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Dissertations / Theses on the topic 'ANOVA test'
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Liu, Hangcheng. "Comparing Welch's ANOVA, a Kruskal-Wallis test and traditional ANOVA in case of Heterogeneity of Variance." VCU Scholars Compass, 2015. http://scholarscompass.vcu.edu/etd/3985.
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Analysis of variance (ANOVA) is a robust test against the normality assumption, but it may be inappropriate when the assumption of homogeneity of variance has been violated. Welch ANOVA and the Kruskal-Wallis test (a non-parametric method) can be applicable for this case. In this study we compare the three methods in empirical type I error rate and power, when heterogeneity of variance occurs and find out which method is the most suitable with which cases including balanced/unbalanced, small/large sample size, and/or with normal/non-normal distributions.
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Ning, Wei. "A new approach to test for interactions in two-way ANOVA models." Related electronic resource: Current Research at SU : database of SU dissertations, recent titles available full text, 2006. http://proquest.umi.com/login?COPT=REJTPTU0NWQmSU5UPTAmVkVSPTI=&clientId=3739.
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Patrick, Joshua Daniel. "Simulations to analyze Type I error and power in the ANOVA F test and nonparametric alternatives." [Pensacola, Fla.] : University of West Florida, 2009. http://purl.fcla.edu/fcla/etd/WFE0000158.
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Senteney, Michael H. "A Monte Carlo Study to Determine Sample Size for Multiple Comparison Procedures in ANOVA." Ohio University / OhioLINK, 2020. http://rave.ohiolink.edu/etdc/view?acc_num=ohiou160433478343909.
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Opoku-Nsiah, Richard. "A computationally efficient bootstrap-equivalent test for ANOVA in skewed populations with a large number of factor levels." Diss., Kansas State University, 2017. http://hdl.handle.net/2097/38155.
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Doctor of Philosophy<br>Department of Statistics<br>Haiyan Wang<br>Advances in technology easily collect a large amount of data in scientific research such as agricultural screening and micro-array experiments. We are particularly interested in data from one-way and crossed two-way designs that have a large number of treatment combinations but small replications with heteroscedastic variances. In this framework, several test statistics have been proposed in the literature. Even though the form of these proposed test statistics may be different, they all use limiting normal or chi-square distribution to conduct their tests. Such approximation approaches the true distribution very slowly when the sample size ni is small while the number of levels of treatments a gets large. A strategy to obtain better accuracy in the classical large sample size setting is to use the bootstrap procedure with studentized statistic. Unfortunately, the available bootstrap method fails when the number of treatment level combinations is large while the number of replications is small. The Fisher and Hall (1990) asymptotic pivotal statistic under large sample size setting is no longer pivotal under small sample size setting with large number of treatment levels.
In the first part of this dissertation, we start with describing suitable bootstrap statistics and procedures for hypothesis tests in one- and two-way ANOVA with a large number of levels and small sample sizes. We prove that the theoretical type I error-rate of Akritas and Papadatos (2004) and Wang and Akritas (2006) test statistics and their corresponding bootstrap versions have accuracy of order O(1/√a). We then modify their statistics to obtain asymptotically pivotal statistics in our current framework. We prove that the theoretical type I error-rate of the bootstrap version of the pivotal statistics is accurate up to order O(1/√a). In the second part of the dissertation, we propose a new test statistic in one-way ANOVA which is asymptotically pivotal in the current setting. We improve the accuracy of approximation of the distribution of the test statistic by deriving asymptotic expansion of the statistic under the current framework and define a new test rejection region through Cornish-Fisher expansion of quantiles. The type I error-rate of the new test has a faster convergence rate and is accurate up to order O(1/a). Simulation studies show that our tests performs better in terms of type I error-rate but comparable power with that of Akritas and Papadatos (2004) in the large a small ni setting. The connection between our asymptotic expansions and bootstrap distribution in the large a small ni setting is discussed. Our proposed test based on asymptotic expansion and Cornish-Fisher expansion of quantiles have both the advantage of higher accuracy and computational efficiency due to no resampling is needed.
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Larsson, Stefan. "Mixing Processes for Ground Improvement by Deep Mixing." Doctoral thesis, KTH, Civil and Architectural Engineering, 2003. http://urn.kb.se/resolve?urn=urn:nbn:se:kth:diva-3667.
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<p>The thesis is dealing with mixing processes havingapplication to ground improvement by deep mixing. The mainobjectives of the thesis is to make a contribution to knowledgeof the basic mechanisms in mixing binding agents into soil andimprove the knowledge concerning factors that influence theuniformity of stabilised soil.</p><p>A great part of the work consists of a literature surveywith particular emphasis on literature on the processindustries. This review forms a basis for a profounddescription and discussion of the mixing process and factorsaffecting the process in connection with deep mixingmethods.</p><p>The thesis presents a method for a simple field test for thestudy of influential factors in the mixing process. A number offactors in the installation process of lime-cement columns havebeen studied in two field tests using statistical multifactorexperiment design. The effects of retrieval rate, number ofmixing blades, rotation speed, air pressure in the storagetank, and diameter of the binder outlet on the stabilisationeffect and the coefficient of variation determined byhand-operated penetrometer tests for excavated lime-cementcolumns, were studied.</p><p>The literature review, the description of the mixingprocess, and the results from the field tests provide a morebalanced picture of the mixing process and are expected to beuseful in connection to ground improvement projects and thedevelopment of mixing equipments.</p><p>The concept of sufficient mixture quality, i.e. theinteraction between the mixing process and the mechanicalsystem, is discussed in the last section. By means ofgeostatistical methods, the analysis considers thevolume-variability relationship with reference to strengthproperties. According to the analysis, the design values forstrength properties depends on the mechanical system, the scaleof scrutiny, the spatial correlation structure, and the conceptof safety, i.e. the concept of sufficient mixture quality isproblem specific.</p><p><b>Key words:</b>Deep Mixing, Lime cement columns, Mixingmechanisms, Mixture quality, Field test, ANOVA, Variancereduction.</p>
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Sahlström, Linda. "Att klättra, springa, krypa och kasta : En effektutvärdering inom området rörelseförståelse bland barn: har interventionen ”Rörelsesatsning i skolan” gett någon effekt?" Thesis, Mälardalens högskola, Akademin för hälsa, vård och välfärd, 2019. http://urn.kb.se/resolve?urn=urn:nbn:se:mdh:diva-45321.
