The origins of testing scientific models with statistical techniques go back to 18th century mathematics. However, the modern theory of statistical testing was primarily developed through the work of Sir R.A. Fisher, Jerzy Neyman, and Egon Pearson in the inter-war period. Some of Fisher's papers on testing were published in economics journals (Fisher, 1923, 1935) and exerted a notable influence on the discipline. The development of econometrics and the rise of quantitative economic models in the mid-20th century made (...) statistical significance testing a commonplace, albeit controversial tool within economics. -/- In the debate about significance testing, methodological controversies intertwine with epistemological issues and sociological developments. Our aim in this chapter is to expound these connections and to show how the use of, and the debate about, significance testing in economics differs from other social sciences, such as psychology. (shrink)

Item analysis is a general term that refers to the specific methods used in education to evaluate test items, typically for the purpose of test construction and revision. Construction and analysis of science examinations in high school curricula needs the integration of integrated process and skill type which help students develop their rational and logical thinking. This exploratory study aimed to investigate the comparative results of item analyses using Rasch Model Analysis and SPSS. It examined the reliability, mean difficulty, mean (...) ability, discrimination index, mean trend scores, infit and misfit, and item-person and fit maps using the results of the Basic & Integrated Science Process and Skill Test (BISPST) administered to secondary science high school teachers in the Division of Nueva Vizcaya. The Rasch Model Analysis and SPSS revealed the same unsatisfactory value of internal consistency or the reliability coefficient Cronbach’s alpha (0.66 and 0.67), mean score (19.52) and standard deviation (4.53) of the BISPST. The mean item difficulty was set at 0 by definition (SD = 2.02) and the mean examinee ability was 1.56 (SD = 0.98), which means that the examinees were able to correctly answer 61% of items on average. 33 items with difficulty lower than the least able examinee. The mean ability using Rasch Model Analysis per item showed that high performers in the test got the correct answers compared to the low performing group. This is the same and consistent with the results of the mean trend scores of the upper, middle and lower groups as generated by the SPSS. Choices in the BISPST were found to be effective distracters. Although most items needs revision as revealed by the values generated by both softwares, no items were found to be misfit in the distribution. (shrink)

To estimate causal relationships, time series econometricians must be aware of spurious correlation, a problem first mentioned by Yule (1926). To deal with this problem, one can work either with differenced series or multivariate models: VAR (VEC or VECM) models. These models usually include at least one cointegration relation. Although the Bayesian literature on VAR/VEC is quite advanced, Bauwens et al. (1999) highlighted that “the topic of selecting the cointegrating rank has not yet given very useful and convincing results”. The (...) present article applies the Full Bayesian Significance Test (FBST), especially designed to deal with sharp hypotheses, to cointegration rank selection tests in VECM time series models. It shows the FBST implementation using both simulated and available (in the literature) data sets. As illustration, standard non informative priors are used. (shrink)

Gignac and Zajenkowski (2020) find that “the degree to which people mispredicted their objectively measured intelligence was equal across the whole spectrum of objectively measured intelligence”. This Comment shows that Gignac and Zajenkowski’s (2020) finding of homoscedasticity is likely the result of a recoding choice by the experimenters and does not in fact indicate that the Dunning-Kruger Effect is a mere statistical artifact. Specifically, Gignac and Zajenkowski (2020) recoded test subjects’ responses to a question regarding self-assessed comparative IQ onto (...) a linear IQ scale when a normal IQ scale would likely have been more appropriate. More generally, researchers studying self-assessed intelligence should be aware of potential measurement problems that may arise when transforming an ordinal scale onto an interval scale. (shrink)

During multiple testing, researchers often adjust their alpha level to control the familywise error rate for a statistical inference about a joint union alternative hypothesis (e.g., “H1,1 or H1,2”). However, in some cases, they do not make this inference. Instead, they make separate inferences about each of the individual hypotheses that comprise the joint hypothesis (e.g., H1,1 and H1,2). For example, a researcher might use a Bonferroni correction to adjust their alpha level from the conventional level of 0.050 to (...) 0.025 when testing H1,1 and H1,2, find a significant result for H1,1 (p < 0.025) and not for H1,2 (p > .0.025), and so claim support for H1,1 and not for H1,2. However, these separate individual inferences do not require an alpha adjustment. Only a statistical inference about the union alternative hypothesis “H1,1 or H1,2” requires an alpha adjustment because it is based on “at least one” significant result among the two tests, and so it refers to the familywise error rate. Hence, an inconsistent correction occurs when a researcher corrects their alpha level during multiple testing but does not make an inference about a union alternative hypothesis. In the present article, I discuss this inconsistent correction problem, including its reduction in statistical power for tests of individual hypotheses and its potential causes vis-à-vis error rate confusions and the alpha adjustment ritual. I also provide three illustrations of inconsistent corrections from recent psychology studies. I conclude that inconsistent corrections represent a symptom of statisticism, and I call for a more nuanced inference-based approach to multiple testing corrections. (shrink)

Statistical evidence is crucial throughout disparate impact’s three-stage analysis: during (1) the plaintiff’s prima facie demonstration of a policy’s disparate impact; (2) the defendant’s job-related business necessity defense of the discriminatory policy; and (3) the plaintiff’s demonstration of an alternative policy without the same discriminatory impact. The circuit courts are split on a vital question about the “practical significance” of statistics at Stage 1: Are “small” impacts legally insignificant? For example, is an employment policy that causes a one percent (...) disparate impact an appropriate policy for redress through disparate impact litigation? This circuit split calls for a comprehensive analysis of practical significance testing across disparate impact’s stages. Importantly, courts and commentators use “practical significance” ambiguously between two aspects of practical significance: the magnitude of an effect and confidence in statistical evidence. For example, at Stage 1 courts might ask whether statistical evidence supports a disparate impact (a confidence inquiry) and whether such an impact is large enough to be legally relevant (a magnitude inquiry). Disparate impact’s texts, purposes, and controlling interpretations are consistent with confidence inquires at all three stages, but not magnitude inquiries. Specifically, magnitude inquiries are inappropriate at Stages 1 and 3—there is no discriminatory impact or reduction too small or subtle for the purposes of the disparate impact analysis. Magnitude inquiries are appropriate at Stage 2, when an employer defends a discriminatory policy on the basis of its job-related business necessity. (shrink)

