An Assessment of the Performances of Several Univariate Tests of Normality

The importance of checking the normality assumption in most statistical procedures especially parametric tests cannot be over emphasized as the validity of the inferences drawn from such procedures usually depend on the validity of this assumption. Numerous methods have been proposed by different authors over the years, some popular and frequently used, others, not so much. This study addresses the performance of eighteen of the available tests for different sample sizes, significance levels, and for a number of symmetric and asymmetric distributions by conducting a Monte-Carlo simulation. The results showed that considerable power is not achieved for symmetric distributions when sample size is less than one hundred and for such distributions, the kurtosis test is most powerful provided the distribution is leptokurtic or platykurtic. The Shapiro-Wilk test remains the most powerful test for asymmetric distributions. We conclude that different tests are suitable under different characteristics of alternative distributions.

An Alternative Goodness-of-fit Test for Normality with Unknown Parameters

Goodness-of-fit tests have been studied by many researchers. Among them, an alternative statistical test for uniformity was proposed by Chen and Ye (2009). The test was used by Xiong (2010) to test normality for the case that both location parameter and scale parameter of the normal distribution are known. The purpose of the present thesis is to extend the result to the case that the parameters are unknown. A table for the critical values of the test statistic is obtained using Monte Carlo simulation. The performance of the proposed test is compared with the Shapiro-Wilk test and the Kolmogorov-Smirnov test. Monte-Carlo simulation results show that proposed test performs better than the Kolmogorov-Smirnov test in many cases. The Shapiro Wilk test is still the most powerful test although in some cases the test proposed in the present research performs better.

International stock portfolio selection and performance measures recognizing higher moments of return distributions

Since the seminal works of Markowitz (1952), Sharpe (1964), and Lintner (1965), numerous studies on portfolio selection and performance measure have been based upon the mean-variance framework. However, several researchers (e.g., Arditti (1967, and 1971), Samuelson (1970), and Rubinstein (1973)) argue that the higher moments cannot be neglected unless there is reason to believe that: (i) the asset returns are normally distributed and the investor's utility function is quadratic, or (ii) the empirical evidence demonstrates that higher moments are irrelevant to the investor's decision. Based on the same argument, this dissertation investigates the impact of higher moments of return distributions on three issues concerning the 14 international stock markets.^ First, the portfolio selection with skewness is determined using: the Polynomial Goal Programming in which investor preferences for skewness can be incorporated. The empirical findings suggest that the return distributions of international stock markets are not normally distributed, and that the incorporation of skewness into an investor's portfolio decision causes a major change in the construction of his optimal portfolio. The evidence also indicates that an investor will trade expected return of the portfolio for skewness. Moreover, when short sales are allowed, investors are better off as they attain higher expected return and skewness simultaneously.^ Second, the performance of international stock markets are evaluated using two types of performance measures: (i) the two-moment performance measures of Sharpe (1966), and Treynor (1965), and (ii) the higher-moment performance measures of Prakash and Bear (1986), and Stephens and Proffitt (1991). The empirical evidence indicates that higher moments of return distributions are significant and relevant to the investor's decision. Thus, the higher moment performance measures should be more appropriate to evaluate the performances of international stock markets. The evidence also indicates that various measures provide a vastly different performance ranking of the markets, albeit in the same direction.^ Finally, the inter-temporal stability of the international stock markets is investigated using the Parhizgari and Prakash (1989) algorithm for the Sen and Puri (1968) test which accounts for non-normality of return distributions. The empirical finding indicates that there is strong evidence to support the stability in international stock market movements. However, when the Anderson test which assumes normality of return distributions is employed, the stability in the correlation structure is rejected. This suggests that the non-normality of the return distribution is an important factor that cannot be ignored in the investigation of inter-temporal stability of international stock markets. ^

Disciplining democracy: United Nations peacekeeping, international security and democratization in the post -Cold War era

After the end of the Cold War, democratization and good governance became the organizing concepts for activities of the United Nations, regional organizations and states in the fields of peace, development and security. How can this increasing interest in democratization and its connection with international security be explained? This dissertation applies the theoretical tools developed by Michel Foucault in his discussions of disciplinarity and government to the analysis of the United Nations debate on democracy in the 1990s, and of two United Nations pro-democracy peacekeeping operations and their aftermath: the United Nations interventions in Haiti and Croatia. It probes “how” certain techniques of power came into being and describes their effects, using as data the texts that elaborate the United Nations understanding of democracy and the texts that constitute peacekeeping. ^ In the face of the proliferation of unpredictable threats in the last decades of the twentieth century a new form of international power emerged. Order in the international arena increasingly was maintained through activities aimed at reducing risk and increasing predictability through the normalization of “rogue” states. The dissertation shows that in the context of these activities, which included but were not limited to UN peacekeeping, normality was identified with democracy, non-democratic regimes with international threats, and democratization with international security. “Good governance” doctrines translated the political debate on democracy into the technical language of functioning state institutions. International organizations adopted good governance as the framework that made democratization a universal task within the reach of their expertise. In Haiti, the United Nations engaged in efforts to transform punishment institutions (the judiciary, police and the prison) into disciplined and disciplinary machines. In Croatia, agreements signed in the context of peacekeeping established in detail the rules of functioning of administrations and the monitoring mechanisms for their implementation. However, in Haiti, the institutions promoted were not sustainable. And in Croatia reforms are stalled by lack of consensus. ^ This dissertation puts efforts to bring about democracy through peacekeeping in the context of a specific modality of power and suggests caution in engaging in universal normalizing endeavors. ^