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Övervikt är en av de ledande folkhälsoutmaningarna i världen där cirka en tredjedel av världens befolkning är övervikta eller har fetma vilket medför negativa hälsoeffekter och sjukdomar. Övervikt och fetma drabbar även barn och unga där en kraftig ökning har skett under de senaste 40 åren. Fysisk aktivitet utgör en viktig komponent för att minska fetmaepidemin, dock förekommer även en ökad andel fysiskt inaktiva barn och unga i Sverige. Skolan ses som en bra arena för folkhälsoarbete men det förekommer dock spridd forskning gällande effekterna av interventioner som syftar att öka den fysiska aktiviteten. Syftet med studien var att genomföra en effektutvärdering av projektet ”Rörelsesatsning i skolan” genom en före- och eftermätning av primärutfallet som var skolelevernas fysiska aktivitet samt sekundärutfall som idrottsengagemanget, välmåendet samt klassrumsro. En kvantitativ metod genomfördes med en Single Case Experimental Design där totalt 148 elever deltog vid baslinjemätning och 125 elever vid uppföljningen, eleverna gick i årskurserna 3–6 på en skola i Västerås. Resultatet analyserades genom chi2-test samt ANOVA. Resultatet visar att interventionen gett effekt på utövandet av bollsporter/klättra/springa på rasterna samt att utöva bollsport med ledare på fritiden. Även liten effekt på ökad andel cyklande till skolan och andel som orienterade/cyklade på fritiden med ledare kunde ses.
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Giosa, Francesca. "I test d'ipotesi e la loro declinazione in ambito medico." Master's thesis, Alma Mater Studiorum - Università di Bologna, 2018. http://amslaurea.unibo.it/15992/.
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Una domanda di rilevante interesse in ambito medico e in particolare nell'ambito della ricerca medica è: avendo a disposizione un certo numero di farmaci quale di questi è più efficace? E' chiaro quanto sia importante conoscere l'efficacia di un farmaco prima di somministrarlo e la statistica medica con lo strumento statistico comunemente chiamato Test d'ipotesi si occupa di rispondere a queste domande e di limitare il più possibile gli errori di valutazione che si possono commettere. Lo scopo della mia tesi è spiegare l'utilizzo dei test d'ipotesi e in particolare di analizzare il confronto tra due e più popolazioni (gaussiane e non), ponendo attenzione alle varie possibilità di impostazione del problema a seconda delle ipotesi che vengono di volta in volta soddisfatte.
Infatti a seconda del disegno sperimentale del problema che si vuole trattare, molto spesso si fa un uso diverso della stessa tecnica e la maggior parte degli errori nella letteratura biomedica riguarda proprio errori basilari nel disegno sperimentale, come per esempio una errata procedura di randomizzazione o l'omissione del gruppo di controllo, oppure l'utilizzo non appropriato del test t per confronti multipli. Pertanto è bene fare attenzione alle diverse possibilità e capire quali sono le più adatte nei vari casi.
Per questo motivo il percorso seguito nella mia tesi è basato sulla importanza della adeguatezza del modello utilizzato e della verifica delle ipotesi che permettono di utilizzare un metodo di risoluzione piuttosto che un altro. Inoltre ho presentato un esempio tratto da una situazione reale, con dati forniti dall'istituto per lo scompenso cardiaco di Bologna. Questo esempio è volto a mettere in evidenza l'importanza della adeguatezza del modello e i problemi pratici in cui si può incorrere.
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Mu, Zhiqiang. "Comparing the Statistical Tests for Homogeneity of Variances." Digital Commons @ East Tennessee State University, 2006. https://dc.etsu.edu/etd/2212.
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Testing the homogeneity of variances is an important problem in many applications since statistical methods of frequent use, such as ANOVA, assume equal variances for two or more groups of data. However, testing the equality of variances is a difficult problem due to the fact that many of the tests are not robust against non-normality. It is known that the kurtosis of the distribution of the source data can affect the performance of the tests for variance. We review the classical tests and their latest, more robust modifications, some other tests that have recently appeared in the literature, and use bootstrap and permutation techniques to test for equal variances. We compare the performance of these tests under different types of distributions, sample sizes and true ratios of variances of the populations. Monte-Carlo methods are used in this study to calculate empirical powers and type I errors under different settings.
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Laird, Daniel T. "Analysis of Covariance with Linear Regression Error Model on Antenna Control Unit Tracking." International Foundation for Telemetering, 2015. http://hdl.handle.net/10150/596393.
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ITC/USA 2015 Conference Proceedings / The Fifty-First Annual International Telemetering Conference and Technical Exhibition / October 26-29, 2015 / Bally's Hotel & Convention Center, Las Vegas, NV<br>Over the past several years DoD imposed constraints on test deliverables, requiring objective measures of test results, i.e., statistically defensible test and evaluation (SDT&E) methods and results. These constraints force the tester to employ statistical hypotheses, analyses and perhaps modeling to assess test results objectively, i.e., based on statistical metrics, probability of confidence and logical inference to supplement rather than rely solely on expertise, which is too subjective. Experts often disagree on interpretation. Numbers, although interpretable, are less variable than opinion. Logic, statistical inference and belief are the bases of testable, repeatable and refutable hypothesis and analyses. In this paper we apply linear regression modeling and analysis of variance (ANOVA) to time-space position information (TSPI) to determine if a telemetry (TM) antenna control unit (ACU) under test (AUT) tracks statistically, thus as efficiently, in C-band while receiving both C- and S-band signals. Together, regression and ANOVA compose a method known as analysis of covariance (ANCOVA). In this, the second of three papers, we use data from a range test, but make no reference to the systems under test, nor to causes of error. The intent is to present examples of tools and techniques useful for SDT&E methodologies in testing.
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Widerberg, Carl. "The Two-Sample t-test and the Influence of Outliers : - A simulation study on how the type I error rate is impacted by outliers of different magnitude." Thesis, Uppsala universitet, Statistiska institutionen, 2019. http://urn.kb.se/resolve?urn=urn:nbn:se:uu:diva-375767.
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This study investigates how outliers of different magnitude impact the robustness of the twosample t-test. A simulation study approach is used to analyze the behavior of type I error rates when outliers are added to generated data. Outliers may distort parameter estimates such as the mean and variance and cause misleading test results. Previous research has shown that Welch’s ttest performs better than the traditional Student’s t-test when group variances are unequal. Therefore these two alternative statistics are compared in terms of type I error rates when outliers are added to the samples. The results show that control of type I error rates can be maintained in the presence of a single outlier. Depending on the magnitude of the outlier and the sample size, there are scenarios where the t-test is robust. However, the sensitivity of the t-test is illustrated by deteriorating type I error rates when more than one outlier are included. The comparison between Welch’s t-test and Student’s t-test shows that the former is marginally more robust against outlier influence.
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Laird, Daniel T. "Logistics Regression Model on Antenna Control Unit Autotracking Mode." International Foundation for Telemetering, 2015. http://hdl.handle.net/10150/596414.
