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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:	\( \mu_1 = \mu_2 = ... = \mu_k \)
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.

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
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