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.

Operator-induced errors in Hartmann-Shack wavefront sensing:model eye study

Purpose: To evaluate the effects of instrument realignment and angular misalignment during the clinical determination of wavefront aberrations by simulation in model eyes. Setting: Aston Academy of Life Sciences, Aston University, Birmingham, United Kingdom. Methods: Six model eyes were examined with wavefront-aberration-supported cornea ablation (WASCA) (Carl Zeiss Meditec) in 4 sessions of 10 measurements each: sessions 1 and 2, consecutive repeated measures without realignment; session 3, realignment of the instrument between readings; session 4, measurements without realignment but with the model eye shifted 6 degrees angularly. Intersession repeatability and the effects of realignment and misalignment were obtained by comparing the measurements in the various sessions for coma, spherical aberration, and higher-order aberrations (HOAs). Results: The mean differences between the 2 sessions without realignment of the instrument were 0.020 μm ± 0.076 (SD) for Z3 - 1(P = .551), 0.009 ± 0.139 μm for Z3 1(P = .877), 0.004 ± 0.037 μm for Z4 0 (P = .820), and 0.005 ± 0.01 μm for HO root mean square (RMS) (P = .301). Differences between the nonrealigned and realigned instruments were -0.017 ± 0.026 μm for Z3 - 1(P = .159), 0.009 ± 0.028 μm for Z3 1 (P = .475), 0.007 ± 0.014 μm for Z4 0(P = .296), and 0.002 ± 0.007 μm for HO RMS (P = 0.529; differences between centered and misaligned instruments were -0.355 ± 0.149 μm for Z3 - 1 (P = .002), 0.007 ± 0.034 μm for Z3 1(P = .620), -0.005 ± 0.081 μm for Z4 0(P = .885), and 0.012 ± 0.020 μm for HO RMS (P = .195). Realignment increased the standard deviation by a factor of 3 compared with the first session without realignment. Conclusions: Repeatability of the WASCA was excellent in all situations tested. Realignment substantially increased the variance of the measurements. Angular misalignment can result in significant errors, particularly in the determination of coma. These findings are important when assessing highly aberrated eyes during follow-up or before surgery. © 2007 ASCRS and ESCRS.

A longitudinal study of vergence adaptation in incipient presbyopia

Background: To investigate vergence adaptation during the incipient phase of presbyopia, when the amplitude of accommodation approaches the level where the first reading addition is required. The study aimed to assess the ability of the vergence system to counteract changes in the component contributions to the overall vergence response with the decline in the amplitude of accommodation in presbyopia, although previous reports on the nature of changes in accommodative, tonic and proximal vergence are equivocal. Methods: Using a 'flashed' Maddox rod technique, an assessment of vergence adaptation to 6 Δ base-out and 6Δ base-in prism was made for 28 subjects (aged 35-45 years at the commencement of the study). The measurements were taken four times over a 2-year period. Results: Using a repeated measures analysis of variance, the results show that with the decline in amplitude of accommodation, there is a statistically significant reduction in the magnitude of vergence adaptation to both base-out (p < 0.05) and base-in prism (p < 0.01). Conclusions: This study shows that with ageing, there is a decrease in the ability of the slow vergence mechanism to overcome a change in fusional vergence demand and would suggest that either the fast component of fusional vergence must cope with any change in fusional vergence demand or that the sum of the accommodative, tonic and proximal vergence responses are virtually stable with age. © 2003 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 10: the two-way analysis of variance

The two-way design has been variously described as a matched-sample F-test, a simple within-subjects ANOVA, a one-way within-groups ANOVA, a simple correlated-groups ANOVA, and a one-factor repeated measures design! This confusion of terminology is likely to lead to problems in correctly identifying this analysis within commercially available software. The essential feature of the design is that each treatment is allocated by randomization to one experimental unit within each group or block. The block may be a plot of land, a single occasion in which the experiment was performed, or a human subject. The ‘blocking’ is designed to remove an aspect of the error variation and increase the ‘power’ of the experiment. If there is no significant source of variation associated with the ‘blocking’ then there is a disadvantage to the two-way design because there is a reduction in the DF of the error term compared with a fully randomised design thus reducing the ‘power’ of the analysis.