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ITC/USA 2015 Conference Proceedings / The Fifty-First Annual International Telemetering Conference and Technical Exhibition / October 26-29, 2015 / Bally's Hotel & Convention Center, Las Vegas, NV<br>Over the past several years DoD imposed constraints on test deliverables, requiring objective measures of test results, i.e., statistically defensible test and evaluation (SDT&E) methods and results. These constraints force testers to employ statistical hypotheses, analyses and modeling to assess test results objectively, i.e., based on statistical metrics, analytical methods, probability of confidence complemented by, rather than solely on expertise, which is too subjective. In this and companion papers we discuss methods of objectifying testing. We employ an earth coordinate model and statistical modeling of telemetry (TM) tracking antenna employing time-space position information (TSPI) and derived statistical measures for tracking-error and auto-tracking mode. Test data were statistically analyzed via analysis of covariance (ANCOVA) which revealed that the antenna control unit (ACU) under test (AUT) does not track statistically identically, nor as practically or efficiently in C-band while receiving data carriers in both S- and C-bands. The conclusions of this paper add support to that hypothesis. In this third of three papers we use data from a range test, but make no reference to the systems under test as the purpose of this paper is to present an example of tools useful for employing a SDT&E methodology.
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Bensmail, Erica. "Studio dei cambiamenti di colore e del contenuto in clorofille e carotenoidi di oli di semi di canapa durante un test di stoccaggio accelerato." Bachelor's thesis, Alma Mater Studiorum - Università di Bologna, 2022.
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Il presente lavoro di tesi mira a valutare i cambiamenti relativi al colore e al contenuto in clorofille e carotenoidi in 7 differenti oli alimentari di semi di canapa spremuti a freddo, sottoposti a un test di stoccaggio accelerato. Questa matrice alimentare è particolarmente incline all’ossidazione, a causa dell’elevato contenuto in acidi grassi polinsaturi, che può determinare un peggioramento della qualità nutrizionale e sensoriale del prodotto. I 7 oli sono stati posti in stufa a 60°C per 18 giorni, ed è stato effettuato per ognuno di questi oli un campionamento al tempo 0 e ogni 3 giorni, per un totale di 7 campionamenti. In queste condizioni (Schaal oven test) 1 giorno a 60°C dovrebbe corrispondere a un mese a temperatura ambiente; al fine di verificare tale corrispondenza, due ulteriori campioni di olio di semi di canapa spremuto a freddo sono stati conservati 3 giorni a 60°C e 3 mesi a temperatura ambiente. La determinazione del colore è avvenuta mediante analisi spettrofotometrica UV-VIS dell’olio tal quale, alle lunghezze d’onda comprese tra 380 e 780 nm. La determinazione del contenuto in pigmenti è avvenuta mediante analisi spettrofotometrica dell’olio diluito con cicloesano, rispettivamente alle lunghezze d’onda di 670 nm e 470 nm.
I risultati ottenuti hanno mostrato un impatto rilevante del fenomeno ossidativo sul colore degli oli, così come sul contenuto in carotenoidi e clorofille, soprattutto dopo i primi 3 giorni a 60°C. In particolare, con il procedere dell’ossidazione, è stata riscontrata una perdita del contenuto in clorofille (in media pari al 61%) e in carotenoidi (in media pari al 66%) e un aumento del valore della coordinata colorimetrica L* (luminosità). Inoltre, è stato evidenziato che le modificazioni che avvengono a 60°C non corrispondano a quanto avviene in 3 mesi a temperatura ambiente (25°C±1°C), indicando una forte influenza della temperatura sull’avanzamento del fenomeno ossidativo.
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Flamigni, Luca. "Analisi del Cammino in Pazienti Affetti da Idrocefalo Normoteso Attraverso IMU Indossabili." Master's thesis, Alma Mater Studiorum - Università di Bologna, 2016.
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L’idrocefalo normoteso idiopatico (iNPH) è una patologia che si sviluppa in età senile ed è caratterizzata da un insieme di sintomi generici tra cui disturbi della marcia che rendono difficoltosa la diagnosi. La presente attività di tesi mira ad identificare parametri motori specificamente alterati in pazienti affetti da iNPH rispetto a pazienti con sintomatologie simili, che siano quindi un possibile ausilio alla diagnosi differenziale oltre ad essere sensibili all’intervento terapeutico. Trenta pazienti hanno preso parte allo studio (15 idrocefali, 9 misti e 6 con altre patologie) e sono stati valutati pre, post 24h e post 72h rispetto ad un intervento di drenaggio di liquor cefalorachidiano (CSF tapping). Ciascun paziente, ad ogni valutazione ha eseguito due task motori standardizzati: l’instrumented 18m walk (i18W) e l’instrumented Timed Up and Go (iTUG). Il metodo proposto è stato in grado di estrapolare i parametri prefissati da tali prove e quindi fornire un report dettagliato del singolo paziente. Successivamente, l’analisi statistica eseguita tra pazienti appartenenti allo stesso gruppo (intra gruppo) e quella tra pazienti di gruppi diversi (inter gruppo) ha mostrato un complessivo trend di miglioramento delle performance per i soli soggetti con diagnosi di idrocefalo o con alcuni segni clinici caratteristici di idrocefalo. I pazienti affetti da altre patologie, come si era ipotizzato, non subiscono sostanziali cambiamenti a seguito dell’intervento.
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Söderberg, Max Joel, and Axel Meurling. "Feature selection in short-term load forecasting." Thesis, KTH, Skolan för elektroteknik och datavetenskap (EECS), 2019. http://urn.kb.se/resolve?urn=urn:nbn:se:kth:diva-259692.
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This paper investigates correlation between energy consumption 24 hours ahead and features used for predicting energy consumption. The features originate from three categories: weather, time and previous energy. The correlations are calculated using Pearson correlation and mutual information. This resulted in the highest correlated features being those representing previous energy consumption, followed by temperature and month. Two identical feature sets containing all attributes1 were obtained by ranking the features according to correlation. Three feature sets were created manually. The first set contained seven attributes representing previous energy consumption over the course of seven days prior to the day of prediction. The second set consisted of weather and time attributes. The third set consisted of all attributes from the first and second set. These sets were then compared on different machine learning models. It was found the set containing all attributes and the set containing previous energy attributes yielded the best performance for each machine learning model. 1In this report, the words ”attribute” and ”feature” are used interchangeably.<br>I denna rapport undersöks korrelation och betydelsen av olika attribut för att förutspå energiförbrukning 24 timmar framåt. Attributen härstammar från tre kategorier: väder, tid och tidigare energiförbrukning. Korrelationerna tas fram genom att utföra Pearson Correlation och Mutual Information. Detta resulterade i att de högst korrelerade attributen var de som representerar tidigare energiförbrukning, följt av temperatur och månad. Två identiska attributmängder erhölls genom att ranka attributen över korrelation. Tre attributmängder skapades manuellt. Den första mängden innehåll sju attribut som representerade tidigare energiförbrukning, en för varje dag, sju dagar innan datumet för prognosen av energiförbrukning. Den andra mängden bestod av väderoch tidsattribut. Den tredje mängden bestod av alla attribut från den första och andra mängden. Dessa mängder jämfördes sedan med hjälp av olika maskininlärningsmodeller. Resultaten visade att mängden med alla attribut och den med tidigare energiförbrukning gav bäst resultat för samtliga modeller.
