Statnote 5: Is one set of data more variable than another?

There may be circumstances where it is necessary for microbiologists to compare variances rather than means, e,g., in analysing data from experiments to determine whether a particular treatment alters the degree of variability or testing the assumption of homogeneity of variance prior to other statistical tests. All of the tests described in this Statnote have their limitations. Bartlett’s test may be too sensitive but Levene’s and the Brown-Forsythe tests also have problems. We would recommend the use of the variance-ratio test to compare two variances and the careful application of Bartlett’s test if there are more than two groups. Considering that these tests are not particularly robust, it should be remembered that the homogeneity of variance assumption is usually the least important of those considered when carrying out an ANOVA. If there is concern about this assumption and especially if the other assumptions of the analysis are also not likely to be met, e.g., lack of normality or non additivity of treatment effects then it may be better either to transform the data or to carry out a non-parametric test on the data.

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.

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.

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.

The correlation between tests of visual function and perceived visual ability in central field loss patients

Purpose: To investigate the correlation between tests of visual function and perceived visual ability recorded with a 'quality-of-life' questionnaire for patients with central field loss. Method: 12 females and 7 males (mean age = 53.1 years; Range = 23 - 80 years) with subfoveal neovascular membranes underwent a comprehensive assessment of visual function. Tests included unaided distance vision, high and low contrast distance logMAR visual acuity (VA), Pelli-Robson contrast senstivity (at 1m), near logMAR word VA and text reading speed. All tests were done both monocularly and binocularly. The patients also completed a 28 point questionnaire separated into a 'core' section consisting of general questions about perceived visual function and a 'module' section with specific questions on reading function. Results: Step-wise multiple regression analysis was used to determine which visual function tests were correlated with the patients's perceived visual function and to rank them in order of importance. The visual function test that explains most of the variance in both 'core' score (66%0 and the 'module' score (68%) of the questionnaire is low contrast VA in the better eye (P<0.001 in both cases). Further, the module score also accounts for a significant proportion of the variance (P<0.01) of the distance logMAR VA in both the better and worse eye, and the near logMAR in both the better eye and binocularly. Conclusions: The best predictor of both perceived reading ability and of general perceived visual ability in this study is low contrast logMAR VA. The results highlight that distance VA is not the only relevant measure of visual fucntion in relation to a patients's perceived visual performance and should not be considered a determinant of surgical or management success.

The role of hemifield sector analysis in multifocal visual evoked potential objective perimetry in the early detection of glaucomatous visual field defects

Objective: The purpose of this study was to examine the effectiveness of a new analysis method of mfVEP objective perimetry in the early detection of glaucomatous visual field defects compared to the gold standard technique. Methods and patients: Three groups were tested in this study; normal controls (38 eyes), glaucoma patients (36 eyes), and glaucoma suspect patients (38 eyes). All subjects underwent two standard 24-2 visual field tests: one with the Humphrey Field Analyzer and a single mfVEP test in one session. Analysis of the mfVEP results was carried out using the new analysis protocol: the hemifield sector analysis protocol. Results: Analysis of the mfVEP showed that the signal to noise ratio (SNR) difference between superior and inferior hemifields was statistically significant between the three groups (analysis of variance, P<0.001 with a 95% confidence interval, 2.82, 2.89 for normal group; 2.25, 2.29 for glaucoma suspect group; 1.67, 1.73 for glaucoma group). The difference between superior and inferior hemifield sectors and hemi-rings was statistically significant in 11/11 pair of sectors and hemi-rings in the glaucoma patients group (t-test P<0.001), statistically significant in 5/11 pairs of sectors and hemi-rings in the glaucoma suspect group (t-test P<0.01), and only 1/11 pair was statistically significant (t-test P<0.9). The sensitivity and specificity of the hemifield sector analysis protocol in detecting glaucoma was 97% and 86% respectively and 89% and 79% in glaucoma suspects. These results showed that the new analysis protocol was able to confirm existing visual field defects detected by standard perimetry, was able to differentiate between the three study groups with a clear distinction between normal patients and those with suspected glaucoma, and was able to detect early visual field changes not detected by standard perimetry. In addition, the distinction between normal and glaucoma patients was especially clear and significant using this analysis. Conclusion: The new hemifield sector analysis protocol used in mfVEP testing can be used to detect glaucomatous visual field defects in both glaucoma and glaucoma suspect patients. Using this protocol, it can provide information about focal visual field differences across the horizontal midline, which can be utilized to differentiate between glaucoma and normal subjects. The sensitivity and specificity of the mfVEP test showed very promising results and correlated with other anatomical changes in glaucomatous visual field loss. The intersector analysis protocol can detect early field changes not detected by the standard Humphrey Field Analyzer test. © 2013 Mousa et al, publisher and licensee Dove Medical Press Ltd.

Intrapartum tests for group B streptococcus:accuracy and acceptability of screening

Objective: To assess the accuracy and acceptability of polymerase chain reaction (PCR) and optical immunoassay (OIA) tests for the detection of maternal group B streptococcus (GBS) colonisation during labour, comparing their performance with the current UK policy of risk factor-based screening. Design Diagnostic test accuracy study. Setting and population Fourteen hundred women in labour at two large UK maternity units provided vaginal and rectal swabs for testing. Methods The PCR and OIA index tests were compared with the reference standard of selective enriched culture, assessed blind to index tests. Factors influencing neonatal GBS colonisation were assessed using multiple logistic regression, adjusting for antibiotic use. The acceptability of testing to participants was evaluated through a structured questionnaire administered after delivery. Main outcome measures The sensitivity and specificity of PCR, OIA and risk factor-based screening. Results Maternal GBS colonisation was 21% (19-24%) by combined vaginal and rectal swab enriched culture. PCR test of either vaginal or rectal swabs was more sensitive (84% [79-88%] versus 72% [65-77%]) and specific (87% [85-89%] versus 57% [53-60%]) than OIA (P <0.001), and far more sensitive (84 versus 30% [25-35%]) and specific (87 versus 80% [77-82%]) than risk factor-based screening (P <0.001). Maternal antibiotics (odds ratio, 0.22 [0.07-0.62]; P = 0.004) and a positive PCR test (odds ratio, 29.4 [15.8-54.8]; P <0.001) were strongly related to neonatal GBS colonisation, whereas risk factors were not (odds ratio, 1.44 [0.80-2.62]; P = 0.2). Conclusion Intrapartum PCR screening is a more accurate predictor of maternal and neonatal GBS colonisation than is OIA or risk factor-based screening, and is acceptable to women. © RCOG 2010 BJOG An International Journal of Obstetrics and Gynaecology.

The effects of non-trading on the illiquidity ratio

Using a simulation analysis we show that non-trading can cause an overstatement of the observed illiquidity ratio. Our paper shows how this overstatement can be eliminated with a very simple adjustment to the Amihud illiquidity ratio. We find that the adjustment improves the relationship between the illiquidity ratio and measures of illiquidity calculated from transaction data. Asset pricing tests show that without the adjustment, illiquidity premia estimates can be understated by more than 17% for NYSE securities and by more than 24% for NASDAQ securities.