In this paper, we propose the introduction of a neutrosophic chi-square-test for consistency, incorporating neutrosophic statistics. Our aim is to modify the existing chi-square -test for consistency in order to analyze imprecise data. We present a novel test statistic for the neutrosophic chi-square -test for consistency, which accounts for the uncertainties inherent in the data. To evaluate the performance of the proposed test, we compare it with the traditional chi-square -test for consistency based on classical statistics. By conducting a comparative (...) analysis, we assess the efficiency and effectiveness of our proposed neutrosophic chi-square-test for consistency. Furthermore, we illustrate the application of the proposed test through a numerical example, demonstrating how it can be utilized in practical scenarios. Through this implementation, we aim to provide empirical evidence of the improved performance of our proposed test when compared to the traditional chi-square-test for consistency based on classical statistics. We anticipate that the proposed neutrosophic chi-square-test for consistency will outperform its classical counterpart, offering enhanced accuracy and reliability when dealing with imprecise data. This advancement has the potential to contribute significantly to the field of statistical analysis, particularly in situations where data uncertainty and imprecision are prevalent. (shrink)

This proposed study would seek to test for a causal relationship between theory of mind (ToM) and consciousness by conducting a single-variable experiment. Further, the theory proposed to explain this relationship includes that it must exist as a quantum superposition. The independent variable of ToM would be manipulated by randomly assigning participants to two groups. The two groups would represent a higher and lower level of the ToM variable by exposing participants to dramatic material chosen, in the first group, to (...) evoke ToM at a high level; and in the second group, at a lower level. After viewing the material, subjects would receive the Reading the Mind in the Eyes Test (RMET) for theory of mind, demonstrating a higher and lower level of ToM corresponding to which material they viewed. The participants would then complete the Phenomenology of Consciousness Inventory (PCI). The researcher would then compare the scores on the PCI between the two groups, using appropriate statistical tests. If there is a statistically significant difference between the groups, it would suggest that the presence of theory of mind causes the existence of consciousness. (shrink)

Statistical tests that detect and measure deviation from the Hardy-Weinberg equilibrium (HWE) have been devised but are limited when testing for deviation at multiallelic DNA loci is attempted. Here we present the full Bayesian significance test (FBST) for the HWE. This test depends neither on asymptotic results nor on the number of possible alleles for the particular locus being evaluated. The FBST is based on the computation of an evidence index in favor of the HWE hypothesis. A great (...) deal of forensic inference based on DNA evidence assumes that the HWE is valid for the genetic loci being used. We applied the FBST to genotypes obtained at several multiallelic short tandem repeat loci during routine parentage testing; the locus Penta E exemplifies those clearly in HWE while others such as D10S1214 and D19S253 do not appear to show this. (shrink)

Racial discrimination uses race as grounds to discriminate in the treatment owed to others; sexual discrimination uses people’s sexual features as grounds for determining how they should be treated compared to others. Analogously, statistical discrimination treats statistical inferences about the groups to which individuals belong as grounds for discriminating amongst them in thought, word and deed. Examples of statistical discrimination include the employer who won’t hire women of childbearing age, because they are likely to take maternity leave (...) at some point in their careers; or insurers who wish to charge more to young drivers than to more experienced ones, because they are more likely to have accidents than the latter – or to favour women over men in the cost of premiums for similar reasons. Finally, a famous – infamous – example of statistical discrimination is racial profiling for police purposes, where statistical evidence of differential propensities to crime are used to justify preventive police measures, such as ‘stop and search’, which mainly target young black men, and other racialized minorities. The philosophical appeal of the concept of statistical discrimination is fairly easy to see: it draws our attention to the way that probabilistic claims figure, or might figure, in the distribution of social costs and benefits such as jobs, security, insurance. It therefore gives us a way to test our moral intuitions across different cases, enables us to see how far our moral judgements can be generalised, and whether they have been affected by particularly emotive examples, or by the particular features of a real or hypothetical case. But does that mean that statistical discrimination is unproblematic? This article takes issue with some arguments of Kasper Lippert Rasmussen on the topic. (shrink)

A new Evidence Test is applied to the problem of testing whether two Poisson random variables are dependent. The dependence structure is that of Holgate’s bivariate distribution. These bivariate distribution depends on three parameters, 0 < theta_1, theta_2 < infty, and 0 < theta_3 < min(theta_1, theta_2). The Evidence Test was originally developed as a Bayesian test, but in the present paper it is compared to the best known test of the hypothesis of independence in a frequentist framework. It is (...) shown that the Evidence Test is considerably more powerful when the correlation is not too close to zero, even for small samples. (shrink)

“Dutch Book” arguments and references to gambling theorems are typical in the debate between Bayesians and scientists committed to “classical” statistical methods. These arguments have rarely convinced non-Bayesian scientists to abandon certain conventional practices, partially because many scientists feel that gambling theorems have little relevance to their research activities. In other words, scientists “don’t bet.” This article examines one attempt, by Schervish, Seidenfeld, and Kadane, to progress beyond such apparent stalemates by connecting “Dutch Book”–type mathematical results with principles actually (...) endorsed by practicing experimentalists. (shrink)

We review the definition of the Full Bayesian Significance Test (FBST), and summarize its main statistical and epistemological characteristics. We review also the Abstract Belief Calculus (ABC) of Darwiche and Ginsberg, and use it to analyze the FBST’s value of evidence. This analysis helps us understand the FBST properties and interpretation. The definition of value of evidence against a sharp hypothesis, in the FBST setup, was motivated by applications of Bayesian statistical reasoning to legal matters where the sharp (...) hypotheses were defendants statements, to be judged according to the Onus Probandi juridical principle. (shrink)