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Mankayi, Dolphia Thozama. "An investigation into the relationship between satisfaction with life and sense of coherence amongst the unemployed." University of the Western Cape, 1996. http://hdl.handle.net/11394/7861.
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Magister Commercii (Industrial Psychology) - MCom(IPS)<br>The present study investigated the relationship between the Sense Of Coherence and Satisfaction With Life amongst the unemployed.
The study attempted to test the following hypotheses. 1. People with a high Sense Of Coherence tend to be satisfied with their lives in general. 2. Demographic variables such as age, gender, race and level of education have an influence on the subjects' scores on the Sense Of Coherence and Satisfaction With Life scales. 3. Length of unemployment has an impact on the subjects' Sense Of Coherence and Satisfaction With Life. In this study, subjects were drawn from the Department of Manpower in the Western Cape region. The data were obtained from a sample of 100 participants. Of this 100, 52 were males. Subjects were asked to complete the Sense Of Coherence and the Satisfaction With Life scales. Statistical procedures that were used are Multiple Linear Regression analysis, Product Moment Correlational Co-efficients, Analysis of Variance test (ANOVA) and the Cronbach Alphas of the various scales. It was found that Sense Of Coherence correlated significantly with Satisfaction With Life, thus supporting the first hypothesis. This led to the conclusion that a person with a strong Sense Of Coherence tends to be more satisfied with his/her life. However, a person with a weaker Sense Of Coherence finds it difficult to make sense out of his/her life. It was also found that most of the demographic variables did not reach any statistical significance. The general trend in this sample was that younger people had higher education and had been unemployed for fewer years. In comparison, older people were found to have less education and had been unemployed for more years. It was concluded that formal and informal education system will be necessary to develop and equip both young and older people with the experience and skills to use at work. This study was concluded by the discussion of the implications of the findings and suggestions for future research.
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Kossaï, Mohamed. "Les Technologies de L’Information et des Communications (TIC), le capital humain, les changements organisationnels et la performance des PME manufacturières." Thesis, Paris 9, 2013. http://www.theses.fr/2013PA090035/document.
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Les TIC sont un facteur clé de performance dans les pays développés. Cette thèse s’intéresse à l’adoption des TIC et leur impact sur la performance des PME manufacturières d’un pays en développement. A la suite d’une première partie qui présente le cadre théorique et conceptuel, le reste de la thèse est organisé en trois études empiriques. La première étude propose une modélisation Probit afin d’identifier les déterminants d’adoption des TIC. Le capital humain est la variable explicative la plus significative. Se basant sur la régression linéaire à variables muettes, la causalité de Granger, le test de Kruskal-Wallis et le test de l’ANOVA de Welch, suivis des tests post-hoc correspondants, la deuxième étude met en évidence l’existence d’un fort lien statistique significatif entre le niveau d’adoption des TIC et la rentabilité. Dans une troisième étude, plusieurs modélisations Probit (simple, ordonné et multivarié) ont été testées sur différentes mesures de performance. Nous montrons, premièrement, que les TIC ont un impact positif sur la productivité, la rentabilité et la compétitivité. Deuxièmement, les TIC, le capital humain et la formation sont les déterminants de la performance globale. Enfin, la contribution des TIC à la performance globale est forte lorsqu’elles sont combinées au capital humain qualifié. En définitive, nos résultats empiriques ont montré un effet positif des TIC, du capital humain et du changement organisationnel sur la performance des PME<br>ICT is a key performance factor in developed countries. This PhD thesis focuses on the adoption of ICTs and their impact on the performance of manufacturing SMEs in a developing country. Following a first part covering the theoretical and conceptual framework, the rest of the thesis is organized in three empirical studies. The first study uses a Probit model in order to identify the determinants of ICT adoption. Human capital seems to be the most significant explanatory variable. Based on linear regression of dummy variables, Granger causality, Kruskal-Wallis test, ANOVA test of Welch, followed by corresponding post-hoc tests, the second study highlights the existence of a strong statistically significant relationship between the level of ICT adoption and profitability. In a third study, many Probit models (simple, ordered and multivariate) were tested on different measures of performance. Firstly, we show that ICT have a positive impact on productivity, profitability and competitiveness of SMEs. Secondly, ICT, human capital and training are determinants of firm overall performance. Thirdly, when combined together, ICT and highly skilled human resources have an important contribution to the global performance. In conclusion, our empirical results demonstrate a positive impact of ICT, human capital and organizational change on firm performance
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Rajapaksha, Kosman Watte Gedara Dimuthu Hansana. "WALD TYPE TESTS WITH THE WRONG DISPERSION MATRIX." OpenSIUC, 2021. https://opensiuc.lib.siu.edu/dissertations/1949.
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A Wald type test with the wrong dispersion matrix is used when the dispersion matrix is not a consistent estimator of the asymptotic covariance matrixof the test statistic. One class of such tests occurs when there are k groups and it is assumed that the population covariance matrices from the k groups are equal, but the common covariance matrix assumption does not hold. The pooled t test, one way AVOVA F test, and one way MANOVA F test are examples of this class. Two bootstrap confidence regions are modified to obtain large sample Wald type tests with the wrong dispersion matrix.
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Pisinthpunth, C. "A Guideline for Environmental Games (GEG) and a randomized controlled evaluation of a game to increase environmental knowledge related to human population growth." Thesis, Coventry University, 2015. http://curve.coventry.ac.uk/open/items/ab227155-e0c9-4389-a76c-33b9f8283fcf/1.
