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Impact of unbalancedness and heteroscedasticity on classic parametric significance tests of two-way fixed-effects ANOVA testsChaka, Lyson 31 October 2017 (has links)
Classic parametric statistical tests, like the analysis of variance (ANOVA), are powerful tools
used for comparing population means. These tests produce accurate results provided the data
satisfies underlying assumptions such as homoscedasticity and balancedness, otherwise biased
results are obtained. However, these assumptions are rarely satisfied in real-life. Alternative
procedures must be explored. This thesis aims at investigating the impact of heteroscedasticity
and unbalancedness on effect sizes in two-way fixed-effects ANOVA models. A real-life
dataset, from which three different samples were simulated was used to investigate the changes
in effect sizes under the influence of unequal variances and unbalancedness. The parametric
bootstrap approach was proposed in case of unequal variances and non-normality. The results
obtained indicated that heteroscedasticity significantly inflates effect sizes while unbalancedness
has non-significant impact on effect sizes in two-way ANOVA models. However, the impact
worsens when the data is both unbalanced and heteroscedastic. / Statistics / M. Sc. (Statistics)
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Statistical Properties of Preliminary Test EstimatorsKorsell, Nicklas January 2006 (has links)
<p>This thesis investigates the statistical properties of preliminary test estimators of linear models with normally distributed errors. Specifically, we derive exact expressions for the mean, variance and quadratic risk (i.e. the Mean Square Error) of estimators whose form are determined by the outcome of a statistical test. In the process, some new results on the moments of truncated linear or quadratic forms in normal vectors are established.</p><p>In the first paper (Paper I), we consider the estimation of the vector of regression coefficients under a model selection procedure where it is assumed that the analyst chooses between two nested linear models by some of the standard model selection criteria. This is shown to be equivalent to estimation under a preliminary test of some linear restrictions on the vector of regression coefficients. The main contribution of Paper I compared to earlier research is the generality of the form of the test statistic; we only assume it to be a quadratic form in the (translated) observation vector. Paper II paper deals with the estimation of the regression coefficients under a preliminary test for homoscedasticity of the error variances. In Paper III, we investigate the statistical properties of estimators, truncated at zero, of variance components in linear models with random effects. Paper IV establishes some new results on the moments of truncated linear and/or quadratic forms in normally distributed vectors. These results are used in Papers I-III. In Paper V we study some algebraic properties of matrices that occur in the comparison of two nested models. Specifically we derive an expression for the inertia (the number of positive, negative and zero eigenvalues) of this type of matrices.</p>
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Statistical Properties of Preliminary Test EstimatorsKorsell, Nicklas January 2006 (has links)
This thesis investigates the statistical properties of preliminary test estimators of linear models with normally distributed errors. Specifically, we derive exact expressions for the mean, variance and quadratic risk (i.e. the Mean Square Error) of estimators whose form are determined by the outcome of a statistical test. In the process, some new results on the moments of truncated linear or quadratic forms in normal vectors are established. In the first paper (Paper I), we consider the estimation of the vector of regression coefficients under a model selection procedure where it is assumed that the analyst chooses between two nested linear models by some of the standard model selection criteria. This is shown to be equivalent to estimation under a preliminary test of some linear restrictions on the vector of regression coefficients. The main contribution of Paper I compared to earlier research is the generality of the form of the test statistic; we only assume it to be a quadratic form in the (translated) observation vector. Paper II paper deals with the estimation of the regression coefficients under a preliminary test for homoscedasticity of the error variances. In Paper III, we investigate the statistical properties of estimators, truncated at zero, of variance components in linear models with random effects. Paper IV establishes some new results on the moments of truncated linear and/or quadratic forms in normally distributed vectors. These results are used in Papers I-III. In Paper V we study some algebraic properties of matrices that occur in the comparison of two nested models. Specifically we derive an expression for the inertia (the number of positive, negative and zero eigenvalues) of this type of matrices.