Much forensic inference based upon DNA evidence is made assuming Hardy-Weinberg Equilibrium (HWE) for the genetic loci being used. Several statistical tests to detect and measure deviation from HWE have been devised, and their limitations become more obvious when testing for deviation within multiallelic DNA loci. The most popular methods-Chi-square and Likelihood-ratio tests-are based on asymptotic results and cannot guarantee a good performance in the presence of low frequency genotypes. Since the parameter space dimension increases at a (...) quadratic rate on the number of alleles, some authors suggest applying sequential methods, where the multiallelic case is reformulated as a sequence of “biallelic” tests. However, in this approach it is not obvious how to assess the general evidence of the original hypothesis; nor is it clear how to establish the significance level for its acceptance/rejection. In this work, we introduce a straightforward method for the multiallelic HWE test, which overcomes the aforementioned issues of sequential methods. The core theory for the proposed method is given by the Full Bayesian Significance Test (FBST), an intuitive Bayesian approach which does not assign positive probabilities to zero measure sets when testing sharp hypotheses. We compare FBST performance to Chi-square, Likelihood-ratio and Markov chain tests, in three numerical experiments. The results suggest that FBST is a robust and high performance method for the HWE test, even in the presence of several alleles and small sample sizes. (shrink)

The Full Bayesian Significance Test (FBST) for precise hypotheses is presented, with some applications relevant to reliability theory. The FBST is an alternative to significance tests or, equivalently, to p-ualue.s. In the FBST we compute the evidence of the precise hypothesis. This evidence is the probability of the complement of a credible set "tangent" to the sub-manifold (of the para,rreter space) that defines the null hypothesis. We use the FBST in an application requiring a quality control of used components, (...) based on remaining life statistics. (shrink)

Although logical consistency is desirable in scientific research, standard statistical hypothesis tests are typically logically inconsistent. To address this issue, previous work introduced agnostic hypothesis tests and proved that they can be logically consistent while retaining statistical optimality properties. This article characterizes the credal modalities in agnostic hypothesis tests and uses the hexagon of oppositions to explain the logical relations between these modalities. Geometric solids that are composed of hexagons of oppositions illustrate the conditions for (...) these modalities to be logically consistent. Prisms composed of hexagons of oppositions show how the credal modalities obtained from two agnostic tests vary according to their threshold values. Nested hexagons of oppositions summarize logical relations between the credal modalities in these tests and prove new relations. (shrink)

This is a trend study of School Size, Location and Enrolment Figures of Junior secondary schools in Akwa Ibom State of Nigeria covering 2008 – 2016 with implications on sustainable development. The study was tailored to follow the ex-post facto research design. This study was a census, hence the entire population of 227 public secondary schools were used. Secondary quantitative data were obtained using “School Size, Location and Enrolment Figures Checklist (SSLEFC)” were analysed using descriptive statistics, while line graphs and (...) bar charts were used to illustrate the statistical trends. The hypotheses were tested using the independent t-test statistical approach. Findings showed that higher rates of enrolment were recorded in large and urban schools than in small schools and rural schools respectively. The mean differences in the enrolment trend among urban and provincial schools were factually huge. It was presumed that there is an upward pattern in enrolment in all the schools from 2008 – 2013 and a descending pattern from 2015– 2016. Based on this conclusion, implications were discussed, while it was recommended, among others, that infrastructural provisions and adequate supply of qualified personnel be allocated to urban and rural schools evenly, to discourage rural-urban migration but promote active rural participation in Education, as well as foster sustainability in schools. (shrink)

The Full Bayesian Significance Test, FBST, is extensively reviewed. Its test statistic, a genuine Bayesian measure of evidence, is discussed in detail. Its behavior in some problems of statistical inference like testing for independence in contingency tables is discussed.

ABSTRACTIn this article, we discuss the benefits of Bayesian statistics and how to utilize them in studies of moral education. To demonstrate concrete examples of the applications of Bayesian statistics to studies of moral education, we reanalyzed two data sets previously collected: one small data set collected from a moral educational intervention experiment, and one big data set from a large-scale Defining Issues Test-2 survey. The results suggest that Bayesian analysis of data sets collected from moral educational studies can provide (...) additional useful statistical information, particularly that associated with the strength of evidence supporting alternative hypotheses, which has not been provided by the classical frequentist approach focusing on P-values. Finally, we introduce several practical guidelines pertaining to how to utilize Bayesian statistics, including the utilization of newly developed free statistical software, Jeffrey’s Amazing Statistics Program, and thresholding based on Bayes Factors, to scholars in the field of moral education. (shrink)

We present experimental evidence that an interpretation was accurate. Current wisdom notwithstanding, we could interpret from the text alone because its information is redundant: repetition provides internal checks. Knowing neither dreamer nor their associations we made falsifiable predictions that we tested by subsequently gathering information about the dreamer. Predictions were supported. Results were repeated with seven additional dreams. Each dream was tightly crafted, used humor, drama or hyperbole to penetrate the dreamer’s defenses, and furthered the emergence of personality. Our experiment (...) compliments fMRI and statistics because it studies a whole text as a unique narrative: one iteration identified healing steps during therapy; another confirmed the psychological meaning of a myth. Our experiment might generate a body of objective knowledge about interpretation and make interpretation itself more accurate. In the US 20% live with mental illness. Our experiment supports talk therapy against pressure from the drug and insurance industries. (shrink)

In this paper epistemological, ontological and sociological questions concerning the statistical significance of sharp hypotheses in scientific research are investigated within the framework provided by Cognitive Constructivism and the FBST (Full Bayesian Significance Test). The constructivist framework is contrasted with the traditional epistemological settings for orthodox Bayesian and frequentist statistics provided by Decision Theory and Falsificationism.

The full Bayesian signi/cance test (FBST) for precise hypotheses is presented, with some illustrative applications. In the FBST we compute the evidence against the precise hypothesis. We discuss some of the theoretical properties of the FBST, and provide an invariant formulation for coordinate transformations, provided a reference density has been established. This evidence is the probability of the highest relative surprise set, “tangential” to the sub-manifold (of the parameter space) that defines the null hypothesis.