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People often have very little knowledge about the impact of unsustainable human population growth on the environment and social well-being especially in developing countries. Therefore, an efficient method should be explored in order to educate, and if possible, to convince the members of the public to realize the environmental and social problems caused by the unsustainable population growth. Digital Game-Based Learning (DGBL) has been highlighted by some studies as an innovative tool for learning enhancement. While only a handful of studies have scientifically evaluated the impact of DGBL on knowledge outcomes, the approach is an attractive tool to increase knowledge and motivate engagement with environmental issues surrounding population growth because of its potential to improve learners’ motivation and engagement thereby compared to traditional learning approaches. Therefore, the three primary research questions for this study are: 1) "Can a single-player digital game be an appropriate and attractive learning application for the players to gain insight about the relationship between the growing human population and the environmental issues?" 2) "How can we design environmental games for the players to gain insights about the relationship between the growing human population and the environmental issues via playing a game?" and 3) "What are the obstacles preventing the players from adapting environmental knowledge obtained from the learning mediums into the real-life?" To inform the development of an efficacious DGBL game to impact learning outcomes, critical reviews of environmental issues related to population growth as well as critical reviews of commercial and serious environmental games in terms of their educational and motivational values were undertaken in this study. The results of these critical reviews informed the development of a Guideline for Environmental Games (or GEG). The GEG was developed by combining the engaging game technology with environmental learning and persuasion theories. The GEG was then used to inform the development of a prototype game called THE GROWTH; a single-player, quiz-based, city-management game targeting young adolescents and adults. Multiple evaluation methods of the game were used to answer the three key research questions mentioned earlier. These methods included: 1) The Randomized Controlled Trial approach (RCT) where the participants were systematically divided into the experimental and the control group respectively and their knowledge scores (quantitative data) compared and analyzed, 2) The participants’ abilities to recall and describe the environmental and well-being issues were collected and analyzed qualitatively using The Content Analysis method (CA) and, 3) The participants’ overall feedback on the learning mediums was collected and analyzed to evaluate the motivational values of THE GROWTH itself. To this end, THE GROWTH was evaluated with 82 Thai-nationality participants (70 males and 12 females). The results showed that participants assigned to play THE GROWTH demonstrated greater environmental and social-well-being knowledge related to population growth (F(1,40) = 43.86, p = .006) compared to the control group participants assigned to a non-interactive reading activity (consistent with material presented in THE GROWTH). Furthermore, participants who played THE GROWTH recalled on average more content presented in the game when compared to participants who were presented with similar content in the reading material (t (59) = 3.35, p = .001). In terms of level of engagement, the study suggested that participants assigned to the game were more engaging with their learning medium on average when compared to participants assigned to the non-interactive reading activity. This is evidenced by the longer time participants spent on the task, the activity observed from participants’ recorded gameplay, and their positive responses in the survey. The semi-structured interviews used in this study highlighted the participants’ attitudes towards the environmental, social, and technological issues. Although the participants’ perceived behavioural intention towards the environmental commitments were not statistically differed between the two study group, their responses still provide some evidences that leaps may occur from the learning mediums to the real-world context. Furthermore, these responses can be valuable evidences for the policy makers and for the future development of environmental serious games. Overall, the results suggested that digital environmental games such as THE GROWTH might be an effective and motivational tool in promote the learning about sustainable population size, the environment, and the social well-being. The game’s ability to convince the participants to change towards sustainable lifestyles, however, might be subjected to the future research and other real-world circumstances such as the governmental and public supports. In summary, the research in this thesis makes the following contributions to knowledge: • The Guideline for Environmental Games (GEG) contributes to knowledge about making theoretically-based environmental games. It has particular significance because the guideline was validated by demonstrating learning improvements in a systematic randomized controlled trial. • The use of Multi-Strategy Study Design where multiple systematic evaluation methods were used in conjunction to provide conclusive findings about the efficacy of DGBL to impact outcomes. • THE GROWTH itself is a contribution to applied research as an example of an effective DGBL learning tool.
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Rasch, Dieter, Thomas Rusch, Marie Simeckova, Klaus D. Kubinger, Karl Moder, and Petr Simecek. "Tests of additivity in mixed and fixed effect two-way ANOVA models with single sub-class numbers." Springer, 2009. http://dx.doi.org/10.1070/s00362-009-0254-4.
Full textAbstract:
In variety testing as well as in psychological assessment, the situation occurs that in a
two-way ANOVA-type model with only one replication per cell, analysis is done under
the assumption of no interaction between the two factors. Tests for this situation are
known only for fixed factors and normally distributed outcomes. In the following we will
present five additivity tests and apply them to fixed and mixed models and to quantitative
as well as to Bernoulli distributed data. We consider their performance via simulation
studies with respect to the type-I-risk and power. Furthermore, two new approaches
will be presented, one being a modification of Tukey's test and the other being a new
experimental design to test for interactions.
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Al-Abdullatif, Fatimah. "Discriminant Function Analysis Versus Univariate ANOVAs as Post Hoc Procedures Following Significant MANOVA Test: A Monte Carlo Study." Ohio University / OhioLINK, 2020. http://rave.ohiolink.edu/etdc/view?acc_num=ohiou1585072063453955.
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Sousa, Isaac Diego Pereira de. "Design and testing Of blades for small wind turbines with different geometrical correction in root and tip of blade." Universidade Federal do CearÃ, 2014. http://www.teses.ufc.br/tde_busca/arquivo.php?codArquivo=12320.
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CoordenaÃÃo de AperfeÃoamento de Pessoal de NÃvel Superior<br>The work aims to build , using the BEM (Blade Element Moment) theory , and test three wind rotors , each one consisting of three blades, which were constructed and used for assembling three SWT (Small Wind Turbine) with TSR (Tip Speed Ratio) equal to seven. The three rotors with blades of 2 meters length, distinguished themselves in their geometries as follows: 1) blades without any correction, 2) blades with only tip correction, 3) blades with only root correction. The NREL S809 airfoil developed by the U.S. National Renewable Energy Laboratory (NREL) was used. This airfoil is characterized by having been specially developed for wind turbines. The airfoil experimental data, such as the lift and drag coefficients as a function of angle of attack, were obtained based on wind tunnel test results for Reynolds number of 3 x 105. Also, field tests were conducted to collect torque in the main shaft of the wind rotor [N ∙ m], angular velocity [rad/s] and wind speed [m/s] data, using proper instrumentation and a data collection system. The data collected in the field for each turbine, were analyzed by statistical inference. The power coefficient data were grouped by TSR ranges, and was observed that the data of the last two ranges were the only intervals that showed a normal distribution of data of the Cp . These data were subjected to a one-way ANOVA. And the results showed no significant difference between the average of the rotors SC and CP. Already the data did not exhibit a normal distribution were analyzed by Exponentially Weighted Moving Average (MMEP). It was also observed that the three rotors showed no difference between the power coefficients, of the statistical point of view. An important finding of the experiments was that the CR blades had higher average values of power coefficients for each band TSR.<br>O trabalho visou construir, atravÃs da Teoria do BEM (Blade Element Moment), e testar trÃs rotores eÃlicos, cada um destes constituÃdos de trÃs pÃs, as quais foram construÃdas e aplicadas na montagem de trÃs TEPP (Turbinas EÃlicas de Pequeno Porte) com TSR (Tip Speed Ratio de projeto igual a sete. Os trÃs rotores, com pÃs de 2 metros de comprimento, distinguiram-se, em suas geometrias, do seguinte modo: 1) pÃs sem correÃÃo alguma, 2) pÃs com correÃÃo somente na ponta e 3) pÃs com correÃÃo somente na raiz. O aerofÃlio aplicado foi o NREL S809, desenvolvido pelo laboratÃrio norte americano de energias renovÃveis (NREL). Este aerofÃlio à caracterizado por ter sido projetado para uso especÃfico em turbinas eÃlicas. Os dados experimentais do aerofÃlio, como os coeficientes de sustentaÃÃo e arrasto em funÃÃo do Ãngulo de ataque, foram obtidos com base nos resultados de testes em tÃnel de vento para um nÃmero de Reynolds de 3 x 105. Realizou-se, tambÃm, testes em campo, utilizando-se de uma instrumentaÃÃo necessÃria para a coleta de dados de torque no eixo principal do rotor eÃlico [N.m], velocidade angular do rotor [rad/s], e velocidade do vento, por meio de um sistema de coleta de dados. Os dados colhidos em campo, de cada turbina, foram analisados por inferÃncia estatÃstica. Os dados de Cp foram agrupados por faixas de TSR, e observou-se que os dados das duas Ãltimas faixas foram os Ãnicos intervalos que apresentaram uma distribuiÃÃo normal de probabilidade dos dados de Cp . Estes dados foram submetidos a uma ANOVA com um fator. E os resultados mostraram que nÃo hà uma diferenÃa significativa entre as mÃdias dos rotores SC e CP. Jà os dados que nÃo apresentaram uma distribuiÃÃo normal foram analisados pela MÃdia MÃvel Exponencialmente Ponderada (MMEP). Verificou-se tambÃm que os trÃs rotores nÃo apresentaram diferenÃa entre os coeficientes de potÃncia, do ponto de vista estatÃstico. Uma importante constataÃÃo dos experimentos realizados foi a de que as pÃs CR apresentaram valores mÃdios de Cp superiores para cada faixa de TSR.
