Statnote 13: a more complex analysis of variance incorporating a 'repeated measures' factor

Experiments combining different groups or factors and which use ANOVA are a powerful method of investigation in applied microbiology. ANOVA enables not only the effect of individual factors to be estimated but also their interactions; information which cannot be obtained readily when factors are investigated separately. In addition, combining different treatments or factors in a single experiment is more efficient and often reduces the sample size required to estimate treatment effects adequately. Because of the treatment combinations used in a factorial experiment, the degrees of freedom (DF) of the error term in the ANOVA is a more important indicator of the ‘power’ of the experiment than the number of replicates. A good method is to ensure, where possible, that sufficient replication is present to achieve 15 DF for the error term of the ANOVA testing effects of particular interest. Finally, it is important to always consider the design of the experiment because this determines the appropriate ANOVA to use. Hence, it is necessary to be able to identify the different forms of ANOVA appropriate to different experimental designs and to recognise when a design is a split-plot or incorporates a repeated measure. If there is any doubt about which ANOVA to use in a specific circumstance, the researcher should seek advice from a statistician with experience of research in applied microbiology.

The use of analysis of variance (ANOVA) in applied microbiology

Experiments combining different groups or factors and which use ANOVA are a powerful method of investigation in applied microbiology. ANOVA enables not only the effect of individual factors to be estimated but also their interactions; information which cannot be obtained readily when factors are investigated separately. In addition, combining different treatments or factors in a single experiment is more efficient and often reduces the number of replications required to estimate treatment effects adequately. Because of the treatment combinations used in a factorial experiment, the DF of the error term in the ANOVA is a more important indicator of the ‘power’ of the experiment than the number of replicates. A good method is to ensure, where possible, that sufficient replication is present to achieve 15 DF for each error term of the ANOVA. Finally, it is important to consider the design of the experiment because this determines the appropriate ANOVA to use. Some of the most common experimental designs used in the biosciences and their relevant ANOVAs are discussed by. If there is doubt about which ANOVA to use, the researcher should seek advice from a statistician with experience of research in applied microbiology.

Data methods in optometry Part 9: experimental design and analysis of variance

The key to the correct application of ANOVA is careful experimental design and matching the correct analysis to that design. The following points should therefore, be considered before designing any experiment: 1. In a single factor design, ensure that the factor is identified as a 'fixed' or 'random effect' factor. 2. In more complex designs, with more than one factor, there may be a mixture of fixed and random effect factors present, so ensure that each factor is clearly identified. 3. Where replicates can be grouped or blocked, the advantages of a randomised blocks design should be considered. There should be evidence, however, that blocking can sufficiently reduce the error variation to counter the loss of DF compared with a randomised design. 4. Where different treatments are applied sequentially to a patient, the advantages of a three-way design in which the different orders of the treatments are included as an 'effect' should be considered. 5. Combining different factors to make a more efficient experiment and to measure possible factor interactions should always be considered. 6. The effect of 'internal replication' should be taken into account in a factorial design in deciding the number of replications to be used. Where possible, each error term of the ANOVA should have at least 15 DF. 7. Consider carefully whether a particular factorial design can be considered to be a split-plot or a repeated measures design. If such a design is appropriate, consider how to continue the analysis bearing in mind the problem of using post hoc tests in this situation.

Analysing Conjoint Analysis Data by a Random Coefficient Regression Model

2000 Mathematics Subject Classification: 62J12, 62K15, 91B42, 62H99.

The relationship between socioeconomic status, course delivery method, and student success at a state college: A single institution analysis