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.

Perceptions of technological change : the attitude of managers towards group technology in the United States food equipment industry

In the center of today's continued and rapid technological change and ever competitive environment of the next millennium, manufacturers must realize that unless they are ready to consider and evaluate new technologies brought onto them, they may fail to adequately respond to the challenges that lie ahead of them. This research was designed to determine the consistency of the perceptions of technical and non-technical administrators, in manufacturing environment, towards technological change and group technology as an advanced manufacturing system. This research has included a review of literature with references to technological change, justification and implementation processes, and various manufacturing systems including group technology and its benefits. This research has used the research method of empirical analysis (quantitative) and case studies (qualitative) to research perceptions of technical and non-technical administrators towards technological change and group technology. Sixty-four (64) technical and fifty-one (51) nontechnical administrators from fifty (50) manufacturing organizations in the United States of America responded to the mail survey questionnaire used in this research. Responses were analyzed using the Repeated Measures ANOVA procedure to compare mean responses of each group. Two correlation analyses, Cronback Coefficient Alpha and Pearson Correlation Coefficient, were also performed to determine the reliability of the questionnaire as well as the degree of correlation of perceptions between these two groups. This research, through the empirical analysis, has found that perceptions of the technical and non-technical administrators towards group technology were not consistent. In other words, they did not perceive the benefits of group technology in the same manner to the overall organizational performance. This finding was significant since it provided the first clear and comprehensive view of the technical and non-technical administrators' perception towards group technology and technological change, in Food Equipment Manufacturer Industry, in United States of America. In addition, a number of cases were analyzed and the results have supported those of the quantitative analysis. Therefore, this research not only has provided basic data, which was unavailable prior to this investigation, but it also provided a basis for future studies.

Tablet App halometer for the assessment of dysphotopsia

Purpose To assess the validity and repeatability of the Aston Halometer. Setting University clinic, United Kingdom. Design Prospective, repeated-measures experimental study. Methods The halometer comprises a bright light-emitting-diode (LED) glare source in the center of an iPad4. Letters subtending 0.21° (∼0.3 logMAR) were moved centrifugally from the LED in 0.05 degree steps in 8 orientations separated by 45 degrees for each of 4 contrast levels (1000, 500, 100, and 25 Weber contrast units [Cw]) in random order. Bangerter occlusion foils were inserted in front of the right eye to simulate monocular glare conditions in 20 subjects (mean age 27.7 ± 3.1 years). Subjects were positioned 2 meters from the screen in a dark room with the iPad controlled from an iPhone via Bluetooth operated by the researcher. The C-Quant straylight meter was also used with each of the foils to measure the level of straylight over the retina. Halometry and straylight repeatability was assessed at a second visit. Results Halo size increased with the different occlusion foils and target contrasts (F = 29.564, P <.001) as expected and in a pattern similar to straylight measures (F = 80.655, P <0.001). Lower contrast letters showed better sensitivity but larger glare-obscured areas, resulting in ceiling effects caused by the screen's field-of-view, with 500 Cw being the best compromise. Intraobserver and interobserver repeatability of the Aston Halometer was good (500Cw: 0.84 to 0.93 and 0.53 to 0.73) and similar to the straylight meter. Conclusion The halometer provides a sensitive, repeatable way of quantifying a patient-recognized form of disability glare in multiple orientations to add objectivity to subjectively reported discomfort glare.

