Basic Statistics

Bu ders notları, eğitim bilimleri, sosyal bilimler ve davranış bilimleri alanlarında, lisans ve lisansüstü programlarda öğrenim görmekte olan öğrencilere ve araştırmacılara temel istatistik kapsamında katkı sağlamak amacıyla hazırlanmıştır. Kavramsal anlatımın ve tartışmaların yanı sıra uygulama örneklerine de yer verilmiştir. Uygulamalarda elle hesaplamaların yanı sıra excell ve SPSS yazılımlarının kullanımı da örneklendirilmiştir.

For a long time, one of my dreams was to describe the nature of uncertainty axiomatically, and it looks like I've finally done it in my co∼eventum mechanics! Now it remains for me to explain to everyone the co∼eventum mechanics in the most approachable way. This is what I'm trying to do in this work. The co∼eventum mechanics is another name for the co∼event theory, i.e., for the theory of experience and chance which I axiomatized in 2016 [1, 2]. In my opinion, this name best reflects the co∼event-based idea of the new dual theory of uncertainty, which combines the probability theory as a theory of chance, with its dual half, the believability theory as a theory of experience. In addition, I like this new name indicates a direct connection between the co∼event theory and quantum mechanics, which is intended for the physical explanation and description of the conict between quantum observers and quantum observations [4]. Since my theory of uncertainty satises the Kolmogorov axioms of probability theory, to explain this co∼eventum mechanics I will use a way analogous to the already tested one, which explains the theory of probability as a theory of chance describing the results of a random experiment. The simplest example of a random experiment in probability theory is the " tossing a coin ". Therefore, I decided to use this the simplest random experiment itself, as well as the two its analogies: the " "flipping a coin " and the " spinning a coin " to explain the co∼eventum mechanics, which describes the results of a combined experienced random experiment. I would like to resort to the usual for the probability theory " coin-based " analogy to explain (and first of all for myself) the logic of the co∼eventum mechanics as a logic of experience and chance. Of course, this analogy one may seem strange if not crazy. But I did not come up with a better way of tying the explanations of the logic of the co∼eventum mechanics to the coin-based explanations that are commonly used in probability theory to explain at least for myself the logic of the chance through a simple visual " coin-based " model that clarifies what occurs as a result of a combined experienced random experiment in which the experience of observer faces the chance of observation. I hope this analogy can be useful not only for me in understanding the co∼eventum mechanics.

Während meines Studiums der Wirtschaftsinformatik an der Hochschule Harz hatte ich in den Jahren 2002 bis 2005 das große Glück, als Tutor für verschiedene Statistik-Vorlesungen von Dr. Walter Strube tätig werden zu dürfen. Zu Beginn meiner Tutorentätigkeit konnte ich eine über die Jahre von Tutor zu Tutor weiterentwickelte Aufgabensammlung in Form einer ,,Lose-Blatt-Sammlung" von meiner direkten Vorgängerin, Frau Weinert, übernehmen. Um den Studierenden die Arbeit mit den Übungsaufgaben zu erleichtern, habe ich damals für sämtliche Aufgaben Musterlösungen und Erläuterungen verfasst und den Teilnehmern meiner Tutorien in Form von Handouts zur Verfügung gestellt. In den vergangenen sieben Jahren bin ich immer wieder von Studierenden nach dieser Sammlung von Aufgaben mit Musterlösungen gefragt worden, so dass ich mich dazu entschlossen habe, sie noch einmal zu überarbeiten, mit einigen weiteren Erläuterungen zu versehen und über den GRIN-Verlag sowie verschiedene Webseiten als kostenfreien Download zur Verfügung zu stellen. Ich hoffe, dass sie so vielleicht auch für den einen oder anderen Studierenden außerhalb unserer Hochschule von Nutzen sein kann.

You yourself, or what is the same, your experience is such ``coin'' that, while you aren't questioned, it rotates all the time in ``free flight''. And only when you answer the question the ``coin'' falls on one of the sides: ``Yes'' or ``No'' with the believability that your experience tells you.

Исследуются условия применимости критериев Стьюдента и Манна–Уитни – наиболее распространенных методов оценки сдвига центральных тенденций выборок. Последствия нарушений данных условий оцениваются методом Монте-Карло, т.е. моделированием случайных величин с соответствующими распределениями, формированием выборок с помощью их испытаний и оценки частот ошибок первого рода при использовании критериев. Даны рекомендации по выбору
подходящего критерия.