In an effort to improve instruction and better accommodate the needs of students, community colleges are offering courses delivered in a variety of delivery formats that require students to have some level of technology fluency to be successful in the course. This study was conducted to investigate the relationship between student socioeconomic status (SES), course delivery method, and course type on enrollment, final course grades, course completion status, and course passing status at a state college. ^ A dataset for 20,456 students of low and not low SES enrolled in science, technology, engineering, and mathematics (STEM) course types delivered using traditional, online, blended, and web enhanced course delivery formats at Miami Dade College, a large open access 4-year state college located in Miami-Dade County, Florida, was analyzed. A factorial ANOVA using course type, course delivery method, and student SES found no significant differences in final course grades when used to determine if course delivery methods were equally effective for students of low and not low SES taking STEM course types. Additionally, three chi-square goodness-of-fit tests were used to investigate for differences in enrollment, course completion and course passing status by SES, course type, and course delivery method. The findings of the chi-square tests indicated that: (a) there were significant differences in enrollment by SES and course delivery methods for the Engineering/Technology, Math, and overall course types but not for the Natural Science course type and (b) there were no significant differences in course completion status and course passing status by SES and course types overall and SES and course delivery methods overall. However, there were statistically significant but weak relationships between course passing status, SES and the math course type as well as between course passing status, SES, and online and traditional course delivery methods. ^ The mixed findings in the study indicate that strides have been made in closing the theoretical gap in education and technology skills that may exist for students of different SES levels. MDC's course delivery and student support models may assist other institutions address student success in courses that necessitate students having some level of technology fluency. ^

The reliability and factorial validity of the Adolescent Alcohol Involvement Scale in a large sample in the United Kingdom

The assessment of adolescent drinking behavior is a complex task, complicated by variability in drinking patterns, the transitory and developmental nature of the behavior and the reliance (for large scale studies) on self-report questionnaires. The Adolescent Alcohol Involvement Scale (Mayer & Filstead, 1979) is a 14-item screening tool designed to help to identify alcohol misusers or more problematic drinkers. The present study utilized a large sample (n = 4066) adolescents from Northern Ireland. Results of Confirmatory Factor Analyses and reliability estimates revealed that the 14-items share sufficient common variance that scores can be considered to be reliable and that the 14 items can be scored to provide a composite alcohol use score.

Optimization of the Ion Source-Mass Spectrometry Parameters in Non-Steroidal Anti-Inflammatory and Analgesic Pharmaceuticals Analysis by a Design of Experiments Approach

The flow rates of drying and nebulizing gas, heat block and desolvation line temperatures and interface voltage are potential electrospray ionization parameters as they may enhance sensitivity of the mass spectrometer. The conditions that give higher sensitivity of 13 pharmaceuticals were explored. First, Plackett-Burman design was implemented to screen significant factors, and it was concluded that interface voltage and nebulizing gas flow were the only factors that influence the intensity signal for all pharmaceuticals. This fractionated factorial design was projected to set a full 2(2) factorial design with center points. The lack-of-fit test proved to be significant. Then, a central composite face-centered design was conducted. Finally, a stepwise multiple linear regression and subsequently an optimization problem solving were carried out. Two main drug clusters were found concerning the signal intensities of all runs of the augmented factorial design. p-Aminophenol, salicylic acid, and nimesulide constitute one cluster as a result of showing much higher sensitivity than the remaining drugs. The other cluster is more homogeneous with some sub-clusters comprising one pharmaceutical and its respective metabolite. It was observed that instrumental signal increased when both significant factors increased with maximum signal occurring when both codified factors are set at level +1. It was also found that, for most of the pharmaceuticals, interface voltage influences the intensity of the instrument more than the nebulizing gas flowrate. The only exceptions refer to nimesulide where the relative importance of the factors is reversed and still salicylic acid where both factors equally influence the instrumental signal. Graphical Abstract ᅟ.

Optimization of microwave-assisted extration of phenolic compounds from tomao by full factorial design coupled with response surface methodology

Tomato (Lycopersicon esculentum Mill.), apart from being a functional food rich in carotenoids, vitamins and minerals, is also an important source of phenolic compounds [1 ,2]. As antioxidants, these functional molecules play an important role in the prevention of human pathologies and have many applications in nutraceutical, pharmaceutical and cosmeceutical industries. Therefore, the recovery of added-value phenolic compounds from natural sources, such as tomato surplus or industrial by-products, is highly desirable. Herein, the microwave-assisted extraction of the main phenolic acids and flavonoids from tomato was optimized. A S-Ieve! full factorial Box-Behnken design was implemented and response surface methodology used for analysis. The extraction time (0-20 min), temperature (60-180 "C), ethanol percentage (0-100%), solidlliquid ratio (5-45 g/L) and microwave power (0-400 W) were studied as independent variables. The phenolic profile of the studied tomato variety was initially characterized by HPLC-DAD-ESIIMS [2]. Then, the effect of the different extraction conditions, as defined by the used experimental design, on the target compounds was monitored by HPLC-DAD, using their UV spectra and retention time for identification and a series of calibrations based on external standards for quantification. The proposed model was successfully implemented and statistically validated. The microwave power had no effect on the extraction process. Comparing with the optimal extraction conditions for flavonoids, which demanded a short processing time (2 min), a low temperature (60 "C) and solidlliquid ratio (5 g/L), and pure ethanol, phenolic acids required a longer processing time ( 4.38 min), a higher temperature (145.6 •c) and solidlliquid ratio (45 g/L), and water as extraction solvent. Additionally, the studied tomato variety was highlighted as a source of added-value phenolic acids and flavonoids.

