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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: 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
    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
        
Date created: 06/05/2001
Last updated: 12/11/2023

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