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 analysis methods in optometry Part 4: an introduction to analysis of variance (ANOVA)

In any investigation in optometry involving more that two treatment or patient groups, an investigator should be using ANOVA to analyse the results assuming that the data conform reasonably well to the assumptions of the analysis. Ideally, specific null hypotheses should be built into the experiment from the start so that the treatments variation can be partitioned to test these effects directly. If 'post-hoc' tests are used, then an experimenter should examine the degree of protection offered by the test against the possibilities of making either a type 1 or a type 2 error. All experimenters should be aware of the complexity of ANOVA. The present article describes only one common form of the analysis, viz., that which applies to a single classification of the treatments in a randomised design. There are many different forms of the analysis each of which is appropriate to the analysis of a specific experimental design. The uses of some of the most common forms of ANOVA in optometry have been described in a further article. If in any doubt, an investigator should consult a statistician with experience of the analysis of experiments in optometry since once embarked upon an experiment with an unsuitable design, there may be little that a statistician can do to help.

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.

Phenotypic and genotypic characterisation of Clostrum Difficile

Clostridium difficile is at present one of the most common nosocomial infections in the developed world. Hypervirulent strains (PCR ribotype 027) of C. difficile which produce enhanced levels of toxins have also been associated with other characteristics such as a greater rate of sporulation and resistance to fluoroquinolones. Infection due to C. difficile PCR ribotype 027 has also been associated with greater rates of morbidity and mortality. The aim of this thesis was to investigate both the phenotypic and genotypic characteristics of two populations of toxigenic clinical isolates of C. difficile which were recovered from two separate hospital trusts within the UK. Phenotypic characterisation of the isolates was undertaken using analytical profile indexes (APIs), minimum inhibitory concentrations(MICs) and S-layer protein typing. In addition to this, isolates were also investigated for the production of a range of extracellular enzymes as potential virulence factors. Genotypic characterisation was performed using a random amplification of polymorphic DNA(RAPD) PCR protocol which was fully optimised in this study, and the gold standard method, PCR ribotyping. The discriminatory power of both methods was compared and the similarity between the different isolates also analysed. Associations between the phenotypic and genotypic characteristics and the recovery location of the isolate were then investigated. Extracellular enzyme production and API testing revealed little variation between the isolates; with S-layer typing demonstrating low discrimination. Minimum inhibitory concentrations did not identify any resistance towards either vancomycin or metronidazole; there were however significant differences in the distribution of antibiogram profiles of isolates recovered from the two different trusts. The RAPD PCR protocol was successfully optimised and alongside PCR ribotyping, effectively typed all of the clinical isolates and also identified differences in the number of types defined between the two locations. Both PCR ribotyping and RAPD demonstrated similar discriminatory power; however, the two genotyping methods did not generate amplicons that mapped directly onto each other and therefore clearly characterised isolates based on different genomic markers. The RAPD protocol also identified different subtypes within PCR ribotypes, therefore demonstrating that all isolates defined as a particular PCR ribotype were not the same strain. No associations could be demonstrated between the phenotypic and genotypic characteristics observed; however, the location from which an isolate was recovered did appear to influence antibiotic resistance and genotypic characteristics. The phenotypic and genotypic characteristics observed amongst the C. difficile isolates in this study, may provide a basis for the identification of further targets which may be potentially incorporated into future methods for the characterisation of C. difficile isolates.

