ÇOKLU KARŞILAŞTIRMALARDA DAĞILIŞLA VE VARYANS YAPISIYLA İLGİLİ FARAZİYELERDEN AYRILIŞLARIN TEST ÖZELLİKLERİNE ETKİLERİ ÜZERİNDE BİR ARAŞTIRMA

Yıl 1974, Cilt: 5 Sayı: 4, - , 15.12.2010

Mehmet Cudi Okur

Öz

OZET
Çoklu karşılaştırma testlerinde,n en fazla kullanılan LSD,
Duncan, SNK ve Tukey testlerinin teorik özelliklerJ mc'elenerek
temel fıa.raziyelerdeki aksamaların bu testleri nasıl etkileyeceği
incelenmiştir. Simulasyon teknikleriyle teşkil tadilen .de·
nemeler yeter sayıda1ekrarlanarak teıst!erin h:a.ta seviyeleri değişik'populasyonlar
ve örnek genişlikleri ,esas alınarak tesbit
edilmiştir. Normal şartlar için beklenen hata seviyeleri normal
dağıliş ve homojen varyans faraziyelerininbozulduğu çeşitli
durumlarda ortaya çıkan hata seviyeleriyle karşılaştırılarak
hangi testlerin ne ölçüde etkilendiği incelenmiştir. Böylece,
testlerin sağlamlık yönünden genel ve birbirlerine katşı durumları
ortaya konmuştur.

SUMMARY
A Researoh on the Effects of Nonnormality and Variance Heterogeneity on the, Structure of Multiple Comparison Tests.

When tıhe fixed model is u-sed,
the aim of the analysis of variance
is to determine the differences
between the pQpulation means.
As the F, test used for general
nulI hypotıheses is not sufficient,
the analysis of variance has got
. to be completed by the multiple
comparison tests. in order to
detect tıhe differences among the
population means, 'some parametric
and non parametric test procedures
have been developed. In
this researah some properties of
the parametric tests, s'llchas L.s.
d., Duncan, SNK and Tukey, were
investigated by using sampiing
experiments.
Multiple comparison tests
are the main coİnponents of the
analysis of variance. For this rea~
son, the validity of the comparisons
depends on the accuracy of
the knowledge thaıt is essential
for the analysis of variance. There
fore the assuımptioll's,of the
aınalysiş of vaPİance can also 1?e
.extended for the multiple compariıson
tests. The oecurance of
some departures from the underlying
assu,mptions invıalidates the
multiple compadsçm tests as the
F tests, and causes wrong decisions.
The error rate and theoreti·
cal s;tıruoture of multiple comparisıon
procedures are 'different
/from eamother. Therefore : :tJlıe
levels of type i and type 11 errOrs
and their powers are not the
SMTle. Because of the differences
in tıhe error rates, the decisions
and the results obtained by the
use of these tests are different.
In tlüs researc,h the sampling
.experiments obtained by using
Monte-Car1o methods. The error
rates of the multiple comparison
'te9ts were investigated nder
different conditiQns. The error
rates obtained for the nonnal
case have been taken as a crlterion
to compare the other cases
where some departures from the
underlyıing assumptions.
Taking two poission distribution
witth the' parametres L = 2
'and L = 3, the departures from
'the nonnal1ty were considered.
'57
Taking the samples of 5 groups,
each with sample sizes of 3 and
7, type i error rates were estimated
according to various error
rate cri:teria. With the departures
from the nQrmality the error
rates of the Duncan, SNK, and
Tukey's niethods were mareased.
Th1s prıaotically arises when the
sample sizes are smaIl.
Effeots of the heterogeneity
of the variances were also mvestigated
for various combinamons
of the group variançes. On each
sampling, 4 and 5 groups ea'.ch
having 3 and 7 observations were
ohosen, Applying the analysis of
v:ariance and the multiple 'comparison
tests, type i error rates
were calculated it has been revealed
that high heterogeneity of
variance ended up with the increase
of type T error mates of
multiple comparison tests except
L.S.D.. In the case of low heterogeneity,
however, did not prove
accordingly giying slightly decreasing
error rates.

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