An introduction to analysis of variance (ANOVA) with special reference to data from clinical experiments in optometry

This article is aimed primarily at eye care practitioners who are undertaking advanced clinical research, and who wish to apply analysis of variance (ANOVA) to their data. ANOVA is a data analysis method of great utility and flexibility. This article describes why and how ANOVA was developed, the basic logic which underlies the method and the assumptions that the method makes for it to be validly applied to data from clinical experiments in optometry. The application of the method to the analysis of a simple data set is then described. In addition, the methods available for making planned comparisons between treatment means and for making post hoc tests are evaluated. The problem of determining the number of replicates or patients required in a given experimental situation is also discussed. Copyright (C) 2000 The College of Optometrists.

The application of analysis of variance (ANOVA) to different experimental designs in optometry

Analysis of variance (ANOVA) is the most efficient method available for the analysis of experimental data. Analysis of variance is a method of considerable complexity and subtlety, with many different variations, each of which applies in a particular experimental context. Hence, it is possible to apply the wrong type of ANOVA to data and, therefore, to draw an erroneous conclusion from an experiment. This article reviews the types of ANOVA most likely to arise in clinical experiments in optometry including the one-way ANOVA ('fixed' and 'random effect' models), two-way ANOVA in randomised blocks, three-way ANOVA, and factorial experimental designs (including the varieties known as 'split-plot' and 'repeated measures'). For each ANOVA, the appropriate experimental design is described, a statistical model is formulated, and the advantages and limitations of each type of design discussed. In addition, the problems of non-conformity to the statistical model and determination of the number of replications are considered. © 2002 The College of Optometrists.

Statnote 23: Non-parametric analysis of variance (ANOVA)

To carry out an analysis of variance, several assumptions are made about the nature of the experimental data which have to be at least approximately true for the tests to be valid. One of the most important of these assumptions is that a measured quantity must be a parametric variable, i.e., a member of a normally distributed population. If the data are not normally distributed, then one method of approach is to transform the data to a different scale so that the new variable is more likely to be normally distributed. An alternative method, however, is to use a non-parametric analysis of variance. There are a limited number of such tests available but two useful tests are described in this Statnote, viz., the Kruskal-Wallis test and Friedmann’s analysis of variance.

Statnote 6: post-hoc ANOVA tests

If data are analysed using ANOVA, and a significant F value obtained, a more detailed analysis of the differences between the treatment means will be required. The best option is to plan specific comparisons among the treatment means before the experiment is carried out and test them using ‘contrasts’. In some circumstances, post-hoc tests may be necessary and experimenters should think carefully which of the many tests available should be used. Different tests can lead to different conclusions and careful consideration as to the appropriate test should be given in each circumstance.

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.

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.

Buy three but get only two: The smallest effect in a 2 × 2 ANOVA is always uninterpretable

Loftus (Memory & Cognition 6:312-319, 1978) distinguished between interpretable and uninterpretable interactions. Uninterpretable interactions are ambiguous, because they may be due to two additive main effects (no interaction) and a nonlinear relationship between the (latent) outcome variable and its indicator. Interpretable interactions can only be due to the presence of a true interactive effect in the outcome variable, regardless of the relationship that it establishes with its indicator. In the present article, we first show that same problem can arise when an unmeasured mediator has a nonlinear effect on the measured outcome variable. Then we integrate Loftus's arguments with a seemingly contradictory approach to interactions suggested by Rosnow and Rosenthal (Psychological Bulletin 105:143-146, 1989). We show that entire data patterns, not just interaction effects alone, produce interpretable or noninterpretable interactions. Next, we show that the same problem of interpretability can apply to main effects. Lastly, we give concrete advice on what researchers can do to generate data patterns that provide unambiguous evidence for hypothesized interactions.

Effectuation & newness : an intertwined relationship?

