Dataplot Vol 1 Vol 2

# F LOCATION TEST

Name:
F LOCATION TEST
Type:
Analysis Command
Purpose:
Perform a 1-factor F location test for the homogeneity of locations across samples.
Description:
The F location test is actually a simplified 1-factor analysis of variance. Dataplot includes the F location test as a distinct command in order to support the MIL-17 Handbook standard. The MIL-17 Handbook is a Department of Defense document concerned with the analysis of composite materials. Dataplot supports most of the techniques in chapter 8 of Volume 1 of the MIL-17 Handbook as support for the RECIPE fits.

More formally, the F location test is defined as:

 H0: $$\mu_1 = \mu_2 = ... = \mu_k$$ Ha: $$\mu_i \not= \mu_j$$     for at least one set of i and j. Test Statistic: The F location test statistic is: $$F = \frac{\sum_{i=1}^{k}{n_i(\bar{x_i} - \bar{x})^2/(k-1)}} {\sum_{i=1}^{k}{\sum_{j=1}^{n_i}{(x_{ij} - \bar{x_i})^2/(n-k)}}}$$ where k is the number of samples, $$\bar{X}$$ is the overall mean, $$\bar{x}_{i}$$ is the mean of the ith sample, ni is the number of observations in group i, and xij is the jth observation in the ith group. Significance Level: $$\alpha$$     (typically = 0.05). Criticial Region: $$F > F_{(1 - \alpha,k-1,n-k)}$$ where $$F_{(1 - \alpha,k-1,n-k)}$$ is the percent point function of the F distribution with k-1 and n-k degrees of freedom.

Syntax:
F LOCATION TEST <y> <groupid>             <SUBSET/EXCEPT/FOR qualification>
where <y> is the response variable;
<groupid> is group (sample) identifier variable;
and where the <SUBSET/EXCEPT/FOR qualification> is optional.
Examples:
F LOCATION TEST Y1 GROUP
F LOCATION TEST Y1 GROUP SUBSET GROUP > 2
Note:
The various values printed by the F LOCATION TEST command are saved as parameters that can be used later by the analyst. Specifically, the following parameters are saved:

STATVAL = value of F location test statistic
STATCDF = F CDF value of F location test statistic
CUTOFF0 = F percent point value (p=0)
CUTOFF50 = F percent point value (p=.50)
CUTOFF75 = F percent point value (p=.75)
CUTOFF90 = F percent point value (p=.90)
CUTOFF95 = F percent point value (p=.95)
CUTOFF99 = F percent point value (p=.99)
CUTOF999 = F percent point value (p=.999)

Some of these parameters were not saved correctly in versions of Dataplot prior to 2000/9.

Default:
None
Synonyms:
None
Related Commands:
 LEVENE TEST = Compute Levene's test. BOX PLOT = Generate a box plot. RECIPE FIT = Perform a RECIPE analysis. GRUBBS TEST = Compute a Grubbs test for outliers. ANOVA = Perform an analysis of variance.
Reference:
"MIL-HDBK-17 Volume 1: Guidelines for Characterization of Structural Materials", Depeartment of Defense, chapter 8. The URL for MIL-HDBK-17 is http://mil-17.udel.edu/.
Applications:
Tolerance Studies in Reliability of Materials
Implementation Date:
1997/12
Program:

SKIP 25
SET WRITE DECIMALS 5
F LOCATION TEST Y X

The following output is generated:
            F-Test for Shift in Location
(Assumption: Normality)

Response Variable: Y
Group-ID Variable: X

H0: Groups are Homogeneous with
Respect to Location
Ha: Groups are Not Homogeneous with
Respect to Location

Summary Statistics:
Total Number of Observations:            45
Number of Groups:                        3

F Location Test Statistic Value:         45.30680
CDF of Test Statistic:                   1.00000
P-Value:                                 0.00000

Percent Points of the F Reference Distribution
-----------------------------------
Percent Point               Value
-----------------------------------
0.0    =          0.000
50.0    =          0.705
75.0    =          1.433
90.0    =          2.434
95.0    =          3.220
97.5    =          4.033
99.0    =          5.149
99.9    =          8.179

Conclusions (Upper 1-Tailed Test)
----------------------------------------------
Alpha    CDF   Critical Value     Conclusion
----------------------------------------------
10%    90%            2.434      Reject H0
5%    95%            3.220      Reject H0
2.5%  97.5%            4.033      Reject H0
1%    99%            5.149      Reject H0


NIST is an agency of the U.S. Commerce Department.

Date created: 6/5/2001
Last updated: 10/14/2015