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Restrições da correlação nos testes de germinação de sementes e emergência de plântulas / Restrictions of the correlation in the tests of seed germination and seedling emergenceCursino, Celso 27 December 2006 (has links)
Coefficient of Pearson r is used to compare scientific tests. In seeds technology
it is used to compare results of procedures that measure vigour. When the correspondly
similar results are not found in very similar conditions, Person s correlation faces
criticism mainly due to two factors. The first one comes from statistics for whose usage
of Person s correlation there are prescriptions that are not always observed, when they
are not understood as assumption. Variables naturally associated are required with
bivariated normal distribution, pairing; homoscedasticity, rectilinear dispersion;
detection of outliers. Added to them, there are practical observations in what refers the
correlation to be valid only in a restrict range of the data series, the necessity to create
value ranges to consider this correlation as good or bad , the need of the graphical
analysis, the use and interpretation of the significance, among others. The second cause
of odd results would be the existence of several biological factors, which are sometimes
support for the reserarcher conclusions. With the objective of identifying applicability
of correlations and the causes for odd results of r, there have been compared data
existent in the Seeds Analysis Laboratory of ICIAG of the Universidade Federal de
Uberlândia-MG, as well as tests of germination of acelerated aging in optimal
conditions of repetibility done in laboratory, and tests of field seedling emergency, as
well as other simulated variables. The results showed odd results. The normal
scattergram between X and Y is enough clear to elucidate only correlated variables of
large samples. Although, if the covariance is not as obvious the dispersion Y=f(X) is not
enough to show simultaneous increasing or decreasing between variables. With an
alternative methodology of plotting the variables related to another auxiliar variable Z of
the same n elements of X and Y, we could study the variable behavior in an individual
way. It was possible to create graphic criteria to assess non-valid correlations, such as
similarity of variables comparable to homoscedastity; influence of outliers on small or
big n; grouping of outliers in a dissident range , influence of treatments effect. In the
analysed cases, we concluded that, comparing seeds vigour with only laboratory results,
as well as its relation with the field results and among simulated data, the results
inconsistency of correlations are prevalent as they do not follow the literature
prescriptions, among others. The magnitude of the distortions due to statistical causes
did not leave space for measuring effects of the variation of the biological seeds
conditions, temporal alterations related to management or the edafoclimatic ones.
Keywords: 1. Failure in correlations 2. Correlation reliability / Coeficiente de Pearson r é usado para comparar experimentos científicos. Em
tecnologias de sementes serve para comparar resultados de procedimentos que medem
vigor. Quando se prognosticam resultados de correlações baseados em condições
similares e eles não acontecem, a correlação de Pearson enfrenta críticas, atribuídas
principalmente a duas causas. Primeiramente pela estatística, para cuja utilização da
correlação de Pearson existem prescrições nem sempre observadas, talvez por não
serem entendidas como pressuposições. Exigem-se variáveis métricas naturalmente
associadas, com distribuição normal bivariada, pareamento, homoscedasticidade, nuvem
de dispersão retilínea; detectção de outliers. Somam-se observações práticas quanto à
validade restrita a um trecho da série de dados, da criação de faixas de valores para
considerá-la de baixa a alta , da necessidade da análise gráfica, da interpretação de
significância, entre outras. A segunda causa seria justamente a existência de variação
biológica devido a fatores diversos externos e interno às sementes, servindo às vezes de
sustentáculo para conclusões de interesse do pesquisador. No objetivo de identificar
aplicabilidade das correlações e as causas de resultados estranhos, foram comparados
dados existentes no Laboratório de Análises de Sementes do ICIAG da Universidade
Federal de Uberlândia-MG, testes germinação de envelhecimento acelerado em
condições ideais de repetibilidade em laboratório, e teste de emergência de plântulas em
campo, e outras variáveis simuladas, havendo incidência de resultados estranhos. A
representação gráfica normal da dispersão entre X e Y mostra satisfatoriamente o
correlacionamento de variáveis naturalmente associadas com n grande. Entretanto, se a
covariância não é tão óbvia, a disperção Y=f(X) não é suficiente para mostrar
crescimento ou decréscimo simultâneo entre as variáveis. Usando metodologia
alternativa de plotagem das variáveis em relação a uma variável auxiliar Z, de mesmos n
elementos que X e Y, pôde-se estudar individualmente o comportamento das variáveis.
O método gráfico permitiu taxar correlações em válidas ou não pela similaridade das
variáveis, comparável à homoscedasticidade; verificar outliers em n pequeno ou grande;
agrupamento de outliers em trecho dissidente e mostrar efeito de tratamentos. Nos
casos analisados, concluiu-se que, comparando vigor de sementes com resultados só de
laboratório, tão bem como no seu relacionamento com os de campo; e entre dados
simulados, as inconsistências de resultados de correlações são preponderantes por não
seguirem as prescrições da literatura, entre outras. A magnitude das distorções por
causas estatísticas não deixou espaço para mensurar efeitos da variação de condições
biológicas de sementes, alterações temporais relativas a manuseio ou edafoclimáticas. / Mestre em Agronomia
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