Data analysis methods in optometry: is there a difference between two samples? Part 2.

In this second article, statistical ideas are extended to the problem of testing whether there is a true difference between two samples of measurements. First, it will be shown that the difference between the means of two samples comes from a population of such differences which is normally distributed. Second, the 't' distribution, one of the most important in statistics, will be applied to a test of the difference between two means using a simple data set drawn from a clinical experiment in optometry. Third, in making a t-test, a statistical judgement is made as to whether there is a significant difference between the means of two samples. Before the widespread use of statistical software, this judgement was made with reference to a statistical table. Even if such tables are not used, it is useful to understand their logical structure and how to use them. Finally, the analysis of data, which are known to depart significantly from the normal distribution, will be described.

Data analysis methods in optometry Part 3: the analysis of frequencies and proportions

In some studies, the data are not measurements but comprise counts or frequencies of particular events. In such cases, an investigator may be interested in whether one specific event happens more frequently than another or whether an event occurs with a frequency predicted by a scientific model.

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 analysis methods in optometry. Part 5: correlation

1. Pearson's correlation coefficient only tests whether the data fit a linear model. With large numbers of observations, quite small values of r become significant and the X variable may only account for a minute proportion of the variance in Y. Hence, the value of r squared should always be calculated and included in a discussion of the significance of r. 2. The use of r assumes that a bivariate normal distribution is present and this assumption should be examined prior to the study. If Pearson's r is not appropriate, then a non-parametric correlation coefficient such as Spearman's rs may be used. 3. A significant correlation should not be interpreted as indicating causation especially in observational studies in which there is a high probability that the two variables are correlated because of their mutual correlations with other variables. 4. In studies of measurement error, there are problems in using r as a test of reliability and the ‘intra-class correlation coefficient’ should be used as an alternative. A correlation test provides only limited information as to the relationship between two variables. Fitting a regression line to the data using the method known as ‘least square’ provides much more information and the methods of regression and their application in optometry will be discussed in the next article.

Data analysis methods in optometry Part 7: multiple linear regression

Multiple regression analysis is a complex statistical method with many potential uses. It has also become one of the most abused of all statistical procedures since anyone with a data base and suitable software can carry it out. An investigator should always have a clear hypothesis in mind before carrying out such a procedure and knowledge of the limitations of each aspect of the analysis. In addition, multiple regression is probably best used in an exploratory context, identifying variables that might profitably be examined by more detailed studies. Where there are many variables potentially influencing Y, they are likely to be intercorrelated and to account for relatively small amounts of the variance. Any analysis in which R squared is less than 50% should be suspect as probably not indicating the presence of significant variables. A further problem relates to sample size. It is often stated that the number of subjects or patients must be at least 5-10 times the number of variables included in the study.5 This advice should be taken only as a rough guide but it does indicate that the variables included should be selected with great care as inclusion of an obviously unimportant variable may have a significant impact on the sample size required.

Data analysis methods in optometry Part 8: Principal components analysis (PCA) and factor analysis (FA)

PCA/FA is a method of analyzing complex data sets in which there are no clearly defined X or Y variables. It has multiple uses including the study of the pattern of variation between individual entities such as patients with particular disorders and the detailed study of descriptive variables. In most applications, variables are related to a smaller number of ‘factors’ or PCs that account for the maximum variance in the data and hence, may explain important trends among the variables. An increasingly important application of the method is in the ‘validation’ of questionnaires that attempt to relate subjective aspects of a patients experience with more objective measures of vision.

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.

Data methods in optometry. Part 10: non-linear regression analysis

1. The techniques associated with regression, whether linear or non-linear, are some of the most useful statistical procedures that can be applied in clinical studies in optometry. 2. In some cases, there may be no scientific model of the relationship between X and Y that can be specified in advance and the objective may be to provide a ‘curve of best fit’ for predictive purposes. In such cases, the fitting of a general polynomial type curve may be the best approach. 3. An investigator may have a specific model in mind that relates Y to X and the data may provide a test of this hypothesis. Some of these curves can be reduced to a linear regression by transformation, e.g., the exponential and negative exponential decay curves. 4. In some circumstances, e.g., the asymptotic curve or logistic growth law, a more complex process of curve fitting involving non-linear estimation will be required.