Ocular biometric correlates of ciliary muscle thickness in human myopia

Purpose - Anterior segment optical coherent tomography (AS-OCT) is used to further examine previous reports that ciliary muscle thickness (CMT) is increased in myopic eyes. With reference to temporal and nasal CMT, interrelationships between biometric and morphological characteristics of anterior and posterior segments are analysed for British-White and British-South-Asian adults with and without myopia. Methods - Data are presented for the right eyes of 62 subjects (British-White n = 39, British-South-Asian n = 23, aged 18–40 years) with a range of refractive error (mean spherical error (MSE (D)) -1.74 ± 3.26; range -10.06 to +4.38) and separated into myopes (MSE (D) <-0.50, range -10.06 to -0.56; n = 30) and non-myopes (MSE (D) =-0.50, -0.50 to +4.38; n = 32). Temporal and nasal ciliary muscle cross-sections were imaged using a Visante AS-OCT. Using Visante software, manual measures of nasal and temporal CMT (NCMT and TCMT respectively) were taken in successive posterior 1 mm steps from the scleral spur over a 3 mm distance (designated NCMT1, TCMT1 et seq). Measures of axial length and anterior chamber depth were taken with an IOLMaster biometer. MSE and corneal curvature (CC) measurements were taken with a Shin-Nippon auto-refractor. Magnetic resonance imaging was used to determine total ocular volume (OV) for 31 of the original subject group. Statistical comparisons and analyses were made using mixed repeated measures anovas, Pearson's correlation coefficient and stepwise forward multiple linear regression. Results - MSE was significantly associated with CMT, with thicker CMT2 and CMT3 being found in the myopic eyes (p = 0.002). In non-myopic eyes TCMT1, TCMT2, NCMT1 and NCMT2 correlated significantly with MSE, AL and OV (p < 0.05). In contrast, myopic eyes failed generally to exhibit a significant correlation between CMT, MSE and axial length but notably retained a significant correlation between OV, TCMT2, TCMT3, NCMT2 and NCMT3 (p < 0.05). OV was found to be a significantly better predictor of TCMT2 and TCMT3 than AL by approximately a factor of two (p < 0.001). Anterior chamber depth was significantly associated with both temporal and nasal CMT2 and CMT3; TCMT1 correlated positively with CC. Ethnicity had no significant effect on differences in CMT. Conclusions - Increased CMT is associated with myopia. We speculate that the lack of correlation in myopic subjects between CMT and axial length, but not between CMT and OV, is evidence that disrupted feedback between the fovea and ciliary apparatus occurs in myopia development.

Dapagliflozin add-on to metformin in type 2 diabetes inadequately controlled with metformin:a randomized, double-blind, placebo-controlled 102-week trial

Background: Management of type 2 diabetes with metformin often does not provide adequate glycemic control, thereby necessitating add-on treatment. In a 24-week clinical trial, dapagliflozin, an investigational sodium glucose cotransporter 2 inhibitor, improved glycemic control in patients inadequately controlled with metformin. The present study is an extension that was undertaken to evaluate dapagliflozin as long-term therapy in this population.Methods: This was a long-term extension (total 102 weeks) of a 24-week phase 3, multicenter, randomized, placebo-controlled, double-blind, parallel-group trial. Patients were randomly assigned (1:1:1:1) to blinded daily treatment (placebo, or dapagliflozin 2.5 to 5, or 10 mg) plus open-label metformin (=1,500 mg). The previously published primary endpoint was change from baseline in glycated hemoglobin (HbA1c) at 24 weeks. This paper reports the follow-up to week 102, with analysis of covariance model performed at 24 weeks with last observation carried forward; a repeated measures analysis was utilized to evaluate changes from baseline in HbA1c, fasting plasma glucose (FPG), and weight.Results: A total of 546 patients were randomized to 1 of the 4 treatments. The completion rate for the 78-week double-blind extension period was lower for the placebo group (63.5%) than for the dapagliflozin groups (68.3% to 79.8%). At week 102, mean changes from baseline HbA1c (8.06%) were +0.02% for placebo compared with -0.48% (P = 0.0008), -0.58% (P