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Havlásek, Radim. "Statistické plánování experimentů pro účely optimalizace kvality." Master's thesis, Vysoké učení technické v Brně. Fakulta elektrotechniky a komunikačních technologií, 2009. http://www.nusl.cz/ntk/nusl-217910.
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This thesis is aimed to Design of Experiments methodology. Main purpose of this thesis is to create detailed materials for lessons of Design of Experiments in Quality Control courses. Thesis contains case studies which are applicable for education purposes. Design of Experiments has been applied for solder joints quality evaluation. Solder joints have been modeled in software ANSYS and finite element method has been applied for thermomechanical stress evaluation.
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Tejkal, Martin. "Vybrané transformace náhodných veličin užívané v klasické lineární regresi." Master's thesis, Vysoké učení technické v Brně. Fakulta strojního inženýrství, 2017. http://www.nusl.cz/ntk/nusl-318798.
Full textAbstract:
Klasická lineární regrese a z ní odvozené testy hypotéz jsou založeny na předpokladu normálního rozdělení a shodnosti rozptylu závislých proměnných. V případě že jsou předpoklady normality porušeny, obvykle se užívá transformací závisle proměnných. První část této práce se zabývá transformacemi stabilizujícími rozptyl. Značná pozornost je udělena náhodným veličinám s Poissonovým a negativně binomickým rozdělením, pro které jsou studovány zobecněné transformace stabilizující rozptyl obsahující parametry v argumentu navíc. Pro tyto parametry jsou stanoveny jejich optimální hodnoty. Cílem druhé části práce je provést srovnání transformací uvedených v první části a dalších často užívaných transformací. Srovnání je provedeno v rámci analýzy rozptylu testováním hypotézy shodnosti středních hodnot p nezávislých náhodných výběrů s pomocí F testu. V této části jsou nejprve studovány vlastnosti F testu za předpokladu shodných a neshodných rozptylů napříč výběry. Následně je provedeno srovnání silofunkcí F testu aplikovaného pro p výběrů z Poissonova rozdělení transformovanými odmocninovou, logaritmickou a Yeo Johnsnovou transformací a z negativně binomického rozdělení transformovaného argumentem hyperbolického sinu, logaritmickou a Yeo-Johnsnovou transformací.
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Yuan, Hao. "Optimization of Rib-To-Deck Welds for Steel Orthotropic Bridge Decks." Thesis, Virginia Tech, 2011. http://hdl.handle.net/10919/35935.
Full textAbstract:
Orthotropic steel deck has been widely used over the decades especially on long-span bridges due to its light weight and fast construction. However fatigue cracking problems on the welds have been observed in many countries. Rib-to-deck welds need special care since they are directly under wheel loads, which cause large local stress variations and stress reversals.
<p>
Currently the only requirement by AASHTO bridge code is that the rib-to-deck welds need to be fabricated as one-sided partial penetration welds with minimum penetration of 80% into the rib wall thickness. However considering the thin rib plate thickness, it is very difficult to achieve this penetration without a â melt-throughâ or â blow-throughâ defect. Large cost has been caused for the repair. However recent research has found that the fatigue performance of the rib-to-deck weld is not directly related to its penetration. Other factors contribute to the fatigue performance as well. Therefore, alternative requirements which are more cost-effective and rational are desired.
<p>
The objective of this research is to provide recommendations to the design and fabrication of rib-to-deck welds by investigating their fatigue performance with different weld dimensions, penetrations, and welding processes. Fatigue tests were performed to 95 full-scale single-rib deck segments in 8 specimen series fabricated with different welding processes and root gap openness. Specimens were tested under cyclic loads till failure. Three failure modes were observed on both weld toes and the weld root. Test results showed that the fatigue performance was more affected by other factors such as failure mode, R-ratio and root gap openness, rather than the weld penetration. The failure cycles were recorded for the following S-N curve analysis.
<p>
Finite element analysis was performed to determine the stress state on the fatigue cracking locations. Special considerations were made for the application of hot-spot stress methodology, which post-processes the FEA results to calculate the stress values at cracking locations with the structural configuration taken into account. The hot-spot stress range values were derived and adjusted accounting for the fabrication and test error. Hot-spot S-N curves were established for each specimen series.
<p>
Statistical analyses were performed to study in depth the effect of weld dimensions and test scenarios. Multiple linear regression (MLR) was performed to investigate the effects of different weld dimensions; and multi-way analysis of covariance (Multi-way ANCOVA) for the effects of specimen series, failure mode, R-ratio and weld root gap. It was found that the weld toe size was more relevant to the fatigue performance, other than the weld penetration. The failure mode and R-ratio were very influential on the fatigue performance. Recommendations to the weld geometry were proposed based on the MLR model fitting. S-N data were re-categorized based on ANCOVA results and the lower-bound S-N curve was established. AASHTO C curve was recommended for the deck design.<br>Master of Science
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Lohaka, Hippolyte O. "MAKING A GROUPED-DATA FREQUENCY TABLE: DEVELOPMENT AND EXAMINATION OF THE ITERATION ALGORITHM." Ohio : Ohio University, 2007. http://www.ohiolink.edu/etd/view.cgi?ohiou1194981215.