This study assessed the mode of test administration, birth variables, and students’ academic performance in Mathematics in Obubra Local Government Area of Cross River State, Nigeria. The study was guided by three null hypotheses following a quasi- experimental research design. Simple random and purposive sampling techniques were employed in selecting a sample of 250 respondents from a population of 5,792 students. Birth Order Checklist (BOC) and Mathematics Achievement Test (MAT) were used for data collection. The experimental group was assigned to (...) take a Computer-Based Test (CBT) while the control group took a Paper-Pencil Test (PPT) in mathematics. The null hypotheses were tested at .05 alpha level using two-way analysis of variance. Major findings revealed that, the interactive effects of gender and mode of test administration on the academic performance of students is non- significant [F(1,249)=0.028, p>.05, partial η2=.000]; the interactive effects of gender and birth order on the academic performance of students was not statistically significant [F(3,249)=0.782, p>.05, partial η2=.010]; the interactive effect of gender and birth order on the academic performance of students in mathematics is statistically significant [F(3,249)=2.854, p<.05, partial η2 =.034]. Based on these findings conclusions and recommendations were made for improved academic performance and school system effectiveness. (shrink)

Simultaneous hypothesis tests can fail to provide results that meet logical requirements. For example, if A and B are two statements such that A implies B, there exist tests that, based on the same data, reject B but not A. Such outcomes are generally inconvenient to statisticians (who want to communicate the results to practitioners in a simple fashion) and non-statisticians (confused by conflicting pieces of information). Based on this inconvenience, one might want to use tests that (...) satisfy logical requirements. However, Izbicki and Esteves shows that the only tests that are in accordance with three logical requirements (monotonicity, invertibility and consonance) are trivial tests based on point estimation, which generally lack statistical optimality. As a possible solution to this dilemma, this paper adapts the above logical requirements to agnostic tests, in which one can accept, reject or remain agnostic with respect to a given hypothesis. Each of the logical requirements is characterized in terms of a Bayesian decision theoretic perspective. Contrary to the results obtained for regular hypothesis tests, there exist agnostic tests that satisfy all logical requirements and also perform well statistically. In particular, agnostic tests that fulfill all logical requirements are characterized as region estimator-based tests. Examples of such tests are provided. (shrink)

Statistics play a critical role in biological and clinical research. However, most reports of scientific results in the published literature make it difficult for the reader to reproduce the statistical analyses performed in achieving those results because they provide inadequate documentation of the statistical tests and algorithms applied. The Ontology of Biological and Clinical Statistics (OBCS) is put forward here as a step towards solving this problem. Terms in OBCS, including ‘data collection’, ‘data transformation in statistics’, ‘data (...) visualization’, ‘statistical data analysis’, and ‘drawing a conclusion based on data’, cover the major types of statistical processes used in basic biological research and clinical outcome studies. OBCS is aligned with the Basic Formal Ontology (BFO) and extends the Ontology of Biomedical Investigations (OBI), an OBO (Open Biological and Biomedical Ontologies) Foundry ontology supported by over 20 research communities. We discuss two examples illustrating how the ontology is being applied. In the first (biological) use case, we describe how OBCS was applied to represent the high throughput microarray data analysis of immunological transcriptional profiles in human subjects vaccinated with an influenza vaccine. In the second (clinical outcomes) use case, we applied OBCS to represent the processing of electronic health care data to determine the associations between hospital staffing levels and patient mortality. Our case studies were designed to show how OBCS can be used for the consistent representation of statistical analysis pipelines under two different research paradigms. By representing statistics-related terms and their relations in a rigorous fashion, OBCS facilitates standard data analysis and integration, and supports reproducible biological and clinical research. (shrink)

Math prospective teachers must be able to think creatively and solve problems. The study looked into preservice teachers’ creative thinking and problem-solving abilities in statistics. The investigation was guided by a correlational design in a public university in the Philippines. Stratified random sampling was used to select the 103 study participants from two teacher education programs. Through google forms, data were collected using Torrance et al. (2008)’s tests of creative thinking and researcher-made statistics problem test. The findings revealed that (...) preservice teachers have commendable creative thinking, particularly fluency, flexibility, and elaboration skills. Still, they lack problem-solving skills in statistics, specifically with central tendency, dispersion, and position measures. The correlational analysis revealed no link between creative thinking and problem-solving. Still, creative thinking and problem-solving courses are recommended to help preservice teachers develop their fundamental skills as mathematics educators. (shrink)

Abstract: The Pull Bayesian Significance Test (FBST) for precise hy- potheses is applied to a Multivariate Normal Structure (MNS) model. In the FBST we compute the evidence against the precise hypothesis. This evi- dence is the probability of the Highest Relative Surprise Set (HRSS) tangent to the sub-manifold (of the parameter space) that defines the null hypothesis. The MNS model we present appears when testing equivalence conditions for genetic expression measurements, using micro-array technology.

The unit root problem plays a central role in empirical applications in the time series econometric literature. However, significance tests developed under the frequentist tradition present various conceptual problems that jeopardize the power of these tests, especially for small samples. Bayesian alternatives, although having interesting interpretations and being precisely defined, experience problems due to the fact that that the hypothesis of interest in this case is sharp or precise. The Bayesian significance test used in this article, for the (...) unit root hypothesis, is based solely on the posterior density function, without the need of imposing positive probabilities to sets of zero Lebesgue measure. Furthermore, it is conducted under strict observance of the likelihood principle. It was designed mainly for testing sharp null hypotheses and it is called FBST for Full Bayesian Significance Test. (shrink)