Induced vertical disparity effects on local and global stereopsis

Purpose: Although significant amounts of vertical misalignment could have a noticeable effect on visual performance, there is no conclusive evidence about the effect of very small amount of vertical disparity on stereopsis and binocular vision. Hence, the aim of this study was to investigate the effects of induced vertical disparity on local and global stereopsis at near. Materials and Methods: Ninety participants wearing best-corrected refraction had local and global stereopsis tested with 0.5 and 1.0 prism diopter (Δ) vertical prism in front of their dominant and non-dominant eye in turn. This was compared to local and global stereopsis in the same subjects without vertical prism. Data were analyzed in SPSS.17 software using the independent samples T and the repeated measures ANOVA tests. Results: Induced vertical disparity decreases local and global stereopsis. This reduction is greater when vertical disparity is induced in front of the non-dominant eye and affects global more than local stereopsis. Repeated measures ANOVA showed differences in the mean stereopsis between the different measured states for local and global values. Local stereopsis thresholds were reduced by 10s of arc or less on average with 1.0Δ of induced vertical prism in front of either eye. However, global stereopsis thresholds were reduced by over 100s of arc by the same 1.0Δ of induced vertical prism. Conclusion: Induced vertical disparity affects global stereopsis thresholds by an order of magnitude (or a factor of 10) more than local stereopsis. Hence, using a test that measures global stereopsis such as the TNO is more sensitive to vertical misalignment than a test such as the Stereofly that measures local stereopsis. © 2014 Informa Healthcare USA, Inc. All rights reserved: reproduction in whole or part not permitted.

QT interval prolongation related to psychoactive drug treatment:a comparison of monotherapy versus polytherapy

Background - Several antipsychotic agents are known to prolong the QT interval in a dose dependent manner. Corrected QT interval (QTc) exceeding a threshold value of 450 ms may be associated with an increased risk of life threatening arrhythmias. Antipsychotic agents are often given in combination with other psychotropic drugs, such as antidepressants, that may also contribute to QT prolongation. This observational study compares the effects observed on QT interval between antipsychotic monotherapy and psychoactive polytherapy, which included an additional antidepressant or lithium treatment. Method - We examined two groups of hospitalized women with Schizophrenia, Bipolar Disorder and Schizoaffective Disorder in a naturalistic setting. Group 1 was composed of nineteen hospitalized women treated with antipsychotic monotherapy (either haloperidol, olanzapine, risperidone or clozapine) and Group 2 was composed of nineteen hospitalized women treated with an antipsychotic (either haloperidol, olanzapine, risperidone or quetiapine) with an additional antidepressant (citalopram, escitalopram, sertraline, paroxetine, fluvoxamine, mirtazapine, venlafaxine or clomipramine) or lithium. An Electrocardiogram (ECG) was carried out before the beginning of the treatment for both groups and at a second time after four days of therapy at full dosage, when blood was also drawn for determination of serum levels of the antipsychotic. Statistical analysis included repeated measures ANOVA, Fisher Exact Test and Indipendent T Test. Results - Mean QTc intervals significantly increased in Group 2 (24 ± 21 ms) however this was not the case in Group 1 (-1 ± 30 ms) (Repeated measures ANOVA p < 0,01). Furthermore we found a significant difference in the number of patients who exceeded the threshold of borderline QTc interval value (450 ms) between the two groups, with seven patients in Group 2 (38%) compared to one patient in Group 1 (7%) (Fisher Exact Text, p < 0,05). Conclusions - No significant prolongation of the QT interval was found following monotherapy with an antipsychotic agent, while combination of these drugs with antidepressants caused a significant QT prolongation. Careful monitoring of the QT interval is suggested in patients taking a combined treatment of antipsychotic and antidepressant agents.

