Difference between revisions of "Manuals/calci/FTESTANALYSIS"

Revision as of 14:27, 2 June 2015

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 (syntax error): {\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 first 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.

DATA1
15	27	19	32

DATA2
21	12	30	11

=FTEST(B4:B8,C4:C8)=0.81524906747183

2.

DATA1
5	8	12	45	23

DATA2
10	20	30	40	50

=FTEST(A1:A5,C1:C5)=0.9583035732212274

3.

DATA1
14	26	37

DATA2
45	82	21	17

FTEST(B1:B3,C1:C4} = 0.26412211240525474

4.

DATA1
14

DATA1
45	65

=FTEST(B1,C2:C3)=NAN

References

F Test

@@ Line 1: / Line 1: @@
-<div style="font-size:30px">'''FTEST(ar1,ar2)'''</div><br/>
+<div style="font-size:30px">'''FTESTANALYSIS(ar1,ar2,alpha,newtableflag)'''</div><br/>
 *<math>ar1</math> and <math>ar2 </math> are array of data.
+*<math>alpha</math>  is the significance level.
+*<math>newtableflag</math>  is the logical value.
 ==Description==
-*This function gives the result of F-test.
+*This function gives the analysis of variance.
-*The F-test is designed to test if two population variances are equal.
+*This statistics used to determine the significant difference of three or more variables or multivariate collected from experimental
-*It does this by comparing the ratio of two variances.
+research.
-*So, if the variances are equal, the ratio of the variances will be 1.
+*So this analysis is depending on the hypothesis.
-*Let X1,...Xn and Y1...Ym be independent samples each have a Normal Distribution .
+*The hypotheses for this test are
-*It's sample means:
+ <math>H_0: \sigma_1 = \sigma_2 </math>  (null hypothesis, variances are equal)
-<math>\bar X=\frac{1}{n} \sum_{i=1}^n Xi</math>
+ <math>H_0: \sigma_1 \ne \sigma_2 </math>  (alternative hypothesis, variances are not equal)
-and
+*For example, the comparison of SCORES across GROUPS,where there are two groups.
-:<math>\bar Y =\frac {1}{m} \sum_{i=1}^m Yi</math> .
+*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)
-*The sample variances :
+*In FTESTANALYSIS(ar1,ar2,alpha,newtableflag) where <math>ar1</math> is the data of  first array, <math>ar2</math> is the data of second array.
- <math>SX^2=\frac{1}{n-1} \sum_{i=1}^n (Xi-\bar X)^2</math>
+*<math> alpha </math> is the significance level which ranges from 0 to 1.
-and
+*<math> newtableflag </math> is the logical value like TRUE or FALSE.
-:<math>SY^2=\frac{1}{m-1} \sum_{i=1}^m (Yi-\bar Y)^2</math>
+*TRUE is indicating the result will display in new worksheet.Suppose we are omitted the lv value it will consider the value as FALSE.
-*Then the Test Statistic = <math>\frac {Sx^2}{Sy^2}</math> has an F-distribution with <math>n−1</math> and <math>m−1</math> degrees of freedom.
+*The F statistic of this function calculated by:
-*In FTEST(ar1,ar2) where <math>ar1</math> is the data of  first array, <math>ar2</math> is the data of second array.
+<math>\frac {Sx^2}{Sy^2}</math> has an F-distribution with <math>n−1</math> and <math>m−1</math> degrees of freedom.
-*The array may be any numbers, names, or references that contains numbers.
+*Also <math>Sx^2 </math> is the sample variance of first set of values.
+*And <math>Sy^2 </math> is the sample variance of first 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 <math>ar1</math> or <math>ar2</math> is less than 2 or the variance of the array value is zero, then this function will return the result as error.

Difference between revisions of "Manuals/calci/FTESTANALYSIS"

Revision as of 14:27, 2 June 2015

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Description

Examples

See Also

References

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