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Carroll, Gretchen Kay. "AN EXAMINATION OF THE RELATIONSHIP BETWEEN PERSONALITY TYPE, SELF PERCEPTION ACCURACY AND TRANSFORMATIONAL LEADERSHIP PRACTICES OF FEMALE HOSPITAL LEADERS." Bowling Green State University / OhioLINK, 2010. http://rave.ohiolink.edu/etdc/view?acc_num=bgsu1288189512.
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Aderibigbe, Aderonke. "Rock-Fluid Chemistry Impacts on Shale Hydraulic Fracture and Microfracture Growth." Thesis, 2012. http://hdl.handle.net/1969.1/ETD-TAMU-2012-05-11129.
Full textAbstract:
The role of surface chemical effects in hydraulic fracturing of shale is studied using the results of unconfined compression tests and Brazilian tests on Mancos shale- cored at depths of 20-60 ft. The rock mineralogy, total organic carbon and cation exchange capacity were determined in order to characterize the shale. Adsorption tests to study the interaction of the shale and aqueous fluid mixture were also carried out using surface tension measurements.
The uniaxial compressive strengths and tensile strengths of individual shale samples after four hours exposure to water, 2.85 x 10^-3 M cationic surfactant (dodecyltrimethylammonium bromide-DTAB) and 2.81 x 10^-3 M anionic surfactant (sodium dodecylbenzenesulfonate-SDBS) were analyzed using ANOVA and Bonferroni tests. These mechanical strengths were largely reduced on exposure to the aqueous environments studied, despite the relatively low clay and low swelling clay content of the Mancos shale. Further comparison of the uniaxial compressive strengths and tensile strengths of the shale on exposure to water, to the strengths when exposed to the surfactant solutions showed that their difference was not statistically significant indicating that exposure to water had the greatest effect on strength loss.
The surface tension measurement of 2.85 x 10^-4 M DTAB and 2.81 x 10^-4 M SDBS solutions before and after equilibration with shale showed about 80% increase in surface tension in the DTAB solution and 10% increase in surface tension in the SDBS solution. The probable sorption mechanism is electrostatic attraction with negatively charged sites of the shale as shown by significant loss of the cationic surfactant (DTAB) to the shale surface, and the relatively minor adsorption capacity of the anionic surfactant (SDBS). Although these adsorption tests indicate interaction between the shale and surfactant solutions, within the number of tests carried out and the surfactant concentration used, the interaction does not translate into a significant statistical difference for impacts of surfactants on mechanical strength of this shale compared to the impact of water alone.
The relevance of this work is to facilitate the understanding of how the strength of rock can be reduced by the composition of hydraulic fracturing fluids, to achieve improved fracture performance and higher recovery of natural gas from shale reservoirs.
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Srivastava, Pooja. "Monitoring and risk assessment of polyaromatic hydocarbons (PAHs) in a stretch of river ganges." Thesis, 2016. http://localhost:8080/iit/handle/2074/7104.
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Dacal, Rafael. "The Effects of an Employment Tax Enforcement Regime on US Small Business and Proprietor Payment Compliance." 2017. http://scholarworks.gsu.edu/bus_admin_diss/78.
Full textAbstract:
This study attempted to identify ways to improve voluntary compliance and minimize taxpayer burden, but also tries to understand the behavior of taxpayers’ compliance given the compliance regimen. Most explicitly, it attempted to identify ways to improve payment compliance using regimens already utilized in other parts of the tax code. The research question was whether different tax regimes, such as safe harbor, can change the behavior of employment tax payment for small business or self-employed taxpayers. The idea was to determine if a safe harbor provision can reduce the proclivity of authorized individuals to implement a payroll tax dilemma strategy and whether or regimen can reduce payment noncompliance in time of economic distress. To answer the research question, an online experiment was employed. The experimental design was an impact study. The population of interest in this study was all authorized individuals from small and self-employed firms. The sample size totaled 205, and it was based on the a-priori sample size calculation. Analysis of variance (ANOVA) was chosen as the data analysis technique, but other nonparametric test and logistic regression models were used to further analyze the data. This study showed that for subjects who did not subscribed to safe harbor provision but experienced an increased probability of apprehension increased their payment compliance. Also, the availability of a safe harbor provision lead to a large numbers to a safe harbor provision subscription in order to avoid enforcement. This study was able to show that individuals were willing to improve their payment compliance rate when enforcement was increased. The General Deterrence Theory explains that increased deterrence will lead to higher compliance. The study showed a 10 percent improvement in payment compliance when safe harbor was implemented. The results from this study also suggest that provisions such as a safe harbor can be a method of reducing filing costs and audit costs and ultimately taxpayer burden. On the other hand, the results of this study were inconclusive in determining if such provisions can improve payment compliance. Nevertheless, the outcome of this study can improve timing and accuracy of employment taxes payments and it may improve the accuracy of employment tax payment.
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Wang, YuSheng, and 王昱昇. "Two independent sample T test under the extended ANCOVA model." Thesis, 2004. http://ndltd.ncl.edu.tw/handle/92940893381555898238.
Full textAbstract:
碩士<br>國立臺北大學<br>統計學系<br>92<br>Many experiments are implemented to see if there is a significant mean difference in outcome between two treatments. Two independent sample T test and the analysis of variance (ANOVA) are two major methods. However, sometimes the outcome may be apparently affected by the covariate. The way to remove the influence from the covariate is so-called the analysis of covariance (ANCOVA). Comparing with the two methods, T and F, the ANCOVA can increase the Power to the test.
Neter (1999) used the adjusted covariate term as an independent variable in the regression model. Hicks & Turner (1999) adjusted the sum of squares of the ANOVA model by using the form of sum squares of residual from the simple linear regression model. And they are both a kind of analysis of covariance. However, there are some assumptions coming with the ANCOVA.
The purpose of this thesis is to propose a test that will release the assumption in the ANCOVA model. The basic idea comes from the bivariate-normal distribution of the response variable. The least square method and the regression model are used to do our job. Finally, the Monte Carlo simulations are used to evaluate the performance of the desired level and power.
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Huang, Wei-Hsueh, and 黃為學. "Hierarchical ANOVA and F-Tests for Functional Data with Local Polynomial Fitting." Thesis, 2018. http://ndltd.ncl.edu.tw/handle/699vk2.
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Chaka, Lyson. "Impact of unbalancedness and heteroscedasticity on classic parametric significance tests of two-way fixed-effects ANOVA tests." Diss., 2016. http://hdl.handle.net/10500/23287.