Gender comparisons of fat talk in the United Kingdom and the United States

This study compared different forms of body talk, including "fat talk," among 231 university men and women in central England (UK; n = 93) and the southeastern United States (US; n = 138). A 2 (gender) by 2 (country) repeated measures ANOVA across types of body talk (negative, self-accepting, positive) and additional Chi-square analyses revealed that there were differences across gender and between the UK and US cultures. Specifically, UK and US women were more likely to report frequently hearing or perceiving pressure to engage in fat talk than men. US women and men were also more likely to report pressure to join in self-accepting body talk than UK women and men. © 2010 Springer Science+Business Media, LLC.

Stereoacuity as an indicator of prism adaptation

Purpose: The purpose of this study was to determine whether stereoacuity can be used as an indicator of prism adaptation. In particular, we wanted to know whether the time required for stereoacuity to return to the initial level after viewing through a prism can be used to determine the degree of adaptation. Materials and Methods: Eighteen subjects participated in this study. Stereoacuity and dissociated phoria were determined using the TNO stereotest and the Maddox rod, respectively. Prism vergences were measured using a prism bar. For each participant, prism power equivalent to the blur point of base-in (BI) and base-out (BO) fusional vergence at 40 cm was divided and placed in front of both eyes. At 0, 3, 6, 9 and 12 min after prism introduction, the stereoacuity was measured, and at 0 and 12 min, the heterophoria was measured. Results: The repeated measures ANOVA showed a significant difference between the mean stereoacuity for BI and BO prisms at the different measurement times (p < 0.05). For BO prism, the initial value was different between 0 and 3 min after the prism introduction, whereas for BI prism, a difference in stereoacuity was found between the pre-prism value and the value at 0, 3 and 6 min. The size of the heterophoria with BO and BI prisms was different from 0 to 12 min (p < 0.05). Conclusion: The time required for stereoacuity to return to baseline level was more than 3 min for BO, and more than 6 min for BI prism. In addition, the time required to return to baseline values was not similar for the stereoacuity and heterophoria. The recovery of stereoacuity is slower when adapting to divergence, as when looking from near to far. This implies that stereopsis responds faster to near targets than to distant one, and may precede complete phoria adaptation. © 2014 Informa Healthcare USA, Inc. All rights reserved: reproduction in whole or part not permitted.

Regional variation in peripapillary retinal blood flow in primary open angle glaucoma:a follow-up study

Purpose: To investigate whether regional long-term changes in peripapillary retinal flow, measured by scanning laser Doppler flowmetry (SLDF), occur in patients with primary open angle glaucoma (POAG). Methods: 31 healthy volunteers (mean age: 65 8.3 years) and 33 POAG patients (mean age: 71.2 7.6 years) were followed up every 4 months for 16 months. Using SLDF, three images of the superior and inferior optic nerve head were obtained for each subject. A 1010-pixel frame was used to measure blood flow, volume and velocity in the four quadrants of the peripapillary retina. Central 24-2 visual field testing was carried out at each visit. Repeated measures analysis of covariance was used to assess change over time between the normal and POAG groups for the SLDF parameters. Univariate linear regression analysis for mean deviation and glaucoma change probability (GCP) analysis were used to identify visual field progression. Results: Blood volume, flow and velocity measured in the inferior nasal quadrant of the peripapillary retina decreased significantly over time for the POAG group compared to the normal group (p=0.0073, 0.0097, 0.0095 respectively). Overall, 2 glaucoma patients showed a significantly deteriorating MD slope, while 7 patients showed visual field progression with GPA. All of the patients progressing with GPA, showed change in the superior hemifield and, of those, 14% showed change in the inferior hemifield. Conclusion: Glaucoma patients showed a decrease in blood flow, volume and velocity in the inferior nasal peripapillary retina. A regional variation in microvascular retinal capillary blood flow may provide insight into the pathogenesis of glaucomatous optic neuropathy. Keywords: 331 blood supply • 554 retina • 624 visual fields