Reduction capability of soil humic substances from the Rio Negro basin, Brazil, towards Hg(II) studied by a multimethod approach and principal component analysis (PCA)

This paper characterizes humic substances (HS) extracted from soil samples collected in the Rio Negro basin in the state of Amazonas, Brazil, particularly investigating their reduction capabilities towards Hg(II) in order to elucidate potential mercury cycling/volatilization in this environment. For this reason, a multimethod approach was used, consisting of both instrumental methods (elemental analysis, EPR, solid-state NMR, FIA combined with cold-vapor AAS of Hg(0)) and statistical methods such as principal component analysis (PCA) and a central composite factorial planning method. The HS under study were divided into groups, complexing and reducing ones, owing to different distribution of their functionalities. The main functionalities (cor)related with reduction of Hg(II) were phenolic, carboxylic and amide groups, while the groups related with complexation of Hg(II) were ethers, hydroxyls, aldehydes and ketones. The HS extracted from floodable regions of the Rio Negro basin presented a greater capacity to retain (to complex, to adsorb physically and/or chemically) Hg(II), while nonfloodable regions showed a greater capacity to reduce Hg(II), indicating that HS extracted from different types of regions contribute in different ways to the biogeochemical mercury cycle in the basin of the mid-Rio Negro, AM, Brazil. (c) 2007 Published by Elsevier B.V.

Effect of telmisartan on functional outcome, recurrence, and blood pressure in patients with acute mild ischemic stroke: a PRoFESS subgroup analysis

Background and Purpose—High blood pressure (BP) is common in acute ischemic stroke and associated independently with a poor functional outcome. However, the management of BP acutely remains unclear because no large trials have been completed. Methods—The factorial PRoFESS secondary stroke prevention trial assessed BP-lowering and antiplatelet strategies in 20 332 patients; 1360 were enrolled within 72 hours of ischemic stroke, with telmisartan (angiotensin receptor antagonist, 80 mg/d, n647) vs placebo (n713). For this nonprespecified subgroup analysis, the primary outcome was functional outcome at 30 days; secondary outcomes included death, recurrence, and hemodynamic measures at up to 90 days. Analyses were adjusted for baseline prognostic variables and antiplatelet assignment. Results—Patients were representative of the whole trial (age 67 years, male 65%, baseline BP 147/84 mm Hg, small artery disease 60%, NIHSS 3) and baseline variables were similar between treatment groups. The mean time from stroke to recruitment was 58 hours. Combined death or dependency (modified Rankin scale: OR, 1.03; 95% CI, 0.84–1.26; P0.81; death: OR, 1.05; 95% CI, 0.27–4.04; and stroke recurrence: OR, 1.40; 95% CI, 0.68–2.89; P0.36) did not differ between the treatment groups. In comparison with placebo, telmisartan lowered BP (141/82 vs 135/78 mmHg, difference 6 to 7 mmHg and 2 to 4 mmHg; P0.001), pulse pressure (3 to 4 mmHg; P0.002), and rate-pressure product (466 mmHg.bpm; P0.0004). Conclusion—Treatment with telmisartan in 1360 patients with acute mild ischemic stroke and mildly elevated BP appeared to be safe with no excess in adverse events, was not associated with a significant effect on functional dependency, death, or recurrence, and modestly lowered BP.