The rationale of this study was to examine the interactive effect of gender, test anxiety, and test items sequencing on the academic performance in mathematics among SS3 students in Calabar Education Zone, Cross River State. Two formulated null hypotheses directed the study. The study adopted the quasi-experimental design. Simple random sampling technique was used in drawing a sample of 474 students from a population of 8,549 SS3 students. A Mathematics Achievement Test (MAT) and a Test Anxiety Scale (TAS) were used (...) primarily as the instruments for data collection. The reliability coefficient obtained for both instruments were .88 and .82 respectively. The data collected were analyzed using descriptive statistics such as mean and standard deviation, while the null hypotheses were tested respectively, using Pearson product-moment Correlation, and Analysis of Covariance where applicable. Findings indicated that test anxiety contributes negatively to academic performance in Mathematics; there is a significant interaction effect between item sequencing and gender on academic performance; between item sequencing and test anxiety on academic performance; and between gender and test anxiety on academic performance in Mathematics respectively; The findings also showed that Based on these findings conclusion and recommendations were made. (shrink)

The purpose of this study was to investigate the relationships between the students’ self-efficacy, test anxiety and performance on Mathematics of Saint Joseph College, Junior High School Department for SY 2019- 2020. The respondents of the study were randomly chosen junior high school students. Descriptive correlational method of research was used. The data gathered were statistically treated using the Excel and IBM SPSS programs, which summarize the percentage scores, weighted means, correlation coefficients, independent t-test values, and corresponding p-values of relevant (...) statistical tools. Findings indicated that, at average, the students were not confident on their mathematical self-efficacy, moderately anxious on their mathematical test anxiety and satisfactory on their mathematical performance. More findings showed that the following variables have significant relationships: mathematical anxiety and mathematical self–efficacy; mathematical self-efficacy and mathematical performance; and mathematical test anxiety and mathematical performance. The higher the self-efficacy level, the lower the degree of testanxiety; the higher the self-efficacy, the better the mathematics performance; and the lower the test-anxiety, the better the performance. The study recommends regular conduct of diagnostic tests on mathematical self-efficacy and test anxiety and design programs to address the enhancement of learners’ mathematical self-efficacy and reduce their mathematical test anxiety. The researcher recommends Mathematics Learning Development Program (MLDP) as the output of the study. (shrink)

In this paper, the notion of degree of inconsistency is introduced as a tool to evaluate the sensitivity of the Full Bayesian Significance Test (FBST) value of evidence with respect to changes in the prior or reference density. For that, both the definition of the FBST, a possibilistic approach to hypothesis testing based on Bayesian probability procedures, and the use of bilattice structures, as introduced by Ginsberg and Fitting, in paraconsistent logics, are reviewed. The computational and theoretical advantages of using (...) the proposed degree of inconsistency based sensitivity evaluation as an alternative to traditional statistical power analysis is also discussed. (shrink)

The need to understand statistics in conducting research is very important, especially when working on quantitative data. The significance level is a very important concept that needs to be fully understood, particularly in hypothesis testing. Collado (2015) found out that graduate students have a fair level of understanding of the concepts of significance level; thus she constructed an e-module on the said topic designed for use by graduate students. The e-module was used in conducting true experimental design particularly a randomized (...) pretest-posttest control group design with two classes of graduate Statistics to compare instructions with e-module and without e-module. The class with e-module was only given a brief discussion on the interventions, while the group with e-module was taught with pure lecture method. The students taught with e-module obtained relatively higher scores than the students taught without the e-module only in one cluster of the lesson. After controlling the initial differences in scores, there was no significant difference in the mean scores of graduate students who differ in sex and intervention revealing further that e-module can be a substitute for the lecture method. This implies that e -module could reinforce graduate students’ independent learning and could help them cope with the lessons missed in class. E-module can also be taught in combination with traditional methods to better improve the understanding of the level of significance. (shrink)

The purpose of this paper is to provide a detailed technical protocol analysis of chess masters' evaluative expertise, paying particular attention to the analysis of the structure of their memory process in evaluating foreseen possibilities in games of dynamic equilibrium. The paper has two purposes. First, to publish a results chapter from my DPhil thesis (in revised journal article form) attending to the measurement of foresight in chess masters' evaluation process, testing alternative theories of cognitive expertise in the domain of (...) chess; and second to provide a subset of the technical graphical analysis that corresponds to that measurement to preserve this protocol analysis for access in the academic domain for future studies of expert memory and foresight (e.g., Ericsson & Simon, 1993). The step-by-step protocol analysis consists of: (i) an introduction to foresight cognition as hypothesis testing, (ii) a theoretical review in the domain of chess masters' expertise according to the theoretical frameworks in that field purporting hypotheses relevant to chess masters' evaluative skill processes, and (iii) summary tables and non-parametric statistical analysis corroborating chunking theory frameworks of expert cognition (e.g., DeGroot, 1965; Newell & Simon, 1972; Gobet, 1998; Gobet et al., 2004), and refuting the alternative search-evaluation models (e.g., Holding & Reynolds, 1982). Moreover, the journal article espouses the preservation of the traditional protocol analysis method core to the field of expert cognition (DeGroot, 1969; Kotov, 1971). The full protocol analysis can be found in monograph form here on my SSRN profile in ‘The role of falsification in hypothesis testing’. It takes the form of a specialist population study (e.g., detailed case study work; Luria, 1987). Thus the outline consists of a short introduction, a theoretical methodological review discussing protocol analysis methods for specialist population studies in cognition (with particular attention to the preservation of protocol analysis methods for chess studies in cognition and expert memory/ with a fresh angle on the foresight process), and the full set of protocol analyses with corresponding problem behaviour graphs. A subset of the main results has been published elsewhere (e.g., Cowley & Byrne, 2004; Cowley 2006), receiving scientific and scientific journalistic acclaim (e.g., Nature Online News 2004). (shrink)

This capstone project aimed to develop an offline computer-based assessment (CBA) tool that uses a computer instead of a traditional paper test in evaluating student learning. This addresses the difficulties faced by teachers in administering quarterly assessments. Incorporating technology into student assessment can increase student interest because of the immediate feedback generated automatically and can help teachers improve their work performance. This capstone project employed a developmental approach and utilized a modified ADDIE (Analysis, Design, and Development) model to design the (...) tool using Microsoft PowerPoint and Excel. Ten experts in mathematics, ICT, and assessment validated the face and content validity of the developed CBA tool. Based on the panel’s evaluation, the developed offline CBA tool in Statistics and Probability has passed all the assigned criteria, such as functionality, usability, efficiency, technicality, and accessibility. Overall, the developed CBA tool is suitable for use to address assessment-related issues. (shrink)