Phenotypic and genotypic analysis of intestinal spirochacies

Pulsed field gel electrophoresis of 82 intestinal spirochaete isolates showed specific differentiation of Serpulina pilosicoli and Serpulina hyodysenteriae although considerable heterogeneity was observed, especially amongst S. pilosicoli isolates. In several cases genotypically similar isolates originated from different animals suggesting that cross-species transmission may have occurred. The Caco-2 and Caco-21HT29 cell models have been proposed as potentially realistic models of intestinal infection. Quantitation of adhesion to the cells showed isolate 3 82/91 (from a bacteraemia) to adhere at significantly greater numbers than any other isolate tested. This isolate produced a PFGE profile which differed from other S. pilosicoli isolates and so would be of interest for further study. Comparison of bacteraemic and other S. pilosicoli isolates suggested that bacteraemic isolates were not more specifically adapted for adhesion to, or invasion of the epithelial cell layer than other S. pilosicoli isolates. Genotypically similar isolates from differing animal origins adhered to the Caco-2 model at similar levels. Generation of a random genomic library of S. pilosicoli and screening with species specific monoclonal antibody has enabled the identification of a gene sequence encoding a protein which showed significant homology with an ancestral form of the enzyme pyruvate oxidoreductase. Immunoscreening with polyclonal serum identified the sequences of two gene clusters and a probable arylsulphatase. One gene cluster represented a ribosomal gene cluster which has a similar molecular arrangement to Borrelia burgdorjeri, Treponema pallidum and Thermatoga maritima. The other gene cluster contained an ABC transporter protein, sorbitol dehydrogenase and phosphomannose isomerase. An ELISA type assay was used to demonstrate that isolates of S. pilosicoli could adhere to components of the extracellular matrix such as collagen (type 1), fibronectin, laminin, and porcine gastric mucin.

Genotypic and environmentally derived variation in the cell wall composition of Miscanthus in relation to its use as a biomass feedstock

Fifteen Miscanthus genotypes grown in five locations across Europe were analysed to investigate the influence of genetic and environmental factors on cell wall composition. Chemometric techniques combining near infrared reflectance spectroscopy (NIRS) and conventional chemical analyses were used to construct calibration models for determination of acid detergent lignin (ADL), acid detergent fibre (ADF), and neutral detergent fibre (NDF) from sample spectra. Results generated were subsequently converted to lignin, cellulose and hemicellulose content and used to assess the genetic and environmental variation in cell wall composition of Miscanthus and to identify genotypes which display quality traits suitable for exploitation in a range of energy conversion systems. The NIRS calibration models developed were found to predict concentrations with a good degree of accuracy based on the coefficient of determination (R2), standard error of calibration (SEC), and standard error of cross-validation (SECV) values. Across all sites mean lignin, cellulose and hemicellulose values in the winter harvest ranged from 76–115 g kg-1, 412–529 g kg-1, and 235–338 g kg-1 respectively. Overall, of the 15 genotypes Miscanthus x giganteus and Miscanthus sacchariflorus contained higher lignin and cellulose concentrations in the winter harvest. The degree of observed genotypic variation in cell wall composition indicates good potential for plant breeding and matching feedstocks to be optimised to different energy conversion processes.

Mean-variance Vs. full-scale optimization: broad evidence for the UK

This article investigates the performance of a model called Full-Scale Optimisation, which was presented recently and is used for financial investment advice. The investor’s preferences of expected risk and return are entered into the model, and a recommended portfolio is produced. This model is theoretically more accurate than the mainstream investment advice model, called Mean-Variance Optimization, as there are fewer assumptions made. Our investigation of the model’s performance is broader when it comes to investor preferences, and more general when it comes to investment type, as compared to previous studies. Our investigation shows that Full-Scale Optimisation is more widely applicable than earlier known.

Common variance in amplitude envelope perception tasks and their impact on phoneme duration perception and reading and spelling in Finnish children with reading disabilities

Our goal was to investigate auditory and speech perception abilities of children with and without reading disability (RD) and associations between auditory, speech perception, reading, and spelling skills. Participants were 9-year-old, Finnish-speaking children with RD (N = 30) and typically reading children (N = 30). Results showed significant group differences between the groups in phoneme duration discrimination but not in perception of amplitude modulation and rise time. Correlations among rise time discrimination, phoneme duration, and spelling accuracy were found for children with RD. Those children with poor rise time discrimination were also poor in phoneme duration discrimination and in spelling. Results suggest that auditory processing abilities could, at least in some children, affect speech perception skills, which in turn would lead to phonological processing deficits and dyslexia.

