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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.

Solid Lipid Nanoparticles For Hydrophilic Biotech Drugs: Optimization And Cell Viability Studies (caco-2 & Hepg-2 Cell Lines).

Insulin was used as model protein to developed innovative Solid Lipid Nanoparticles (SLNs) for the delivery of hydrophilic biotech drugs, with potential use in medicinal chemistry. SLNs were prepared by double emulsion with the purpose of promoting stability and enhancing the protein bioavailability. Softisan(®)100 was selected as solid lipid matrix. The surfactants (Tween(®)80, Span(®)80 and Lipoid(®)S75) and insulin were chosen applying a 2(2) factorial design with triplicate of central point, evaluating the influence of dependents variables as polydispersity index (PI), mean particle size (z-AVE), zeta potential (ZP) and encapsulation efficiency (EE) by factorial design using the ANOVA test. Therefore, thermodynamic stability, polymorphism and matrix crystallinity were checked by Differential Scanning Calorimetry (DSC) and Wide Angle X-ray Diffraction (WAXD), whereas the effect of toxicity of SLNs was check in HepG2 and Caco-2 cells. Results showed a mean particle size (z-AVE) width between 294.6 nm and 627.0 nm, a PI in the range of 0.425-0.750, ZP about -3 mV, and the EE between 38.39% and 81.20%. After tempering the bulk lipid (mimicking the end process of production), the lipid showed amorphous characteristics, with a melting point of ca. 30 °C. The toxicity of SLNs was evaluated in two distinct cell lines (HEPG-2 and Caco-2), showing to be dependent on the concentration of particles in HEPG-2 cells, while no toxicity in was reported in Caco-2 cells. SLNs were stable for 24 h in in vitro human serum albumin (HSA) solution. The resulting SLNs fabricated by double emulsion may provide a promising approach for administration of protein therapeutics and antigens.

Inhibitory Effects Of A Cured Antibacterial Bonding System On Viability And Metabolic Activity Of Oral Bacteria.

To evaluate the antimicrobial efficacy of Clearfil SE Protect (CP) and Clearfil SE Bond (CB) after curing and rinsed against five individual oral microorganisms as well as a mixture of bacterial culture prepared from the selected test organisms. Bacterial suspensions were prepared from single species of Streptococcus mutans, Streptococcus sobrinus, Streptococcus gordonii, Actinomyces viscosus and Lactobacillus lactis, as well as mixed bacterial suspensions from these organisms. Dentin bonding system discs (6 mm×2 mm) were prepared, cured, washed and placed on the bacterial suspension of single species or multispecies bacteria for 15, 30 and 60 min. MTT, Live/Dead bacterial viability (antibacterial effect), and XTT (metabolic activity) assays were used to test the two dentin system's antibacterial effect. All assays were done in triplicates and each experiment repeated at least three times. Data were submitted to ANOVA and Scheffe's f-test (5%). Greater than 40% bacteria killing was seen within 15 min, and the killing progressed with increasing time of incubation with CP discs. However, a longer (60 min) period of incubation was required by CP to achieve similar antimicrobial effect against mixed bacterial suspension. CB had no significant effect on the viability or metabolic activity of the test microorganisms when compared to the control bacterial culture. CP was significantly effective in reducing the viability and metabolic activity of the test organisms. The results demonstrated the antimicrobial efficacy of CP both on single and multispecies bacterial culture. CP may be beneficial in reducing bacterial infections in cavity preparations in clinical dentistry.

Effect Of Simulated Microwave Disinfection On The Linear Dimensional Change, Hardness And Impact Strength Of Acrylic Resins Processed By Different Polymerizing Cycles.

This study investigated the effect of simulated microwave disinfection (SMD) on the linear dimensional changes, hardness and impact strength of acrylic resins under different polymerization cycles. Metal dies with referential points were embedded in flasks with dental stone. Samples of Classico and Vipi acrylic resins were made following the manufacturers' recommendations. The assessed polymerization cycles were: A-- water bath at 74ºC for 9 h; B-- water bath at 74ºC for 8 h and temperature increased to 100ºC for 1 h; C-- water bath at 74ºC for 2 h and temperature increased to 100ºC for 1 h;; and D-- water bath at 120ºC and pressure of 60 pounds. Linear dimensional distances in length and width were measured after SMD and water storage at 37ºC for 7 and 30 days using an optical microscope. SMD was carried out with the samples immersed in 150 mL of water in an oven (650 W for 3 min). A load of 25 gf for 10 sec was used in the hardness test. Charpy impact test was performed with 40 kpcm. Data were submitted to ANOVA and Tukey's test (5%). The Classico resin was dimensionally steady in length in the A and D cycles for all periods, while the Vipi resin was steady in the A, B and C cycles for all periods. The Classico resin was dimensionally steady in width in the C and D cycles for all periods, and the Vipi resin was steady in all cycles and periods. The hardness values for Classico resin were steady in all cycles and periods, while the Vipi resin was steady only in the C cycle for all periods. Impact strength values for Classico resin were steady in the A, C and D cycles for all periods, while Vipi resin was steady in all cycles and periods. SMD promoted different effects on the linear dimensional changes, hardness and impact strength of acrylic resins submitted to different polymerization cycles when after SMD and water storage were considered.