Examining moderators of the hindsight bias in the context of civil legal decision -making: Counterfactuals, causal proximity, and self -referencing

The current research sought to clarify the diverging relationships between counterfactual thinking and hindsight bias observed in the literature thus far. In a non-legal context, Roese and Olson (1996) found a positive relationship between counterfactuals and hindsight bias, such that counterfactual mutations that undid the outcome also increased participants’ ratings of the outcome’s a priori likelihood. Further, they determined that this relationship is mediated by causal attributions about the counterfactually mutated antecedent event. Conversely, in the context of a civil lawsuit, Robbennolt and Sobus (1997) found that the relationship between counterfactual thinking and hindsight bias is negative. The current research sought to resolve the conflicting findings in the literature within a legal context. ^ In Experiment One, the manipulation of the normality of the defendant’s target behavior, designed to manipulate participants’ counterfactual thoughts about said behavior, did moderate the hindsight effect of outcome knowledge on mock jurors’ judgments of the foreseeability of that outcome as well as their negligence verdicts. Although I predicted that counterfactual thinking would increase, or exacerbate, the hindsight bias, as found by Roese and Olson (1996), my results provided some support for Robbenolt and Sobus’s (1997) finding that counterfactual thinking decreases the hindsight bias. Behavior normality did not moderate the hindsight effect of outcome knowledge in Experiment Two, nor did causal proximity in Experiment Three. ^ Additionally, my hypothesis that self-referencing may be an effective hindsight debiasing technique received little support across the three experiments. Although both the self-referencing instructions and self-report measure consistently decreased mock jurors’ likelihood of finding the defendant negligent, and self-referencing instructions decreased their foreseeability ratings in studies two and three, the self-referencing manipulation did not interact with outcome knowledge to moderate a hindsight bias effect on either foreseeability or negligence judgments. The consistent pattern of results across the three experiments, however, suggests that self-referencing may be an effective technique in reducing the likelihood of negligence verdicts.^

Using sonic enhancement to augment non-visual tabular navigation

More information is now readily available to computer users than at any time in human history; however, much of this information is often inaccessible to people with blindness or low-vision, for whom information must be presented non-visually. Currently, screen readers are able to verbalize on-screen text using text-to-speech (TTS) synthesis; however, much of this vocalization is inadequate for browsing the Internet. An auditory interface that incorporates auditory-spatial orientation was created and tested. For information that can be structured as a two-dimensional table, links can be semantically grouped as cells in a row within an auditory table, which provides a consistent structure for auditory navigation. An auditory display prototype was tested.^ Sixteen legally blind subjects participated in this research study. Results demonstrated that stereo panning was an effective technique for audio-spatially orienting non-visual navigation in a five-row, six-column HTML table as compared to a centered, stationary synthesized voice. These results were based on measuring the time- to-target (TTT), or the amount of time elapsed from the first prompting to the selection of each tabular link. Preliminary analysis of the TTT values recorded during the experiment showed that the populations did not conform to the ANOVA requirements of normality and equality of variances. Therefore, the data were transformed using the natural logarithm. The repeated-measures two-factor ANOVA results show that the logarithmically-transformed TTTs were significantly affected by the tonal variation method, F(1,15) = 6.194, p= 0.025. Similarly, the results show that the logarithmically transformed TTTs were marginally affected by the stereo spatialization method, F(1,15) = 4.240, p=0.057. The results show that the logarithmically transformed TTTs were not significantly affected by the interaction of both methods, F(1,15) = 1.381, p=0.258. These results suggest that some confusion may be caused in the subject when employing both of these methods simultaneously. The significant effect of tonal variation indicates that the effect is actually increasing the average TTT. In other words, the presence of preceding tones increases task completion time on average. The marginally-significant effect of stereo spatialization decreases the average log(TTT) from 2.405 to 2.264.^

Obesity and Serum High Sensitivity C-Reactive Protein Levels Among Elderly Turkish Immigrants in the Netherlands with Type 2 Diabetes