This study aimed to assess the retention of grade 12 students in statistics and probability, along with a comparative analysis of these retentions across the distinct topics of the subject. Statistics and probability subjects were taken by the students when they were in grade 11. Employing a quantitative approach, the research used descriptive-comparative design to describe the level of retention of the students and compare the retention of the students in each topic. These encompass random variables and probability distribution, normal (...) distribution, sampling and sampling distribution, and estimation parameters. The retention of the students studying at Nueva Vizcaya General Comprehensive High School, a public school in Nueva Vizcaya, Philippines was analyzed through the validated retention test administered to them. Using frequency count and percent, the result revealed that the grade 12 students’ retention was described as “poor retention rate”. Repeated-measures ANOVA confirmed that the retention of the students in all the topics are all poor. Hence, teachers should consider making an intervention to improve the retention of the students in statistics and probability. They may consider innovative ways to engage the students in learning. Also, the factors that influence the students in solving problems in designing the interventions. (shrink)

Assessment of students’ attitudes towards test-taking in secondary schools in Afikpo Education Zone of Ebonyi State, Nigeria was the main thrust of this study. The study was guided by four null hypotheses in line with the ex-post facto research design. Proportionate stratified random sampling technique was employed in selecting a sample 1,276 respondents from a population of 12,763 students distributed across 43 public and 71 private secondary schools in the study area. Students’ Attitudes Towards Test-Taking Questionnaire (SATTQ) with Cronbach's alpha (...) reliability coefficient of .893 was used for data collection. The null hypotheses were all tested at .05 level of significance using population t-test and independent t-test statistical methods. Emerging findings showed that the level of students’ attitudes towards test-taking as an academic activity in secondary schools is significantly high. It was also shown that males students, students in urban and private schools significantly differ in their attitudes towards test-taking as an academic activity, from female students and students in rural and public secondary schools. Based on these findings, it was recommended, amongst others, that all students irrespective of gender, school type and school location should be properly counselled by both teachers and professional counsellors to develop positive attitudes towards taking tests in schools. Keywords:. (shrink)

In this article I give a critical evaluation of the use and limitations of null-model-based hypothesis testing as a research strategy in the biological sciences. According to this strategy, the null model based on a randomization procedure provides an appropriate null hypothesis stating that the existence of a pattern is the result of random processes or can be expected by chance alone, and proponents of other hypotheses should first try to reject this null hypothesis in order to demonstrate their own (...) hypotheses. Using as an example the controversy over the use of null hypotheses and null models in species co-occurrence studies, I argue that null-model-based hypothesis testing fails to work as a proper analog to traditional statistical null-hypothesis testing as used in well-controlled experimental research, and that the random process hypothesis should not be privileged as a null hypothesis. Instead, the possible use of the null model resides in its role of providing a way to challenge scientists’ commonsense judgments about how a seemingly unusual pattern could have come to be. Despite this possible use, null-model-based hypothesis testing still carries certain limitations, and it should not be regarded as an obligation for biologists who are interested in explaining patterns in nature to first conduct such a test before pursuing their own hypotheses. (shrink)

Due to the unprecedented COVID-19 incident, basic education institutions have faced different challenges in their teaching-learning activities. Particularly conducting assessments remotely during COVID-19 has posed extraordinary challenges for basic education institutions owing to lack of preparation superimposed with the inherent problems of remote assessment. Descriptive-evaluation research was employed since the present study attempts to examines the assessment practices and competences on remote learning assessment of teachers in Graceville National High School. For the study, questionnaires were prepared and data nine (9) (...) senior high school teachers and forty-two (42) junior high school teachers were collected and analyzed. The gathered data from this study were subjected to the descriptive and inferential statistics. The data revealed that the most frequent number of the teacher- respondents in the study was 36 - 40 years old at age, female, Technology Livelihood Education (TLE) major, 6 - 10 years in service in Department of Education, and bachelor's degree holders. More so, the teacher respondents' level of teacher competencies on remote learning assessment was observed high competent. In addition, level of assessment practices in terms of clarity of assessment, time and effort on task, quality of feedback, motivational belief and self-esteem to learners, self-assessment and reflection of learning of the learners, and assessment - content and process in adapting teaching to students needs was mostly practice. However, it was completely practicing the interaction and dialogue about learning progress. The results confirmed that there was a significant difference on the teacher respondents' level of competence on the remote learning assessment when group according to their age, gender, areas of specialization, and training attended. On the other hands, teacher year of teaching and educational attainment revealed it has no significant difference on their level of competence on the remote learning assessment. Looking forward, that age, gender, year of teaching, areas of specialization, educational attainment, and training attended significantly differs to the level of assessment practices of the teachers. It also observed that the teachers experiencing highly challenges encountered on the remote learning assessment. It is recommended to implement the proposed school-based testing reforms and should be monitored and evaluated for the optimum advantage of the school and community. (shrink)

The movement called Experimental Philosophy (‘x-Phi’) has now passed its tenth anniversary. Its central insight is compelling: When an argument hinges on accepting certain ‘facts’ about human perception, knowledge, or judging, the evoking of relevant intuitions by thought experiments is intended to make those facts seem obvious. But these intuitions may not be shared universally. Experimentalists propose testing claims that traditionally were intuition-based using real experiments, with real samples. Demanding that empirical claims be empirically supported is certainly reasonable; though experiments (...) are not necessarily the only means available. When experiments are conducted, adequately interpreting their results requires understanding the study’s design (and possibly flaws) that produced them. Experiment-based reports should document the design clearly. If Plato, writing his Meno, replaced accounts of Socrates demonstrating geometry to a slave-boy, with a survey of 100 real boys—some grasping his demonstrations, others not—what conclusions could be reached? Before answering, the reader needs details on key design questions, including (among others): (a) What population are these samples intended to represent? (E.g., ‘all slave boys’?; ‘math-ignorant people’?; ‘everyone’?) (b) What statistical tests were conducted, on what assumptions? (c) How was ‘significance’ of results determined? (d) Was the test instrument’s validity established? For readers wishing to explore x-Phi’s potentials, as contributors or as interpreters of their findings, this paper offers some cautionary considerations. Throughout their literature, examples can be found casting doubt on some experimentalists’ findings, due to design-related issues. Increased awareness of methodological questions would tighten the x-phi literature, going forward . (shrink)