Principal topic: Effectuation theory suggests that entrepreneurs develop their new ventures in an iterative way by selecting possibilities through flexibility and interactions with the market; a focus on affordability of loss rather than maximal return on the capital invested, and the development of pre-commitments and alliances from stakeholders (Sarasvathy, 2001, 2008; Sarasvathy et al., 2005, 2006). In contrast, causation may be described as a rationalistic reasoning method to create a company. After a comprehensive market analysis to discover opportunities, the entrepreneur will select the alternative with the higher expected return and implement it through the use of a business plan. However, little is known about the consequences of following either of these two processes. One aspect that remains unclear is the relationship between newness and effectuation. On one hand it can be argued that the combination of a means-centered, interactive (through pre-commitments and alliances with stakeholders from the early phases of the venture creation) and open-minded process (through flexibility of exploiting contingencies) should encourage and facilitate the development of innovative solutions. On the other hand, having a close relationship with their “future first customers” and focussing too much on the resources and knowledge already within the firm may be a constraint that is not conducive to innovation, or at least not to a radical innovation. While it has been suggested that effectuation strategy is more likely to be used by innovative entrepreneurs (Sarasvathy, 2001), this hypothesis has not been demonstrated yet (Sarasvathy, 2001). Method: In our attempt to capture newness in its different aspects we have considered the following four domains where newness may happen: new product/service; new method for promotion and sales; new production methods/sourcing; market creation. We identified how effectuation may be differently associated with these four domains of newness. To test our four sets of hypotheses a dataset of 1329 firms (702 nascent and 627 young firms) randomly selected in Australia was examined through ANOVA Tukey HSD Test. Results and Implications: Results indicate the existence of a curvilinear relationship between effectuation and newness where low and high levels of newness are associated with low level of effectuation while medium level of newness is associated with high level of effectuation. Implications for academia, practitioners and policy makers are also discussed.

Literacy, numeracy and learning in school-aged children identified as having speech and language impairment in early childhood

The progress of a nationally representative sample of 3632 children was followed from early childhood through to primary school, using data from the Longitudinal Study of Australian Children (LSAC). The aim was to examine the predictive effects of different aspects of communicative ability, and of early vs. sustained identification of speech and language impairment, on children's achievement and adjustment at school. Four indicators identified speech and language impairment: parent-rated expressive language concern; parent-rated receptive language concern; use of speech-language pathology services; below average scores on the adapted Peabody Picture Vocabulary Test-III. School outcomes were assessed by teachers' ratings of language/literacy ability, numeracy/mathematical thinking and approaches to learning. Comparison of group differences, using ANOVA, provided clear evidence that children who were identified as having speech and language impairment in their early childhood years did not perform as well at school, two years later, as their non-impaired peers on all three outcomes: Language and Literacy, Mathematical Thinking, and Approaches to Learning. The effects of early speech and language status on literacy, numeracy, and approaches to learning outcomes were similar in magnitude to the effect of family socio-economic factors, after controlling for child characteristics. Additionally, early identification of speech and language impairment (at age 4-5) was found to be a better predictor of school outcomes than sustained identification (at aged 4-5 and 6-7 years). Parent-reports of speech and language impairment in early childhood are useful in foreshadowing later difficulties with school and providing early intervention and targeted support from speech-language pathologists and specialist teachers.

Reduction of Secondary Degeneration after Spinal Cord Injury by Acute Delivery of Proinflammatory Growth Factors

INTRODUCTION Inflammation is a protective attempt to facilitate the removal of damaged tissue and to initiate the healing response in other tissues. However, after spinal cord injury (SCI), this response is prolonged leading to secondary degeneration and glial scarring. Here, we investigate the potential of sustained delivery of pro-inflammatory factors vascular endothelial growth factor (VEGF) and platelet derived growth factor (PDGF) to increase early inflammatory events and promote inflammatory resolution. Method Animal ethics approval was obtained from the Queensland University of Technology. Adult Wistar-Kyoto rats (12-16 weeks old) were subjected to laminectomies and T10 hemisections. Animals were then randomised to treatment (implantation of osmotic pump (Alzet) loaded with 5ug VEGF & 5 ug PDGF) or control groups (lesion control or lesion plus pump delivering PBS). Rats were sacrificed at one month and the spinal cords were harvested and examined by immunohistology, using anti-neurofilament-200(NF200) and anti- ionized calcium binding adapter molecule 1 (Iba1). One way ANOVA was used for statistic analysis. Results At 1 month, active pump-treated cords showed a high level of axonal filament throughout the defects as compared to the control groups. The mean lesion size, as measured by NF200, was 0.47mm2 for the lesion control, 0.39mm2 for the vehicle control and 0.078mm2 for the active pump group. Significant differences were detected between the active pump group and the two control groups (AP vs LC p= 0.017 AG vs VC p= 0.004). Iba-1 staining also showed significant differences in the post-injury inflammatory response. Discussion We have shown that axons and activated microglia are co-located in the lesion of the treated cord. We hypothesise the delivery of VEGF/PDGF increases the local vessel permeability to inflammatory cells and activates these along with the resident microglia to threshold population, which ultimately resolved the prolonged inflammation. Here, we have shown that maintaining the inflammatory signals for at least 7 days improved the morphology of the injured cord. Conclusion This study has shown that boosting inflammation, by delivery VEGF/PDGF, in the early phase of SCI helps to reduce secondary degeneration and may promote inflammation resolution. This treatment may provide a platform for other neuro-regenrative therapies.

