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AI InsightThe 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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Özet
ÖZET 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.