Psychological Statistics

Past psychological experiments and studies have examined the relationship between question order, paper color and exam performance. In particular, the effect of question order and paper color on exam performance were assessed. This study seeks to explore if and how these two factors affect test performance of University of the Philippines Diliman students on a reading comprehension exam using a two-factor factorial design. The researchers suspect that a student’s skills in reading comprehension might be affected by his/her current degree and hence want to block the effect of this nuisance factor. Thus, the blocking factor “course domain” was also incorporated in the model. The three possible course domains that a student may belong to are: 1) Management and Economics, 2) Arts and Letters, Social Sciences and Law, 3) Science and Technology. Two different sets of question ordering will be employed in the experiment: random and sequential. While four different colors of paper will be used: white, blue, red and yellow. After implementing the research design and performing the analysis of variance, it was found that question order and paper color do not have a significant effect on reading comprehension. The scores of the students from the three different course domains was also found to not be significantly different with each other. The interaction between paper color and question order were also found to not be significant.

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.

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.

Using the paradigm of Solomon Asch’s 1946 study entitled ‘Forming Impressions of Personality, where the influence of data presentation on the formation of an impression of personality was studied. By presenting six (6) characteristics in a Favorable to Unfavorable (F-U) order for the first group and Unfavorable to Favorable (U-F) order in the second group, primacy and recency effect were investigated. There were forty (40) participants in total whom were Assumption College students under different year levels and courses with an exception of Psychology students. Twenty (20) participants were randomly grouped for F-U and the other half for U-F. Wherein results report a p-value of 0.035, indicating that people form impressions on personality based on priming words.

Depression is one of the most common mental disorders in the world and friends is common to be a person's social support. This study searches the relationship between the two variables mentioned. There were multiple tests done to get the relationship. Further results are found in the later part of the paper.

Ang pananaliksik na ito ay ginamitan deskriptiv-analitikal.
Mula sa nakuhang mga datos, ang pangkalahatang resulta ay walang makabuluhang pagkakaiba sa resulta mula sa 4 na salik – pansarili, pangkaibigan, pampamilya at usaping pinansyal – sa pagitan ng tatlong uri ng iskolarship. Mula naman sa resulta ng mga iba pang katanungang katulad ng uri ng kanilang iskolarship.Lumabas sa nasabing mga kasagutan na ang mga iskolar sa financial aid scholarship ay bihirang maapektohan ng oras na ibinibigay para sa pagiging student assistant at sa oras ng pag-aaral. Mula naman sa interpretation sa athletic scholarhip, bihirang maapektohan ng oras ng pag-training sa oras ng pag-aaral at hindi kailaman naapektohan ng training ang pag-aaral nila. Ang huli naman ay ang mga iskolar sa academic scholarship. Ayon sa mean interpretation nito, palaging nape-pressure ang mga akademik iskolar sa nakukuhang grado at palaging nakakaranas ng pagkapuyat dahil sa pag-aaral pero hindi kailanman nahihirapang ibalanse ang oras para sa pag-aaral at sa kaibigan at pamilya. Madalas ding makaapekto sa pag-aaral ng mga akademik iskolar ang kakulangan nila sa oras ng pag-aaral.

Feelings of ownership for the organization have gained great importance by scholars and researchers. In the current study, efforts have been made to understand and look at the relationship between psychological ownership and various attitudes and behaviours at work. 70 managers constituted the total sample that included 35 male and 35 female managers from various banks. The study was based on a correlation design. Data was collected using different scales. The analysis of result involved analysis of Mean, S.D and Correlation. Psychological ownership and various employee attitudes had a positive effect on each other. However psychological ownership and work behaviors did not seem to have any significant relationship.

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

The disadvantages of p-value as a statistical tool are considered, they are:
relation with hypothetical data and researcher’s intentions, dependence on the sample size, the lack of statistical evidence. Interpretive definitions of p-value are opposed a rigorous mathematical definition: p-value as the probability of the data obtained in the study under the condition of the null hypothesis truth. Alternative measure to evaluate the statistical hypotheses likelihood – Bayes factor or likelihood ratio – is presented. Its mathematical and descriptive understanding is outlined. Bayes factor is the ratio of the probability of the data under the condition of the truth of one hypothesis to the probability of the data under the condition of the truth of other. The methods of its interpretation are provided: simple mathematical and based on the evidence conception. The formula of transition from Bayes factor to the assessment of the hypothesis probability under the condition of the data obtained in the study is also considered. The advantages of this factor are shown in the example of research practice in which the use of classical frequentist approach leads to wrong interpretations (absence, presence of differences), although the use of Bayes factor shows insufficient evidence for both the null hypothesis and the alternative hypothesis.
Keywords: Bayes factor, p-value, statistics, hypotheses likelihood, frequentist approach, Bayesian approach, methodological pluralism.

Рассматриваются недостатки p-значения как статистического
инструмента: связь с гипотетическими данными, намерениями
исследователя, зависимость от размера выборки, отсутствие
статистических доказательств. Интерпретационным определениям pзначения противопоставляется точное математическое: p-значение как вероятность данных полученных в исследовании при условии истинности нулевой гипотезы. Представляется альтернативный показатель для оценки правдоподобности статистических гипотез – байесовский фактор – отношение правдоподобия. Излагается его математическое и описательное понимание. Байесовский фактор представляет собой отношение вероятности данных при условии истинности одной гипотезы к вероятности данных при условии истинности другой. Приводятся способы его интерпретации: простой математический и основанный на концепции доказательств. Также рассматривается формула перехода от байесовского фактора к оценке вероятности самой гипотезы при полученных данных. Преимущества данного коэффициента показаны на примере из исследовательской практики, в котором применение классического фреквентистского подхода приводило к неверным интерпретациям (отсутствия, наличия различий), хотя использование байесовского фактора показало недостаточность доказательств как для нулевой, так и для альтернативной гипотез.
Ключевые слова: байесовский фактор, p-значение, статистика,
правдоподобность гипотез, фреквентистский подход, байесовский подход, методологический плюрализм.

Errors in inference can occur with any hypothesis testing method, including Bayesian analysis. The evaluation of expected rates of inferential errors is important when planning confirmatory research, but has rarely been addressed in writings on Bayesian hypothesis testing. The present investigation applied classical and Bayesian hypothesis testing methods to binomial data with certain effects and to data simulating the null hypothesis. The Bayesian analyses generally had substantially lower power (probability of correctly detecting an effect), particularly for small effect size. For data with small effect size and power of .80 for a classical analysis, the probability that the Bayes factor with uniform prior correctly reached 3 or higher supporting the alternative model was only .173. The probability that the Bayes factor was 3 or higher incorrectly supporting the null model was .619. These findings verify that quantitative evaluation of expected inferential error rates is essential when designing confirmatory studies that use Bayesian analyses. The argument that biases in favor of the null model are appropriate for small effect sizes because of potential methodological problems is based on exploratory research and is not appropriate for well-designed confirmatory research that focuses on a pre-established effect size.

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.

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.