Effect Of Simulated Microwave Disinfection On The Linear Dimensional Change, Hardness And Impact Strength Of Acrylic Resins Processed By Different Polymerization Cycles.

This study investigated the effect of simulated microwave disinfection (SMD) on the linear dimensional changes, hardness and impact strength of acrylic resins under different polymerization cycles. Metal dies with referential points were embedded in flasks with dental stone. Samples of Classico and Vipi acrylic resins were made following the manufacturers' recommendations. The assessed polymerization cycles were: A) water bath at 74 ºC for 9 h; B) water bath at 74 ºC for 8 h and temperature increased to 100 ºC for 1 h; C) water bath at 74 ºC for 2 h and temperature increased to 100 ºC for 1 h; and D) water bath at 120 ºC and pressure of 60 pounds. Linear dimensional distances in length and width were measured after SMD and water storage at 37 ºC for 7 and 30 days using an optical microscope. SMD was carried out with the samples immersed in 150 mL of water in an oven (650 W for 3 min). A load of 25 gf for 10 s was used in the hardness test. Charpy impact test was performed with 40 kpcm. Data were submitted to ANOVA and Tukey's test (5%). The Classico resin was dimensionally steady in length in the A and D cycles for all periods, while the Vipi resin was steady in the A, B and C cycles for all periods. The Classico resin was dimensionally steady in width in the C and D cycles for all periods, and the Vipi resin was steady in all cycles and periods. The hardness values for Classico resin were steady in all cycles and periods, while the Vipi resin was steady only in the C cycle for all periods. Impact strength values for Classico resin were steady in the A, C and D cycles for all periods, while Vipi resin was steady in all cycles and periods. SMD promoted different effects on the linear dimensional changes, hardness and impact strength of acrylic resins submitted to different polymerization cycles when after SMD and water storage were considered.

Does The Reciproc File Remove Root Canal Bacteria And Endotoxins As Effectively As Multifile Rotary Systems?

To evaluate the effectiveness of Reciproc for the removal of cultivable bacteria and endotoxins from root canals in comparison with multifile rotary systems. The root canals of forty human single-rooted mandibular pre-molars were contaminated with an Escherichia coli suspension for 21 days and randomly assigned to four groups according to the instrumentation system: GI - Reciproc (VDW); GII - Mtwo (VDW); GIII - ProTaper Universal (Dentsply Maillefer); and GIV -FKG Race(™) (FKG Dentaire) (n = 10 per group). Bacterial and endotoxin samples were taken with a sterile/apyrogenic paper point before (s1) and after instrumentation (s2). Culture techniques determined the colony-forming units (CFU) and the Limulus Amebocyte Lysate assay was used for endotoxin quantification. Results were submitted to paired t-test and anova. At s1, bacteria and endotoxins were recovered in 100% of the root canals investigated (40/40). After instrumentation, all systems were associated with a highly significant reduction of the bacterial load and endotoxin levels, respectively: GI - Reciproc (99.34% and 91.69%); GII - Mtwo (99.86% and 83.11%); GIII - ProTaper (99.93% and 78.56%) and GIV - FKG Race(™) (99.99% and 82.52%) (P < 0.001). No statistical difference were found amongst the instrumentation systems regarding bacteria and endotoxin removal (P > 0.01). The reciprocating single file, Reciproc, was as effective as the multifile rotary systems for the removal of bacteria and endotoxins from root canals.

The Effect Of Soy Dietary Supplement And Low Dose Of Hormone Therapy On Main Cardiovascular Health Biomarkers: A Randomized Controlled Trial.

To assess the effects of a soy dietary supplement on the main biomarkers of cardiovascular health in postmenopausal women compared with the effects of low-dose hormone therapy (HT) and placebo. Double-blind, randomized and controlled intention-to-treat trial. Sixty healthy postmenopausal women, aged 40-60 years, 4.1 years mean time since menopause were recruited and randomly assigned to 3 groups: a soy dietary supplement group (isoflavone 90mg), a low-dose HT group (estradiol 1 mg plus noretisterone 0.5 mg) and a placebo group. Lipid profile, glucose level, body mass index, blood pressure and abdominal/hip ratio were evaluated in all the participants at baseline and after 16 weeks. Statistical analyses were performed using the χ2 test, Fisher's exact test, Kruskal-Wallis non-parametric test, analysis of variance (ANOVA), paired Student's t-test and Wilcoxon test. After a 16-week intervention period, total cholesterol decreased 11.3% and LDL-cholesterol decreased 18.6% in the HT group, but both did not change in the soy dietary supplement and placebo groups. Values for triglycerides, HDL-cholesterol, glucose level, body mass index, blood pressure and abdominal/hip ratio did not change over time in any of the three groups. The use of dietary soy supplement did not show any significant favorable effect on cardiovascular health biomarkers compared with HT. The trial is registered at the Brazilian Clinical Trials Registry (Registro Brasileiro de Ensaios Clínicos - ReBEC), number RBR-76mm75.