What Are Effective Program Characteristics of Self-Management Interventions in Patients With Heart Failure? : An Individual Patient Data Meta-analysis

Background To identify those characteristics of self-management interventions in patients with heart failure (HF) that are effective in influencing health-related quality of life, mortality, and hospitalizations. Methods and Results Randomized trials on self-management interventions conducted between January 1985 and June 2013 were identified and individual patient data were requested for meta-analysis. Generalized mixed effects models and Cox proportional hazard models including frailty terms were used to assess the relation between characteristics of interventions and health-related outcomes. Twenty randomized trials (5624 patients) were included. Longer intervention duration reduced mortality risk (hazard ratio 0.99, 95% confidence interval [CI] 0.97–0.999 per month increase in duration), risk of HF-related hospitalization (hazard ratio 0.98, 95% CI 0.96–0.99), and HF-related hospitalization at 6 months (risk ratio 0.96, 95% CI 0.92–0.995). Although results were not consistent across outcomes, interventions comprising standardized training of interventionists, peer contact, log keeping, or goal-setting skills appeared less effective than interventions without these characteristics. Conclusion No specific program characteristics were consistently associated with better effects of self-management interventions, but longer duration seemed to improve the effect of self-management interventions on several outcomes. Future research using factorial trial designs and process evaluations is needed to understand the working mechanism of specific program characteristics of self-management interventions in HF patients.

Quinn’s Leadership Roles: A Confirmatory Factor Analysis Study in Portuguese Health Services

Purpose: To evaluate psychometric properties of Quinn’s leadership questionnaire (CFV questionnaire; 1988) to the Portuguese health services. Design: Cross-sectional study, using the Quinn’s leadership questionnaire, administered to registered nurses and physicians in Portuguese health care services (N = 687). Method: Self-administered survey applied to two samples. In the first (of convenience; N = 249 Portuguese health professionals) were performed exploratory factor and reliability analysis to the CFV questionnaire. In the second sample (stratified; N = 50 surgical units of 33 Portuguese hospitals) was performed confirmatory factor analysis using LISREL 8.80. Findings: The first sample supported an eight-factor solution accounting for 65.46% of the variance, in an interpretable factorial structure (loadings> .50), with Cronbach’s α upper than .79. This factorial structure, replicated with the second sample, showed reasonable fit for each of the 8 leadership roles, quadrants, and global model. The models evidenced, generally, nomological validity, with scores between good and acceptable (.235 < x2/df < 2.055 e .00 < RMSEA < .077). Conclusions: Quinn’s leadership questionnaire presented good reliability and validity for the eight leadership roles, showing to be suitable for use in hospital health care context. Key-Words: Leadership; Quinn’s CVF questionnaire; health services; Quinn’s competing values.

Raman microscopy of formamide-intercalated kaolinites treated by controlled-rate thermal analysis technology

Raman spectroscopy of formamide-intercalated kaolinites treated using controlled-rate thermal analysis technology (CRTA), allowing the separation of adsorbed formamide from intercalated formamide in formamide-intercalated kaolinites, is reported. The Raman spectra of the CRTA-treated formamide-intercalated kaolinites are significantly different from those of the intercalated kaolinites, which display a combination of both intercalated and adsorbed formamide. An intense band is observed at 3629 cm-1, attributed to the inner surface hydroxyls hydrogen bonded to the formamide. Broad bands are observed at 3600 and 3639 cm-1, assigned to the inner surface hydroxyls, which are hydrogen bonded to the adsorbed water molecules. The hydroxyl-stretching band of the inner hydroxyl is observed at 3621 cm-1 in the Raman spectra of the CRTA-treated formamide-intercalated kaolinites. The results of thermal analysis show that the amount of intercalated formamide between the kaolinite layers is independent of the presence of water. Significant differences are observed in the CO stretching region between the adsorbed and intercalated formamide.

Detailed analysis of a conservative difference approximation for the time fractional diffusion equation

Diffusion equations that use time fractional derivatives are attractive because they describe a wealth of problems involving non-Markovian Random walks. The time fractional diffusion equation (TFDE) is obtained from the standard diffusion equation by replacing the first-order time derivative with a fractional derivative of order α ∈ (0, 1). Developing numerical methods for solving fractional partial differential equations is a new research field and the theoretical analysis of the numerical methods associated with them is not fully developed. In this paper an explicit conservative difference approximation (ECDA) for TFDE is proposed. We give a detailed analysis for this ECDA and generate discrete models of random walk suitable for simulating random variables whose spatial probability density evolves in time according to this fractional diffusion equation. The stability and convergence of the ECDA for TFDE in a bounded domain are discussed. Finally, some numerical examples are presented to show the application of the present technique.