VARYANS ANALİZİNİN FARAZİYELERİ VE BUNLARIN BOZULMASıNDAN DOĞAN DURUMLAR

Yıl 1972, Cilt: 3 Sayı: 3, - , 11.12.2010

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Varyans analizi, müşahedelerin şans değişkenlerinin bir denemede
gerçekleşmiş değerleri oluşu, tesiri kontrol edilebilen faktörler ve
deneme hataslnın toplanabilirfiği, şans unsurlarının bağımsızlığı,
eşit. varyanslılığı ve normal dağııış giistermeleri faraziyelerine dayanır.
Bunlardan biri veya birkaçının bozulması, sonuçların güvenirli/iğin i
bozar. Durum, bazı müşahedelerin ihmali, hata varyansının parçalanması,
serbestiik derecelerinde bir takım düzeltf!leler, bazı özel analiz
metodlan yahut sağlam test/erin kullanılışı ve milşahedelerin transformasyonu
ile düzeltilebilir. Denememizde çarpımlı bir modele
sahip lognormal dağılış ve yanlış model seçimi ile ortaya çıkan durum,
normallik faraziye,sine uymayan Poisson dağılışı gibi faraziyelerdeki
şartları taşımayan durumlar ele alınmış ortaya çıkan aksaklıklara
ve düzeltici tedbirlere işaret edilmiştir.

THE ASSUMPTIONS UNDERLYING THE ANALYSIS OF VARIANCE
AND CONSEQUENCES OF DEPARTURES FROM THEM.

The purpose of this study was to
<leseribe the assumptions underıying
the analysis of ~ariance and ındicate
the effects of d~partures from these
assumptions. Some 'methods to improve
the anaIysis weıe mentioned.
The analysis of variance is used
mainly to estimate fixed effects of
treatments (Model-I) or to estimate
~ome components of variance in a
composite population (Model-II). In
either case, the assumptions required
for validüy of inferences are as follows:
i) The observations must respresent
a ranclom variable, .
2) The treatment effects, the environmental
effects and experimental
errors must be additive,
3) The experimental errors must
be independent and have equal varianres,
, 4) The observations must be nor-'
.mally distributed.
The consequences of departures
fr~m these ussumptions invalitades the
finaI results obtained by an analysis
of variance. The effects depend on the'
special as.sumptions and to the extent
to, which these are violated.-
Same commonIy used methods to
make the analysis nior~ valid in the
case of vioIation of assumptions are :
1- Omission of some observations,
2- Subdivision ofthe error variance,
3- Some adjustments in the degrees
of freedam,
4- Use of some refined techniques
taking into account the violations
(e.g. assignment of one degree of·freedom
for nonaddivtivity, ~liminatioİl
of the correIation between errors by
an analysis of covanance),
5· Applicati?n of robust procedures,
6- Change of scale.
In order to demonstrate the effects
of departures from the aSsumptions,
three Monte-Carlo sampling experiments
were Jperformed. The reslilts are as
follows :
1) Nonadditivity of componen·s:
For this purpose 1) muItiplicative model
is adopted. The ıesulting data are coming
from a Lognormal distribution. The
multiple comparsion oftreatmeDt means
gives too many significant resuıts faı
large means, whereas the significant
differences between small valued ,means
are ffidslred. Here, nonadditivity is'
accompained by the heterogenity of
errors and' nonnorınality.. By taking 10gaıithms
one can improve the results.
2) Nonormality: A comp~etely ran·
domised experiment is siniuIated, the
observations having a Poisson distribution.
As in the Lognormal distribution
the 'multiple comparison between
treatment means gives misleading
results in raw data. This impIies that
both types of error are increased in the
case of Poisson distribution.
3). Choosing a wrong model: The
data are siınulatecl from an Ilxll Latin
square .experim(1ot and analysed by
. usİng the correct model or r21ndomised
blocks by choosİng rows and columns
as blocks, and by cömpletely randomised
design. The omission of some sources ot
variation leads to exaggeration 6t error
variance, ultimately causes loss of information.
The signifiance of some differences
of means are lost by using a wrong
design. in practice the violation may
be more serious, because in reducing the
experimentaI design, theıe is a great pro
·bability that the factor omitted will faU
nonorthogonal to the remainings.

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