Tear analysis and lens-tear interactions:part II. Ocular lipids-nature and fate of meibomian gland phospholipids

Purpose: Published data indicate that the polar lipid content of human meibomian gland secretions (MGS) could be anything between 0.5% and 13% of the total lipid. The tear film phospholipid composition has not been studied in great detail and it has been understood that the relative proportions of lipids in MGS would be maintained in the tear film. The purpose of this work was to determine the concentration of phospholipids in the human tear film. Methods: Liquid chromatography mass spectrometry (LCMS) and thin layer chromatography (TLC) were used to determine the concentration of phospholipid in the tear film. Additionally, an Amplex Red phosphatidylcholine-specific phospholipase C (PLC) assay kit was used for determination of the activity of PLC in the tear film. Results: Phospholipids were not detected in any of the tested human tear samples with the low limit of detection being 1.3 µg/mL for TLC and 4 µg/mL for liquid chromatography mass spectrometry. TLC indicated that diacylglycerol (DAG) may be present in the tear film. PLC was in the tear film with an activity determined at approximately 15 mU/mL, equivalent to the removal of head groups from phosphatidylcholine at a rate of approximately 15 µM/min. Conclusions: This work shows that phospholipid was not detected in any of the tested human tear samples (above the lower limits of detection as described) and suggests the presence of DAG in the tear film. DAG is known to be at low concentrations in MGS. These observations indicate that PLC may play a role in modulating the tear film phospholipid concentration.

Applicability of contact angle techniques used in the analysis of contact lenses, part 1:comparative methodologies

Objectives and Methods: Contact angle, as a representative measure of surface wettability, is often employed to interpret contact lens surface properties. The literature is often contradictory and can lead to confusion. This literature review is part of a series regarding the analysis of hydrogel contact lenses using contact angle techniques. Here we present an overview of contact angle terminology, methodology, and analysis. Having discussed this background material, subsequent parts of the series will discuss the analysis of contact lens contact angles and evaluate differences in published laboratory results. Results: The concepts of contact angle, wettability and wetting are presented as an introduction. Contact angle hysteresis is outlined and highlights the advantages in using dynamic analytical techniques over static methods. The surface free energy of a material illustrates how contact angle analysis is capable of providing supplementary surface characterization. Although single values are able to distinguish individual material differences, surface free energy and dynamic methods provide an improved understanding of material behavior. The frequently used sessile drop, captive bubble, and Wilhelmy plate techniques are discussed. Their use as both dynamic and static methods, along with the advantages and disadvantages of each technique, is explained. Conclusions: No single contact angle technique fully characterizes the wettability of a material surface, and the application of complimenting methods allows increased characterization. At present, there is not an ISO standard method designed for soft materials. It is important that each contact angle technique has a standard protocol, as small protocol differences between laboratories often contribute to a variety of published data that are not easily comparable. © 2013 Contact Lens Association of Ophthalmologists.

Tear analysis and lens-tear interactions:Part I. Protein fingerprinting with microfluidic technology

The purpose of this work is to establish the application of a fully automated microfluidic chip based protein separation assay in tear analysis. It is rapid, requires small sample volumes and is vastly superior to, and more convenient than, comparable conventional gel electrophoresis assays. The protein sizing chip technology was applied to three specific fields of analysis. Firstly tear samples were collected regularly from subjects establishing the baseline effects of tear stimulation, tear state and patient health. Secondly tear samples were taken from lens wearing eyes and thirdly the use of microfluidic technology was assessed as a means to investigate a novel area of tear analysis, which we have termed the 'tear envelope'. Utilising the Agilent 2100 Bioanalyzer in combination with the Protein 200 Plus LabChip kit, these studies investigated tear proteins in the range of 14-200 kDa. Particular attention was paid to the relative concentrations of lysozyme, tear lipocalin, secretory IgA (sIgA), IgG and lactoferrin, together with the overall tear electropherogram 'fingerprint'. Furthermore, whilst lens-tear interaction studies are generally thought of as an investigation into the effects of tears components on the contact lens material, i.e. deposition studies, this report addresses the reverse phenomenon-the effect of the lens, and particularly the newly inserted lens, on the tear fluid composition and dynamics. The use of microfluidic technology provides a significant advance in tear studies and should prove invaluable in tear diagnostics and contact lens performance analysis.

The State of the Nation Debate as part of the democratic parliamentary ritual: Rajoy and Rubalcaba discourse analysis, 2014

In this article we analyze the Debate on the State of the Nation 2014. The methodology consists in coding the speeches of the prime minister, Mariano Rajoy (PP) and the then opposition leader Alfredo Perez Rubalcaba (PSOE) through extracting word clouds, branched maps and word trees that have shown the most common concepts and premises. This preliminary analysis of two dimensions, quantitative and qualitative, makes it much easier and viable subsequent discourse analysis where we focus on the different types of arguments in the communicative act: claim/solution, circumstantial premises, goal premises, value premises, meansgoal premises, alternative options/addressing alternative options.