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This research study is devoted towards exploring the nature of error functions and estimable treatment contrasts in a model involving Graeco Latin square designs (GLSDs) of orders 4 and 5 in situations wherein there are left- and right-neighbor effects present in the underlying linear model. The model is assumed to be circular. It transpires from the current study that data analysis for GLSDs in the presence of neighbor effects has to be carefully handled.

To date, experimental research on the effect of faking on personality measures has used two types of designs: within-subject designs and between-subjects designs. None of these designs permit us to control for the effects of transient error on faking. Using a Latin-square design (LSD), the current study examines the effects of faking on the Big Five as assessed by a quasi-ipsative forced-choice (FC) personality inventory. LSD is a type of experimental design that simultaneously permits us to control for between-subject differences, within-subject variability, and transient error. The sample consisted of 246 participants (four experimental groups, assessed twice, 2-3 week interval). The results showed that (1) faking effect size can be largely attributed to transient error and (2) the quasi-ipsative FC format shows great resistance to faking behavior. The average effect size (Cohen’s d) for the Big Five was 0.21, 0.12, and 0.09 for observed faking, transient error, and true faking, respectively. On average, 62% of observed faking effect size can be attributed to transient error. To conclude, we discuss the implications of these findings for the research and practice of personnel selection.

Experimental designs are commonly used to produce valid, defensible, and supportable conclusions. Among commonly used block designs, the class of Latin square designs is used to study factors or treatment levels expressed as Latin letters and applying two blocking factors in rows and columns to simultaneously control two sources of nuisance variability. Another block design in which the error can be controlled by blocking three nuisance factors is obtained by simply using two superimposed Latin square designs, with one using the Latin letters and the other using the Greek letters. Such a design is termed as a Graeco-Latin square (GLS) design. While observing or measuring data in field or lab experiments, it is often noted to have vague, incomplete, and imprecise data for whatsoever reasons. In this regard, researchers have proposed various emerging approaches, which are based on fuzzy, intuitionistic fuzzy, and neutrosophic logic, and provide deeper understanding, analysis, and interpretations of the data. In this paper, we provide a brief review of the history of GLS designs and propose a neutrosophic Graeco-Latin square design, its model, and the analysis. To illustrate this, we have considered an experimental study which analyzes the effects of different formulations of a rocket propellant, which are used in aircrew escape systems, on the observed burning rate.

This study introduced a novel exact-scheme analysis of variance to tackle the challenge of incomplete data within the Greco-Latin square experimental design (GLSED), specifically for scenarios with a single missing observation across any treatment and block level, thus eliminating the need for conventional data imputation methods. This approach innovatively addresses and mitigates the bias in the treatment sum of squares, a significant drawback of traditional missing plot techniques, by providing a precise, exact-scheme-based formula for calculating the treatment sum of squares in fixed-effect GLSED contexts with unrecorded values. Moreover, it offers a method for correcting biased treatment sum of squares values, presenting an adjustment mechanism for instances where the least squares method was previously employed to estimate missing values. This comprehensive strategy not only enhances the methodological accuracy and integrity of GLSED studies but also contributes significantly to the field by offering a solution to navigate the complexities of incomplete datasets without resorting to data imputation, thus improving the rigor and validity of experimental designs in the face of missing data challenges.

Background Scrolling is a perceived barrier in the use of bring your own device (BYOD) to capture electronic patient reported outcomes (ePROs). This study explored the impact of scrolling on the measurement equivalence of electronic patient-reported outcome measures (ePROMs) in the presence and absence of scrolling. Methods Adult participants with a chronic condition involving daily pain completed ePROMs on four devices with different scrolling properties: a large provisioned device not requiring scrolling; two provisioned devices requiring scrolling – one with a “smart-scrolling” feature that disabled the “next” button until all information was viewed, and a second without this feature; and BYOD with smart-scrolling. The ePROMs included were the SF-12, EQ-5D-5L, and three pain measures: a visual analogue scale, a numeric response scale and a Likert scale. Participants completed English or Spanish versions according to their first language. Associations between ePROM scores were assessed using intraclass correlation coefficients (ICCs), with lower bound of 95% confidence interval (CI) > 0.7 indicating comparability. Results One hundred fifteen English- or Spanish-speaking participants (21-75y) completed all four administrations. High associations between scrolling and non-scrolling were observed (ICCs: 0.71–0.96). The equivalence threshold was met for all but one SF-12 domain score (bodily pain; lower 95% CI: 0.65) and two EQ-5D-5L item scores (pain/discomfort, usual activities; lower 95% CI: 0.64/0.67). Age, language, and device size produced insignificant differences in scores. Conclusions The measurement properties of PROMs are preserved even in the presence of scrolling on a handheld device. Further studies that assess scrolling impact over long-term, repeated use are recommended.