Research in experimental philosophy has increasingly been turning to corpus methods to produce evidence for empirical claims, as they open up new possibilities for testing linguistic claims or studying concepts across time and cultures. The present article reviews the quasi-experimental studies that have been done using textual data from corpora in philosophy, with an eye for the modeling and experimental design that enable statistical inference. I find that most studies forego comparisons that could control for confounds, and that only (...) a little less than half employ statistical testing methods to control for chance results. Furthermore, at least some researchers make modeling decisions that either do not take into account the nature of corpora and of the word-concept relationship, or undermine the experiment's capacity to answer research questions. I suggest that corpus methods could both provide more powerful evidence and gain more mainstream acceptance by improving their modeling practices. (shrink)

This study examined correlations between moral value judgments on a 17-item Moral Intuition Survey (MIS), and participant scores on the Short-D3 “Dark Triad” Personality Inventory—a measure of three related “dark and socially destructive” personality traits: Machiavellianism, Narcissism, and Psychopathy. Five hundred sixty-seven participants (302 male, 257 female, 2 transgendered; median age 28) were recruited online through Amazon Mechanical Turk and Yale Experiment Month web advertisements. Different responses to MIS items were initially hypothesized to be “conservative” or “liberal” in line with (...) traditional public divides. Our demographic data confirmed all of these hypothesized categorizations. We then tested two broad, exploratory hypotheses: (H1) the hypothesis that there would be “many” significant correlations between conservative MIS judgments and the Dark Triad, and (H2) the hypothesis that there would be no significant correlations between liberal MIS judgments and Machiavellianism or Psychopathy, but “some” significant correlations between liberal MIS judgments and Narcissism. Because our hypotheses were exploratory and we ran a large number of statistical tests (62 total), we utilized a Bonferroni Correction to set a very high threshold for significance (p = .0008). Our results broadly supported our two hypotheses. We found eleven significant correlations between conservative MIS judgments and the Dark Triad—all at significance level of p < .00001—but no significant correlations between the Dark Triad and liberal MIS judgments. We believe that these results raise provocative moral questions about the personality bases of moral judgments. In particular, we propose that because the Short-D3 measures three “dark and antisocial” personality traits, our results raise some prima facie worries about the moral justification of some conservative moral judgments. (shrink)

When comparing alternative courses of action, modern military decision makers often must consider both the military effectiveness and the ethical consequences of the available alternatives. The basis, design, calibration, and performance of a principles-based computational model of ethical considerations in military decision making are reported in this article. The relative ethical violation (REV) model comparatively evaluates alternative military actions based upon the degree to which they violate contextually relevant ethical principles. It is based on a set of specific ethical principles (...) deemed by philosophers and ethicists to be relevant to military courses of action. A survey of expert and non-expert human decision makers regarding the relative ethical violation of alternative actions for a set of specially designed calibration scenarios was conducted to collect data that was used to calibrate the REV model. Perhaps unsurprisingly, the survey showed that people, even experts, disagreed greatly amongst themselves regarding the scenarios’ ethical considerations. Despite this disagreement, two significant results emerged. First, after calibration the REV model performed very well in terms of replicating the ethical assessments of human experts for the calibration scenarios. The REV model outperformed an earlier model that was based on tangible consequences rather than ethical principles, that earlier model performed comparably to human experts, the experts outperformed human non-experts, and the non-experts outperformed random selection of actions. All of these performance comparisons were measured quantitatively and confirmed with suitable statistical tests. Second, although humans tended to value some principles over others, none of the ethical principles involved—even the principle of not harming civilians—completely overshadowed all of the other principles. (shrink)

Social integration was theorized to be a ‘secularizing’ process for immigrants in Western Europe. Assuming that immigrants adapt to new social environments by complying with the mainstream culture of their receiving countries, immigrant religiosity is expected to decline as they assimilate in societies where secular norms prevail. Alternatively, religion could be a coping mechanism for immigrants who struggle to assimilate in their receiving countries. ‘Buffer’ theories of religion suggest that religious identity could be interchangeable with ethnicity and nationality to mitigate (...) the identity conflicts immigrants experience. This paper addresses the following research question: What role does religion play in the identity conflict experienced by immigrants who are both an ethnic minority and a national of a Western European country? Particularly, I explore the pertinence of religious identity for first-generation Sub-Saharan African Christian immigrants (SSACI) in Germany and France, where the models of immigrant assimilation diverge. Statistical tests were conducted on data derived from two surveys to compare religious, national, and ethnic self-identities at the group and individual levels. The group comparisons suggest that Christianity was indeed more salient for SSACI than native-born Christians. SSACIs without citizenship were also more likely to experience identity conflict, to which they may cope by associating less with their ethnicity or more with their religious identity. Perceived discrimination was associated with identity conflict only in Germany where immigrant assimilation is traditionally based on a common ancestry, in contrast to the values-based model in France. These are consistent with the predictions derived from ‘buffer’ theories of immigrant religiosity but longitudinal studies are needed for a more robust understanding of these trends. (shrink)

To succeed, political science usually requires either prediction or contextual historical work. Both of these methods favor explanations that are narrow-scope, applying to only one or a few cases. Because of the difficulty of prediction, the main focus of political science should often be contextual historical work. These epistemological conclusions follow from the ubiquity of causal fragility, under-determination, and noise. They tell against several practices that are widespread in the discipline: wide-scope retrospective testing, such as much large-n statistical work; (...) lack of emphasis on prediction; and resources devoted to ‘pure theory’ divorced from frequent empirical application. I illustrate, via Donatella della Porta’s work on political violence, the important role that is still left for theory. I conclude by assessing the scope for political science to offer policy advice. (shrink)