Conditions for Student T-Test and Mann–Whitney U-Test – the most popular methods of shift in central tendencies evaluation – application are analyzed in the article. Effects of violation of the given conditions are estimated by Monte-Carlo method, i.e. by random numbers with corresponding distribution modeling,
forming of samples by means of theirs testing and evaluation of frequency of type I errors when using these tests. Recommendations on appropriate test choosing are given.

Conteúdo
1. Introdução. 2. Estatística Descritiva. 3. Probabilidade. 4. Variável aleatória e distribuição de probabilidade discreta. 5. Variável aleatória contínua e densidade de probabilidade. 6. Amostragem aleatória e distribuição amostral. 7. Inferência Estatística. 8. Análise de regressão e correlação linear simples. 9. Apêndice: Tabelas.

Resumen El lenguaje R es una herramienta muy util para el manejo de datos en la estadistica y probabilidades aplicado a la ingenieria en general, impulsado por la disponibilidad de diversos archivos de datos. En la actualidad se tiene una gran cantidad de paquetes (package) para diversas especialidades recientemente publicados, el fortalecimiento de las comunidades de usuarios en línea y la popularidad de los cursos y eventos de capacitación. En este trabajo, se explora los beneficios y ventajas del uso de R en para la estadistica básica y proporciona una descripción general de un flujo de trabajo típico basado en principios y paquetes reproducibles para la recuperación de datos, análisis espacial, modelado en ingeniería, y el diseño de graficas o visualizaciones. Se toman ejemplos tipicos y aplicaciones que surgen al usar R en estadistica en la ingeniería y herramientas útiles para desafios avanzados, incluido el uso de librerias, documentación y recursos. Por último, este documento proporciona codigos relacionados a la visualizacion de datos hidrologicos, con paquetes R como impulsor del progreso en la ciencia de datos.

Responding to the growing importance of economic reasoning in legal scholarship, this innovative work provides an essential introduction to the economic tools which can usefully be employed in legal reasoning. It is geared specifically towards those without a great deal of exposure to economic thinking and provides law students, legal scholars and practitioners with a practical toolbox to shape their writing, understanding and case preparation.

The book’s clear focus on economic methods poses a refreshing change to conventional textbooks in this area, which tend to focus on content-related theories. Recognising that it is often difficult to derive adequate conclusions for legal arguments without first understanding the methodological limitations of economic studies, this book provides a comprehensive coverage of the most important economic concepts in order to bridge this gap. These include:
• game theory
• public choice and social choice theory
• behavioural economics
• empirical research design
• basic statistics.

Owing to its concise and accessible style, Economic Methods for Lawyers will provide an invaluable companion for legal scholars or practitioners who wish to utilise economic methods for developing legal argument.

The logic of uncertainty is not the logic of experience and as well as it is not the logic of chance. It is the logic of experience and chance. Experience and chance are two inseparable poles. These are two dual reflections of one essence, which is called co∼event. The theory of experience and chance is the theory of co∼events. To study the co∼events, it is not enough to study the experience and to study the chance. For this, it is necessary to study the experience and chance as a single entire, a co∼event. In other words, it is necessary to study their interaction within a co∼event. The new co∼event axiomatics and the theory of co∼events following from it were created precisely for these purposes. In this work, I am going to demonstrate the effectiveness of the new theory of co∼events in a studying the logic of uncertainty. I will do this by the example of a co∼event splitting of the logic of the Bayesian scheme, which has a long history of fierce debates between Bayesionists and frequentists. I hope the logic of the theory of experience and chance will make its modest contribution to the application of these old dual debaters.

Keywords: Eventology, event, probability, probability theory, Kolmogorov’s axiomatics, experience, chance, cause, consequence, co∼event, set of co∼events, bra-event, set of bra-events, ket-event, set of ket-events, believability, certainty, believability theory, certainty theory, theory of co∼events, theory of experience and chance, co∼event dualism, co∼event axiomatics, logic of uncertainty, logic of experience and chance, logic of cause and consequence, logic of the past and the future, Bayesian scheme.

Eventology of multivariate statistics
Eventology and mathematical eventology
Philosophical eventology and philosophy of probability
Practical eventology
Eventology of safety
Eventological economics and psychology
Mathematics in the humanities, socio-economic and natural sciences
Financial and actuarial mathematics
Multivariate statistical analysis
Multivariate complex analysis
Decision-making under risk and uncertainty
Risk measurement and risk models
Theory of fuzzy events and generalized theory of uncertainty
System analysis and events management

EEC'2016 ~ workshop on axiomatizing experience and chance, and Hilbert's sixth problem