The study examined the associations of anthropometric measures of obesity with high sensitivity C-reactive protein (hs-CRP) levels in Turkish immigrants with type 2 diabetes (T2D) living in the Netherlands. A total of 110 participants, physician-diagnosed with T2D, aged 30 years and older were recruited from multiple sources from The Hague, Netherlands. Serum hs-CRP levels were measured with immunoturbidimetric assay. Glycated hemoglobin (A1C) was determined by high-pressure liquid chromatography. Measures of obesity: body weight, body mass index (BMI), waist circumference (WC), hip circumference (HC), waist-to-hip ratio (WHR), and waist-to-height ratio (WHtR) were determined. Statistical analysis included descriptive statistics, Pearson’s correlations and multiple linear regressions (MLR) stratified by gender. Hs-CRP was log transformed to achieve normality. Subjects with hs-CRP levels >10 mg/L (n = 17) were excluded from the analysis. Females had a higher BMI (p = 0.007), HC (p < 0.001), and WHtR (p = 0.011) as compared to males. Conversely, males had a higher weight (p = 0.007), and WHR (p < 0.001) than females. MLR showed that after controlling for covariates, log hs-CRP was positively associated with BMI (B = 0.039, SE = 0.019, β = 0.287, p < 0.05), WC (B = 0.025, SE = 0.011, β = 0.332, p < 0.05) and WHtR (B = 4.015, SE = 1.464, β = 0.376, p < 0.01) in females only. Gender-specific associations between obesity measures and hs-CRP level need to be further investigated in the Turkish immigrant population. Hs-CRP assessment may be added as a standard of care for T2D treatment within this population.

Examining Moderators of the Hindsight Bias in the Context of Civil Legal Decision-Making: Counterfactuals, Causal Proximity, and Self-Referencing

The current research sought to clarify the diverging relationships between counterfactual thinking and hindsight bias observed in the literature thus far. In a non-legal context, Roese and Olson (1996) found a positive relationship between counterfactuals and hindsight bias, such that counterfactual mutations that undid the outcome also increased participants’ ratings of the outcome’s a priori likelihood. Further, they determined that this relationship is mediated by causal attributions about the counterfactually mutated antecedent event. Conversely, in the context of a civil lawsuit, Robbennolt and Sobus (1997) found that the relationship between counterfactual thinking and hindsight bias is negative. The current research sought to resolve the conflicting findings in the literature within a legal context. In Experiment One, the manipulation of the normality of the defendant’s target behavior, designed to manipulate participants’ counterfactual thoughts about said behavior, did moderate the hindsight effect of outcome knowledge on mock jurors’ judgments of the foreseeability of that outcome as well as their negligence verdicts. Although I predicted that counterfactual thinking would increase, or exacerbate, the hindsight bias, as found by Roese and Olson (1996), my results provided some support for Robbenolt and Sobus’s (1997) finding that counterfactual thinking decreases the hindsight bias. Behavior normality did not moderate the hindsight effect of outcome knowledge in Experiment Two, nor did causal proximity in Experiment Three. Additionally, my hypothesis that self-referencing may be an effective hindsight debiasing technique received little support across the three experiments. Although both the self-referencing instructions and self-report measure consistently decreased mock jurors’ likelihood of finding the defendant negligent, and self-referencing instructions decreased their foreseeability ratings in studies two and three, the self-referencing manipulation did not interact with outcome knowledge to moderate a hindsight bias effect on either foreseeability or negligence judgments. The consistent pattern of results across the three experiments, however, suggests that self-referencing may be an effective technique in reducing the likelihood of negligence verdicts.

Lecture by Juan Manuel Echavarria, given at Florida International University, March 7, 2012

Juan Manuel Echavarria discusses his exhibition which includes 24 paintings created by men and women who participated in Colombia’s war. All 35 participants were rank and file soldiers demobilized either under the Ley de Justicia y Paz (Justice and Peace Law), or because they deserted or were wounded in combat. They spent two years painting their personal experiences, illustrating the rural tragedy; witnessing the involvement of drug traffickers, capturing the painful repertoire of violence in Colombia, which for years has played out alongside daily life, blending in with normality. Introduction by Carol Damien.

A Study on the Correlation of Bivariate And Trivariate Normal Models

Suppose two or more variables are jointly normally distributed. If there is a common relationship between these variables it would be very important to quantify this relationship by a parameter called the correlation coefficient which measures its strength, and the use of it can develop an equation for predicting, and ultimately draw testable conclusion about the parent population. This research focused on the correlation coefficient ρ for the bivariate and trivariate normal distribution when equal variances and equal covariances are considered. Particularly, we derived the maximum Likelihood Estimators (MLE) of the distribution parameters assuming all of them are unknown, and we studied the properties and asymptotic distribution of . Showing this asymptotic normality, we were able to construct confidence intervals of the correlation coefficient ρ and test hypothesis about ρ. With a series of simulations, the performance of our new estimators were studied and were compared with those estimators that already exist in the literature. The results indicated that the MLE has a better or similar performance than the others.