Aim: The researcher studied how the teachers at Guangdong Business and Technology University manage change based on the present situation in the country. -/- Methodology: This study utilized the descriptive – comparative research design with 275 teachers as respondents. Statistical test of data includes frequency count and percentage, weighted mean, t- test and/or ANOVA. -/- Results: Teacher respondents are very much ready to manage the change for the teaching and learning based on teaching-related factors which ranked first, as well (...) as on teaching-related factors which ranked second, and on technology-related factors which ranked third. It is noticeable that technology-related factor was the least assessed factors as regards their readiness to manage the change. Generally, an over-all mean value of 3.52 reveals that teachers are very much ready to manage the change for the teaching and learning. Based on the result, teacher respondents strongly agree on their level of motivation on their teaching and learning performance. The result reveals that teachers are highly motivated in performing their job as teachers based on their own assessment. -/- Conclusion: Majority of the respondents are female teachers in middle age aiming to earn their doctoral degree and have been in the university for not more than five years. Teachers believed that they are very much ready to manage the change for the teaching and learning. They also seem to be less ready in terms of accessing professional development opportunities that focus on continuous improvement of digital-age teaching skills. The use of variety of assessment strategies applying the technology and the implementation of alternative strategies in the classroom seems to be less managed by the teachers. They also have relatively the same assessment on how ready they are to manage the change in the teaching and learning regardless of their sex, age, educational level they have attained, and the length of stay in the institution. (shrink)

This article explores some open questions related to the problem of verification of theories in the context of empirical sciences by contrasting three epistemological frameworks. Each of these epistemological frameworks is based on a corresponding central metaphor, namely: (a) Neo-empiricism and the gambling metaphor; (b) Popperian falsificationism and the scientific tribunal metaphor; (c) Cognitive constructivism and the object as eigen-solution metaphor. Each of one of these epistemological frameworks has also historically co-evolved with a certain statistical theory and method for (...) testing scientific hypotheses, respectively: (a) Decision theoretic Bayesian statistics and Bayes factors; (b) Frequentist statistics and p-values; (c) Constructive Bayesian statistics and e-values. This article examines with special care the Zero Probability Paradox (ZPP), related to the verification of sharp or precise hypotheses. Finally, this article makes some remarks on Lakatos’ view of mathematics as a quasi-empirical science. (shrink)

The purpose of this study is to find out that whether the jobs of nurses in Pakistan are fulfilling their necessary requirements or not. This issue is being analyzed by the relation of Person-Job (P-J) Fit with three different JobBehaviors and the whole relation is being tested under the moderation of Agreeableness, which is a personality trait of the Big5 Model. A survey method is deployed, questionnaires are used to obtain data. 120 Nurses were accessed from different hospitals of Islamabad/Rawalpindi. (...) Data were analyzed through statistical tests and regression analysis. Findings of the study highlight that P-J fit is related positively to job satisfaction of nurses and negatively to their Turnover Intentions.Where no significant impact of agreeableness as a moderator is found for this study. The Sample size was too small (120participants). This may restrict the generalizability of the studies. In the Pakistani context, only a limited study has been conducted on nurses. Thus, this piece of research will play a significant role in enhancing and boosting the confidence of deprived nurses of Pakistan by identifying the causes of negative job outcomes and help in mitigating those triggers. (shrink)

This paper introduces pragmatic hypotheses and relates this concept to the spiral of scientific evolution. Previous works determined a characterization of logically consistent statistical hypothesis tests and showed that the modal operators obtained from this test can be represented in the hexagon of oppositions. However, despite the importance of precise hypothesis in science, they cannot be accepted by logically consistent tests. Here, we show that this dilemma can be overcome by the use of pragmatic versions of precise (...) hypotheses. These pragmatic versions allow a level of imprecision in the hypothesis that is small relative to other experimental conditions. The introduction of pragmatic hypotheses allows the evolution of scientific theories based on statistical hypothesis testing to be interpreted using the narratological structure of hexagonal spirals, as defined by Pierre Gallais. (shrink)

The inflation of Type I error rates is thought to be one of the causes of the replication crisis. Questionable research practices such as p-hacking are thought to inflate Type I error rates above their nominal level, leading to unexpectedly high levels of false positives in the literature and, consequently, unexpectedly low replication rates. In this article, I offer an alternative view. I argue that questionable and other research practices do not usually inflate relevant Type I error rates. I begin (...) with an introduction to Type I error rates that distinguishes them from theoretical errors. I then illustrate my argument with respect to model misspecification, multiple testing, selective inference, forking paths, exploratory analyses, p-hacking, optional stopping, double dipping, and HARKing. In each case, I demonstrate that relevant Type I error rates are not usually inflated above their nominal level, and in the rare cases that they are, the inflation is easily identified and resolved. I conclude that the replication crisis may be explained, at least in part, by researchers’ misinterpretation of statistical errors and their underestimation of theoretical errors. (shrink)

How and when do we learn to understand other people’s perspectives and possibly divergent beliefs? This question has elicited much theoretical and empirical research. A puzzling finding has been that toddlers perform well on so-called implicit false belief (FB) tasks but do not show such capacities on traditional explicit FB tasks. I propose a navigational approach, which offers a hitherto ignored way of making sense of the seemingly contradictory results. The proposal involves a distinction between how we navigate FBs as (...) they relate to (1) our current affordances (here & now navigation) as opposed to (2) presently non-actual relations, where we need to leave our concrete embodied/situated viewpoint (counterfactual navigation). It is proposed that whereas toddlers seem able to understand FBs in their current affordance space, they do not yet possess the resources to navigate in abstraction from such concrete affordances, which explicit FB tests seem to require. It is hypothesized that counterfactual navigation depends on the development of “sensorimotor priors,” i.e., statistical expectations of own kinesthetic re-afference, which evidence now suggests matures around age four, consistent with core findings of explicit FB performance. (shrink)