With topics from quantum physics, probability and believability to economics, sociology and psychology, the workshop will be intended for an interdisciplinary discussion on mathematical theories of experience and chance. Topics of discussion include the results, thoughts and ideas on axiomatization of the eventological theory of experience and chance in the framework of the decision of Hilbert sixth problem.
Eventology of experience and chance
Beleivability theory and statistics of experience
Probability theory and statistics of chance
Axiomatizing experience and chance

This is a further formation of the theory of experience and chance. My previous works are devoted to the elements of this new theory, which can also be called the theory of co∼events, or the certainty theory. The theory is a synthesis of two dual theories: Kolmogorov's theory of probability and the believability theory based on the axiomatics, which is a non-trivial extension of Kolmogorov's axiomatics. In my paper " Theory of dual co∼event-based means " (2016), the concepts of two dual co∼event-based means of one co∼event are introduced (the bra-mean and the ket-mean). Here I first suggest the definition of the unifying mean of one co∼event (the bra-ket-mean), and then I enter the general definition of the bra-ket-mean for a finite set of co∼events. The mean co∼event-based characteristics of co∼events play the same role in the theory of experience and chance as the mean numerical characteristics of random variables — in the probability theory, or the mean characteristics of events — in the eventological theory.

In my recent works, I propose a new theory of experience and chance, or the theory of certainties, which is a synthesis of two dual theories: Kolmogorov's theory of probabilities and a new theory of believabilities. The theory of experience and chance is based on axiomatics, adding to the Kolmogorov axiomatics of probability theory an axiom of co~event, a new concept defined as a pair of dual objects, one of which serves as a Kolmogorov event in probability space and the other - as an event in the dualistic believability space. One of my papers gives a theory of dual co~event-based means and examples of its use for processing
statistics of ``approving voting'' in elections and in forestry. In this paper, I will go into more detail in examples of processing the statistics
of ``approving voting'' in forestry, where a group of forestry experts is actually engaged in ``approving voting'' when they label the trees of the
forest, labelling those that according to their opinions must be felling. My goal is to show in these examples that the theory of experience and
chance is an effective tool for constructing co~evnts models of experts' behavior in different fields.

Correlation is a fundamental concept within statistics that, once understood, provides insight into more complex statistical models and ideas. From a conceptual standpoint, correlation summarizes the measured association between variables, meaning the extent to which one variable is affected by the other. Put another way, correlation is simply a measure of association.

Principal Component Analysis (PCA) and Factor Analysis (FA) are common multivariate techniques used for dimensionality reduction. With these techniques it is expected to identify actual number of dimensions while accounting almost all observed variability. Standard PCA is based either on correlation matrix (CORM) or covariance matrix (COVM). When it is based on CORM, scale dependency can be removed but inherent variability cannot be preserved. On the other hand, when PCA is based on COVM, inherent variability can be preserved but scale dependency cannot be removed. As a solution to this issue, this paper suggests scaling each indicator by its mean, resulting in new mean equal to 1 and standard deviation equal to the coefficient of variance (CV). This leads to PCs, which are scale independent while retaining the observed variability. The computation of PCs and factors under the suggested method is derived in the study. The procedure is illustrated using the lowest level administrative division census data of Western province of Sri Lanka.

Very briefly on the new axiomatics of co∼events, it is intended for the rigorous mathematical description of an entanglement between observer and observation. Here we try to consider the new axiomatics in the normal human non-mathematical language, although it uses a new but quite natural terminology: ``a co∼event occurs (as an entanglement of observer and observation), a ket-event happens (as chance of observation), a bra-event is experienced (as an experience of observer) ''. And finally, it seems to me that the new theory in a not very rigorous mathematical language is most conveniently set out in the form of questions and answers that my students, graduate students, and colleagues often asked me during numerous internal and external discussions.

The problem of environmentally friendly treatments against most important diseases affecting potato crops continues to represent a challenge With this aim was conducted this research, which approaches alternative solutions in fighting against Phytophtora infestans Mont. de Bary attack in potato. Unconventional treatments with aqueous solutions of 1.1 % and 2.2 % of Allium sativum L., and selenium enriched Allium sativum L. were used. The trial was developed in 2013, within specific conditions of Transylvanian Plane- Pădurenii village, county of Cluj (470 04 ’ 14’’ N, 240 00 ’ 0’ ’ E), in 1 hectare experimental field, in a private farm, using a genuine potato variety, named Redsec. The best results were obtained when unconventional treatments of aqueous solutions 1.1 % Allium sativum L. (GA2 = 3.11%)and selenium enriched Allium sativum L. (GA6 = 3.54%) were used. The less effective treatments were those withconventional products, Alcupral 50 PU (GA4 = 5.73%) and Infinito 687.5 SC (GA...