PLACEMENT SCORE

PLACEMENT SCORE (LET)

Let Subcommand

Compute the placement scores of two variables.

Given two respoonse variables, say \( Y1 \) and \( Y2 \), the placement score for \( Y1_i \) is defined as the number of observations in \( Y2 \) that are less than \( Y1_i \). Likewise, the placement score for \( Y2_i \) is the number of observations in \( Y1 \) that are less than \( Y2_i \). Values in \( Y2 \) that are equal to \( Y1_i \) (or values in \( Y1 \) that are equal to \( Y2_i \)) add 0.5 rather than 1.

Placement scores are used to compute the Fligner-Policello two sample location test. This is demonstrated in the Program example below.

LET <y1p> <y2p> = PLACEMENT SCORES <y1> <y2>
                  <SUBSET/EXCEPT/FOR qualification> where <y1> is the first response variable;
            <y2> is the second response variable;
            <y1p> is a variable where the computed placement scores for <y1> are saved;
            <y2p> is a variable where the computed placement scores for <y2> are saved;
and where the <SUBSET/EXCEPT/FOR qualification> is optional.

LET Y1P Y2P = PLACEMENT SCORES Y1 Y2
LET Y1P Y2P = PLACEMENT SCORES Y1 Y2 SUBSET Y1 > 0 SUBSET Y2 > 0

None

None

RANK SUM TEST	=	Perform a rank sum test.
MEDIAN TEST	=	Perform a median test.
KRUSKAL WALLIS TEST	=	Perform a Kruskal Wallis test.
T TEST	=	Perform a t test.
ANOVA	=	Perform a fixed effects analysis of variance.
MOOD SCORES	=	Generate Mood scores.
MEDIAN SCORES	=	Generate median scores.
KLOTZ SCORES	=	Generate Klotz scores.
VAN DER WAERDEN SCORES	=	Generate Van Der Waerden scores.
SAVAGE SCORES	=	Generate Savage scores.
CONOVER SCORES	=	Generate Conover scores.
ANSARI BRADLEY SCORES	=	Generate Ansari Bradley scores.

Fligner and Policello (1981), "Robust Rank Procedures for the Behrens-Fisher Problem," Journal of the American Statistical Association, Vol. 76, pp. 162-168.

Nonparametric statistics

2023/06

 
. Step 1:   Define the data
.
skip 25
read natr323.dat y1 y2
retain y2 subset y2 > -90
.
. Step 2: Compute Fligner-Policello Test
.
let y1p y2p = placement scores y1 y2
let pmean1 = mean y1p
let pmean2 = mean y2p
let psum1 = sum y1
let psum2 = sum y2
let temp1 = (y1p - pmean1)**2
let v1 = sum temp1
let temp2 = (y2p - pmean2)**2
let v2 = sum temp2
let num = psum1 - psum2
let den = 2*sqrt(v1+v2_pmean1*pmean2)
let z = num/den
let zabs = abs(z)
.
. Step 3: Print Fligner-Policello Test Results
.
feedback off
print "Fligner-Policello Test"
print "H0: Medians are Equal"
print "Ha: Medians are Not Equal"
print "alpha: 0.05"
print "Test Statistic: ^z"
print "Lower Critical Value: -1.96"
print "Upper Critical Value:  1.96"
if zabs <= 1.96
   print "Conclusion: Accept H0"
else
   print "Conclusion: Reject H0"
end of if
    

The following output is generated

 
Fligner-Policello Test
H0: Medians are Equal
Ha: Medians are Not Equal
alpha: 0.05
Test Statistic: 3.88
Lower Critical Value: -1.96
Upper Critical Value:  1.96
Conclusion: Reject H0