The variance in sales performance explained by the knowledge structures of salespeople

The last major study of sales performance variance explained by salespeople attributes was by Churchill et al. (1985). They examined the effect of role, skills, motivation, personal factors, aptitude, and organizational/environmental factors on sales performance—factors that have dominated the sales performance area. About the same time, Weitz, Sujan, and Sujan (1986) introduced the concepts of salespeople's knowledge structures. Considerable work on the relationship of the elements of knowledge structures and performance can be found in the literature. In this research note, we determine the degree to which sales performance can be explained by knowledge structure variables, a heretofore unexplored area. If knowledge structure variables explain more variance than traditional variables, then this paper would be a call to further research in this area. In examining this research question in a retail context, we find that knowledge structure variables explain 50.2 percent of the variance in sales performance. We also find that variance explained by knowledge structures is significantly different based on gender. The impact of knowledge structures on performance was higher for men than for women. The models using education demonstrated smaller differences.

Statnote 30 : The one-way analysis of variance (ANOVA):fixed effects model

In Statnote 9, we described a one-way analysis of variance (ANOVA) ‘random effects’ model in which the objective was to estimate the degree of variation of a particular measurement and to compare different sources of variation in space and time. The illustrative scenario involved the role of computer keyboards in a University communal computer laboratory as a possible source of microbial contamination of the hands. The study estimated the aerobic colony count of ten selected keyboards with samples taken from two keys per keyboard determined at 9am and 5pm. This type of design is often referred to as a ‘nested’ or ‘hierarchical’ design and the ANOVA estimated the degree of variation: (1) between keyboards, (2) between keys within a keyboard, and (3) between sample times within a key. An alternative to this design is a 'fixed effects' model in which the objective is not to measure sources of variation per se but to estimate differences between specific groups or treatments, which are regarded as 'fixed' or discrete effects. This statnote describes two scenarios utilizing this type of analysis: (1) measuring the degree of bacterial contamination on 2p coins collected from three types of business property, viz., a butcher’s shop, a sandwich shop, and a newsagent and (2) the effectiveness of drugs in the treatment of a fungal eye infection.

Genotypic and antimicrobial characterisation of Propionibacterium acnes isolates from surgically excised lumbar disc herniations

The anaerobic skin commensal Propionibacterium acnes is an underestimated cause of human infections and clinical conditions. Previous studies have suggested a role for the bacterium in lumbar disc herniation and infection. To further investigate this, five biopsy samples were surgically excised from each of 64 patients with lumbar disc herniation. P. acnes and other bacteria were detected by anaerobic culture, followed by biochemical and PCR-based identification. In total, 24/64 (38%) patients had evidence of P. acnes in their excised herniated disc tissue. Using recA and mAb typing methods, 52% of the isolates were type II (50% of culture-positive patients), while type IA strains accounted for 28% of isolates (42% patients). Type III (11% isolates; 21% patients) and type IB strains (9% isolates; 17% patients) were detected less frequently. The MIC values for all isolates were lowest for amoxicillin, ciprofloxacin, erythromycin, rifampicin, tetracycline, and vancomycin (≤1mg/L). The MIC for fusidic acid was 1-2 mg/L. The MIC for trimethoprim and gentamicin was 2 to ≥4 mg/L. The demonstration that type II and III strains, which are not frequently recovered from skin, predominated within our isolate collection (63%) suggests that the role of P. acnes in lumbar disc herniation should not be readily dismissed. © 2013 Jess Rollason et al.

Double decomposition : decomposing the variance in subcomponents of male extra-pair reproductive success

Peer reviewed

Double decomposition : decomposing the variance in subcomponents of male extra-pair reproductive success

Peer reviewed

Double decomposition : decomposing the variance in subcomponents of male extra-pair reproductive success

Peer reviewed