Employing the five-factor mentoring instrument : analysing mentoring practices for teaching primary science.

Primary science education is a concern around the world and quality mentoring within schools can develop preservice teachers’ practices. A five-factor model for mentoring has been identified, namely, personal attributes, system requirements, pedagogical knowledge, modelling, and feedback. Final-year preservice teachers (mentees, n=211) from three Turkish universities were administered a previously validated instrument to gather perceptions of their mentoring in primary science teaching. ANOVA indicated that each of these five factors was statistically significant (p<.001) with mean scale scores ranging from 3.36 to 4.12. Although mentees perceived their mentors to provide evaluation feedback (95%), model classroom management (88%), guide their preparation (96%), and outline the science curriculum (92%), the majority of mentors were perceived not to assist their mentees in 10 of the 34 survey items. Professional development programmes that target the specific needs of these mentors may further enhance mentoring practices for advancing primary science teaching.

Introducing Engineering Education in the Middle School

This paper first describes a new three-year, longitudinal project that is implementing engineering education in three middle schools in Australia (grade levels 7-9). This important domain is untapped in Australia. Hence, as a starting point, we conducted a context analysis to help situate engineering education in a school system. We report on this analysis with respect to findings from one of two literature-based surveys that gathered middle-school student responses in mathematics (n=172) and science (n=166) towards understanding their dispositions for engineering education. ANOVA indicated gender differences for 3 out of 23 items in both mathematics and science. In addition, the majority of students agreed or strongly agreed with 17 of the 23 survey items, however, there were some differences between mathematics and science. We conclude the paper with some recommendations for establishing engineering education in schools, including the development of partnerships among engineering and education faculties, school systems, and industry to develop contemporary engineering resources to support school-level mathematics, science, and technology.

Domestic violence in the urban fringe

Police call data for domestic violence incidents in the city of Brisbane were used to further explore the locational disadvantage thesis. it was hypothesised that the supposed additional burdens and stresses on disadvantaged families living in the outer suburbs may be reflected in significantly higher rates of reported domestic violence. Using an index of relative socioeconomic disadvantage and employing Analysis of variance (ANOVA) this research shows that significantly higher rates of reported domestic violence occur in the inner suburbs relative to the middle or outer suburbs of Brisbane. This finding adds further doubt to the magnitude of locational disadvantage impacts on outer suburban low income family households.

The relationship of loneliness and social anxiety with children's and adolescents' online communication

Children and adolescents are now using online communication to form and/or maintain relationships with strangers and/or friends. Relationships in real life are important for children and adolescents in identity formation and general development. However, social relationships can be difficult for those who experience feelings of loneliness and social anxiety. The current study aimed to replicate and extend research conducted by Valkenburg and Peter (2007b), by investigating differences in online communication patterns between children and adolescents with and without selfreported loneliness and social anxiety. Six hundred and twenty-six students aged 10-16 years completed a questionnaire survey about the amount of time they engaged in online communication, the topics they discussed, who they communicated with, and their purposes of online communication. Following Valkenburg and Peter (2007b), loneliness was measured with a shortened version of the UCLA Loneliness Scale (Version 3) developed by Russell (1996), whereas social anxiety was assessed with a sub-scale of the Social Anxiety Scale for Adolescents (La Greca & Lopez, 1998). The sample was divided into four groups of children and adolescents: 220 were “non-socially anxious and non-lonely”, 139 were “socially anxious but not lonely”, 107 were “lonely but not socially anxious”, and 159 were “lonely and socially anxious”. A one-way ANOVA and chi-square tests were conducted to evaluate the aforementioned differences between these groups. The results indicated that children and adolescents who reported being lonely used online communication differently from those who did not report being lonely. Essentially, the former communicated online more frequently about personal things and intimate topics, but also to compensate for their weak social skills and to meet new people. Further analyses on gender differences within lonely children and adolescents revealed that boys and girls communicated online more frequently with different partners. It was concluded that for these vulnerable individuals online communication may fulfil needs of self-disclosure, identity exploration, and social interactions. However, future longitudinal studies combining a quantitative with a qualitative approach would better address the relationship between Internet use and psychosocial well-being. The findings also suggested the need for further exploration of how such troubled children and adolescents can use the Internet beneficially.