Full textAbstract:
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.<br>Statistics<br>M. Sc. (Statistics)
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Deneke, Tewodros Mesfin. "The influence of service quality on customer satisfaction, customer value and behavioral intentions in the hotel sector of Ethiopia." Thesis, 2015. http://hdl.handle.net/10500/22240.
Full textAbstract:
The basic purpose of this study was to examine the influence of service quality on customer satisfaction, perceived customer value and behavioral intentions, in three, four and five star hotels in Ethiopia. Additionally, an attempt was made to assess the differences pertaining to these constructs across customer profile (e.g., gender, nationality etc.) and hotel characteristics (e.g., star ratings etc.). A quantitative survey approach was used to obtain primary data from the respondents (hotels’ guests/customers) by administering the structured questionnaire. The original SERVPERF dimensions and related items were modified to best fit with hotel sector, by using desk review and preliminary interviews with manager, consultants and corporate clients of the hotels. A pilot study was carried out with 35 hotel customers to test the initial reliability and validity of the instrument. The final questionnaire was distributed to 440 respondents from 44 hotels (under three, four and five star categories), by using stratified (proportionate) random sampling. Of the distributed questionnaires, 435 were collected back (over 98% return rate), as completely filled, and used for the purpose of analysis. Descriptive statistics (mean score and standard deviation) were used to examine the customers’ perceptions of service quality, customer value, satisfaction and behavioral intentions. To identify the key service quality dimensions in the Ethiopian hotel sector, Principal Component Analysis (PCA) was employed. The results revealed six underlying factors, namely: Assurance, Reliability, Responsiveness, Empathy, Room Tangibles and Food & Beverage Tangibles. Regression analysis was carried out to examine the relationship between the study constructs, whereby perceived service quality was found to be maintaining significantly (p<0.05) positive influence on customer value, satisfaction and behavioral intentions (measured as customer revisits and word-of-mouth recommendations) in the Ethiopian hotel sector. Moreover, both customer value and satisfaction were observed to be partially mediating the influence of service quality on behavioral intentions, with higher contribution from satisfaction than perceived value. Finally, the respondents’ nationality, gender, visit purpose, length of stay, hotel location and star category were found to be determining their perceptions of overall service quality. However, further research is needed before generalizing these relationships to other sectors/contexts.<br>Business Management<br>D.B.L.
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Dores, Rute Alexandra Silvestre. "Métodos de análise de variância e regressão na avaliação do desenvolvimento da doença periodontal." Master's thesis, 2020. http://hdl.handle.net/10451/48429.
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Tese de mestrado, Matemática Aplicada à Economia e Gestão, Universidade de Lisboa, Faculdade de Ciências, 2020<br>A doença periodontal engloba um grupo de condições inflamatórias determinadas pela destruição progressiva do periodonto. Esta doença afeta a gengiva e os tecidos dentários de suporte, sendo classificada como gengivite, inflamação reversível da gengiva marginal, e periodontite, quando existe destruição de estruturas que suportam o dente. Um dos principais agentes de desencadeamento dessa patologia é a placa bacteriana. Para o sucesso do tratamento da doença periodontal é importante um diagnostico precoce. Com o rápido envelhecimento da população mundial, sobretudo em Portugal, cuja taxa de envelhecimento tem vindo a aumentar consideravelmente, a melhoria das condições de vida e da prestação dos cuidados de saúde levou a que nos dias de hoje exista uma maior durabilidade da dentição natural e, consequentemente, uma diminuição das patologias orais. Contudo, mesmo com uma maior sensibilização para a saúde oral, a prevalência de patologias orais nos idosos é ainda considerada significativa. A avaliação da doença periodontal e da sua progressão é determinada por meio de observações local a local (figura 1). Os dados periodontais são complexos e estruturados em vários níveis, no entanto iremos avaliar duas medidas envolvidas: o nível de perda de aderência clínica (CAL) e o nível de profundidade clínica (PD), em que o CAL é medida que mede a distância vertical entre a junção cimento-esmalte e o ponto mais baixo usando uma sonda periodontal em escala ordinal, é a medida mais popular para avaliar gravidade da doença periodontal. As medidas obtidas de um paciente específico são intrinsecamente agrupados dentro da boca e locais de dentes proximais têm um CAL semelhante em comparação com locais que estão mais distantes. Já o PD é a distância do fundo de sulco até a margem gengival. Ambas são medidas em seis pontos em torno de cada dente (mésio-vestibular, disto-vestibular, mésio-lingual, disto-lingual, meio-vestibular ou médio-lingual). As observações são recolhidas ao nível do paciente, logo não são independentes. Usando a Análise de Variância (ANOVA) de medidas repetidas, analisaram-se 51 pacientes, dos quais 40 são do sexo masculino e 11 do sexo feminino. Estes dados foram recolhidos em quatro momentos. Um primeiro antes de iniciar o tratamento e posteriormente em outros três, ao longo de um período de 4 consultas. A idade de todos os pacientes é superior a 30 anos.<br>Periodontal pathology includes a group of inflammatory conditions that are determined by the progressive destruction of the periodontium. This medical condition affects the gums and the supporting dental tissues, being classified as gingivitis, reversible inflammation of the marginal gingiva and periodontitis, when the supporting structure of the teeth is destroyed. One of the main causes of the development of this pathology is dental plaque and in order to achieve better results of treatment, it is crucial to do an early diagnosis. Due to the increasing ageing of the world population, especially in Portugal where there is a high ageing rate, the improvement of the quality of life and a better access to healthcare, led to a higher durability of the original teeth, causing therefore a decrease of oral pathologies. Nonetheless, the prevalence of oral pathologies in the elderly is substantially high. The evaluation of the periodontal disease and its progression is determined by local to local observations (image 1). The periodontal data is complex and structured in several levels, however there'll be the evaluation the two involved levels, the clinical attachment level (CAL) and the Probin Depth (PD), where the CAL is what measures the vertical distance between the junction cement-enamel and the lower point, using a periodontal plumb in ordinal scale, which is the most known measurement to evaluate the periodontal disease. The obtained measurements of a specific patient are gathered inside the mouth and locals of proximal teeth have similar CAL values when compared to locals that are more distant. Concerning the PD, it is the distance of groove bottom until the gingival margin. Both are measured in six points (distal-vestibular, medial-vestibular, mesio-vestibular, distal-lingual, medial-lingual and mesio-lingual). The observations are evaluated based on the patient, therefore not independent. Using repeated measures analysis of variance (ANOVA), 51 patients were analyzed, 40 of whom are male and 11 are female. These data were collected in four moments. One, just before the treatment starting and then three other times after the treatment of the disease, over a period of 4 visits. All patients are over 30 years old.