Recently, many image encryption schemes have been developed using Latin squares. When encrypting a color image, these algorithms treat the color image as three greyscale images and encrypt these greyscale images one by one using the Latin squares. Obviously, these algorithms do not sufficiently consider the inner connections between the color image and Latin square and thus result in many redundant operations and low efficiency. To address this issue, in this paper, we propose a new color image encryption algorithm (CIEA) that sufficiently considers the properties of the color image and Latin square. First, we propose a two-dimensional chaotic system called 2D-LSM to address the weaknesses of existing chaotic systems. Then, we design a new CIEA using orthogonal Latin squares and 2D-LSM. The proposed CIEA can make full use of the inherent connections of the orthogonal Latin squares and color image and executes the encryption process in the pixel level. Simulation and security analysis results show that the proposed CIEA has a high level of security and can outperform some representative image encryption algorithms.

Since a substitution box ( S -box) is the nonlinearity part of a symmetric key encryption scheme, it directly determines the performance and security level of the encryption scheme. Thus, generating S -box with high performance and efficiency is attracting. This paper proposes a novel method to construct S -box using the complete Latin square and chaotic system. First, a complete Latin square is generated using the chaotic sequences produced by a chaotic system. Then an S -box is constructed using the complete Latin square. Performance analyses show that the S -box generated by our proposed method has a high performance and can achieve strong ability to resist many security attacks such as the linear attack, differential attack and so on. To show the efficiency of the constructed S -box, this paper further applies the S -box to image encryption application. Security analyses show that the developed image encryption algorithm is able to encrypt different kinds of images into cipher images with uniformly distributed histograms. Performance evaluations demonstrate that it has a high security level and can outperform several state-of-the-art encryption algorithms.

Introduction: To provide the patient with the most convenient mode of administration, there is a need to develop fast-disintegrating tablets, which disintegrate and dissolve rapidly in the saliva, within a few seconds without drinking water. The aim of this study was to analyze the influence of the groups of excipients on technological parameters of metformin orodispersible tablets (ODTs). Materials and Methods: Greco-Latin squares design was used to establish the relations between independent variables such as type of disintegrant, type of diluent, type of sugar-based excipients, type of lubricant, and dependent variables. Results: Orally disintegrating tablets of metformin were prepared by direct compression method. Studying different groups of excipients, it was found that they provide good values of pre-compression parameters of powder mixture and uniformity of weight of tablets. The usage of excipients has provided lower disintegration time (<3 min) and wetting time of tablets. Conclusion: Using Greco-Latin squares design, the influence of four groups of excipients on technological characteristics of metformin ODTs was evaluated. According to the results of desirability function, the best values of technological parameters of metformin ODT were obtained when adding Polyplasdone XL-10 crospovidone, microcrystalline cellulose (MCC) Sanaq ®burst, MCC Vivapur® 200, lactose monohydrate, and Tablube Magnesium Stearate grade Micronized Vegetable to the tablets.

An image encryption algorithm based on Latin square array, instead of the traditional 2D Freidrich architecture, is proposed here. First, two Latin square matrices are used to scrambling and diffusion of the image on the basis of rows and columns. That is, after completing the scrambling and diffusion of the column, the scrambling and diffusion of the row, following those of column, will not stop until all the rows and columns are encrypted. Second, the entire image is subjected to a diffusion operation opposite to the first step line encryption sequence for a further encryption. This algorithm only carries out one-round encryption operation, but simulation experiment results and security analysis show that the algorithm passes statistical tests such as correlation and information entropy, can resist conventional attacks, and is sensitive to keys, so the algorithm has strong security.

Medical image encryption may help protect medical privacy. In this paper, we propose a new medical image encryption scheme combined Latin square and chaotic system. The architecture of permutation and diffusion is adopted. Using Latin square and the plain image information, permutation based on plain image and Latin square (PPILS) is presented to shuffle the pixels of the plain image to different rows and columns, effectively weaken the strong correlations between adjacent pixels, and different images have different permutation effect. To improve the encryption effect, bi-directional adaptive diffusion is proposed to spread little change of plain images to the entire pixels of cipher images. Chaotic sequences employed in permutation and diffusion are generated from the four-dimensional memristive chaotic system, its initial values are computed by SHA 256 hash value of the plain image, and thus the proposed algorithm may withstand known-plaintext and chosen-plaintext attacks. Simulation results and performance analyses show that our image encryption scheme has good security and robustness, and it may be applied for medical image encryption applications.