Dataplot

Vol 1

Auxiliary Chapter

F LOCATION TEST

F LOCATION TEST

Analysis Command

Perform a 1-factor F location test for the homogeneity of locations across samples.

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:
Ha:	for at least one set of i and j.
Test Statistic:	The F location test statistic is: where k is the number of samples, is the overall mean, 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:	(typically = 0.05).
Criticial Region:	where is the percent point function of the F distribution with k-1 and n-k degrees of freedom.

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.

F LOCATION TEST Y1 GROUP
F LOCATION TEST Y1 GROUP SUBSET GROUP > 2

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.

None

None

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.

"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/.

Tolerance Studies in Reliability of Materials

1997/12

SKIP 25
READ VANGEL32.DAT Y X B
F LOCATION TEST Y X
STATUS PARAMETERS


The following output is generated:

      *******************************
      **      F LOCATION TEST Y X  **
      *******************************
 
 
              F-TEST FOR SHIFT IN LOCATION
                 (ASSUMPTION: NORMALITY)
 
1. STATISTICS
      NUMBER OF OBSERVATIONS    =       45
      NUMBER OF GROUPS          =        3
      F LOCATION TEST STATISTIC   =    45.30679
 
 
   FOR F LOCATION TEST STATISTIC
      0          % POINT    =    .0000000
      50         % POINT    =    .7047137
      75         % POINT    =    1.433075
      90         % POINT    =    2.433564
      95         % POINT    =    3.219942
      99         % POINT    =    5.149140
      99.9       % POINT    =    8.179383
 
 
         100.0000       % Point:     45.30679
 
3. CONCLUSION (AT THE 5% LEVEL):
      THERE IS A SHIFT IN LOCATION.
      THUS: NOT HOMOGENOUS WITH RESPECT TO LOCATION.
 
 
      *****************************
      **      STATUS PARAMETERS  **
      *****************************
 
 
 
PARAMETER INFINITY  HAS THE VALUE:      .3340000E+39
PARAMETER PI        HAS THE VALUE:      .3141593E+01
PARAMETER STATVAL   HAS THE VALUE:      .4530679E+02
PARAMETER STATCDF   HAS THE VALUE:      .1000000E+01
PARAMETER CUTOFF0   HAS THE VALUE:      .0000000E+00
PARAMETER CUTOFF50  HAS THE VALUE:      .7047137E+00
PARAMETER CUTOFF75  HAS THE VALUE:      .1433075E+01
PARAMETER CUTOFF90  HAS THE VALUE:      .2433564E+01
PARAMETER CUTOFF95  HAS THE VALUE:      .3219942E+01