1,Array2,Alpha,NewTableFlag) where   is the data of first array,   is the data of second array.
•   is the significance level which ranges from 0 to 1.
•   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:

has an F-distribution with n−1 and m−1 degrees of freedom.

• Also   is the sample variance of first set of values.
• And   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   or   is less than 2 or the variance of the array value is zero, then this function will return the result as error.

## ZOS

• The syntax is to use this function in ZOS is
•   and   are array of data.
•   is the significance level.
•   is the logical value.
• For e.g.,FTESTANALYSIS([17,22,26,31,49],[50,47,45,13,24],0.4,true)
• FTESTANALYSIS([24..30],[45..51],0.4,true)

## Examples

1.

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

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

Result
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.

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)

Result
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

F Distribution