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.

Experimental designs and analysis of data for mixtures

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Do tinted lenses or filters improve visual performance in low vision? A review of the literature

This is a review of studies that have investigated the proposed rehabilitative benefit of tinted lenses and filters for people with low vision. Currently, eye care practitioners have to rely on marketing literature and anecdotal reports from users when making recommendations for tinted lens or filter use in low vision. Our main aim was to locate a prescribing protocol that was scientifically based and could assist low vision specialists with tinted lens prescribing decisions. We also wanted to determine if previous work had found any tinted lens/task or tinted lens/ocular condition relationships, i.e. were certain tints or filters of use for specific tasks or for specific eye conditions. Another aim was to provide a review of previous research in order to stimulate new work using modern experimental designs. Past studies of tinted lenses and low vision have assessed effects on visual acuity (VA), grating acuity, contrast sensitivity (CS), visual field, adaptation time, glare, photophobia and TV viewing. Objective and subjective outcome measures have been used. However, very little objective evidence has been provided to support anecdotal reports of improvements in visual performance. Many studies are flawed in that they lack controls for investigator bias, and placebo, learning and fatigue effects. Therefore, the use of tinted lenses in low vision remains controversial and eye care practitioners will have to continue to rely on anecdotal evidence to assist them in their prescribing decisions. Suggestions for future research, avoiding some of these experimental shortcomings, are made. © 2002 The College of Optometrists.

Statnote 8: statistical power and sample size

Statistical software is now commonly available to calculate Power (P') and sample size (N) for most experimental designs. In many circumstances, however, sample size is constrained by lack of time, cost, and in research involving human subjects, the problems of recruiting suitable individuals. In addition, the calculation of N is often based on erroneous assumptions about variability and therefore such estimates are often inaccurate. At best, we would suggest that such calculations provide only a very rough guide of how to proceed in an experiment. Nevertheless, calculation of P' is very useful especially in experiments that have failed to detect a difference which the experimenter thought was present. We would recommend that P' should always be calculated in these circumstances to determine whether the experiment was actually too small to test null hypotheses adequately.

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.

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.

Disentangle contextual and permanent individual motivations:an application to shopping behavior

Past studies resulted in conflicting definitions of consumer motivation. On the one hand, motivations are seen as the consumer’s characteristics that shape her general behavior (motivational trait). On the other hand, they are seen as contextual variables representing the reason why the individual is behaving specific to today’s context (motivational state). The objective of this research is to stress the difference between these two concepts and to understand the impact of each on consumer behavior. We applied our empirical study to shopping motivations; our results show a strong interaction between motivational trait and motivational state. Problem and Hypothesis On the one hand, Westbrook and Black (1985) consider shopping motivations as individual permanent characteristics. This concept is shared by other researchers (Rohm and Swaminathan 2004), which show that some shoppers are functional (they shop for convenience, information seeking, and time saving) while some others are hedonic (they shop for social interaction, bargain hunting and browsing). On the other hand, Kaltcheva and Weitz (2006) define motivations as a contextual orientation changing over time, depending on the situation, and show that contextual shopping motivations have a strong impact on shopping behavior. From our knowledge, no research specifically examined the respective impact of both these shopping motivation types. To deal with this issue, we used the notions of “traits” and “states” that have been largely used in marketing research to designate respectively a permanent characteristic of the individual and a temporary orientation of the consumer (Mowen 2000). The reversal theory (Apter 2001) suggests that two opposite states exist: the telic and the paratelic states. In the telic state, individuals set goals for themselves, must be disciplined to reach these goals, and do not behave in accordance with their personal trait. In the paratelic state, individuals are seeking arousal and enjoyment, do not set rules, and one could postulate that they act in accordance with their natural tendencies. Based on these considerations, we hypothesize the following process: in situations involving paratelic states, hedonic as well as functional individuals should behave according to their natural traits, whereas in situations involving telic states, hedonic people should inhibit their natural propensity to enjoy shopping and behave similarly to functional people. Hence, we postulate the following: Hypothesis: Compared to shoppers with functional motivational trait, shoppers with hedonic motivational trait will a) significantly display more hedonic shopping behavior intentions in a condition of paratelic motivational state, and b) not display more hedonic shopping behavior intentions in a condition a telic motivational state Empirical Research First, 108 participants were asked to fill a multi-items scale about their shopping habits, which actually measured their shopping motivational traits. This questionnaire allowed us to highlight four different dimensions in shopping motivational traits: social interaction, novelty/utility seeking, bargain hunting, and browsing. According to their scores on different items, participants were classified as functional or as hedonic on each of these four dimensions (a single individual may be hedonic on some dimensions and functional on others). Then, participants were then induced to adopt either a telic or a paratelic shopping motivational state while reading an appropriate scenario. Finally, participants were asked for their shopping behavior intentions in response to the shopping context. Four items were developed, corresponding to the four shopping motivational trait dimensions we found with our factor analysis. Results As we found four dimensions in shopping motivational trait, we set up four quasi-experimental designs to capture the entire phenomenon: for each dimension, a 2 (motivational trait) x 2 (motivational state) design was built, where the dependant variable was the shopping behavior element corresponding to the studied dimension. Four 2 x 2 Anovas were performed to assess the interaction between motivational trait and motivational state. Concerning the three dimensions - browsing, novelty/utility seeking, and bargain hunting- , in the paratelic state scenario participants with hedonic motivational trait displayed significantly more hedonic shopping behavior intentions than participants with a functional motivational trait (resp. F = 9.701, p = .003; F = 4.979, p = .03; F = 5.757, p = .02); and in the telic state scenario, there was no significant difference in behavior intentions between participants with hedonic or functional motivation trait. Each time, the interaction effect between motivational state and motivational trait was significant (resp. F = 4.859, p = .03; F = 3.314, p = .07; F = 2.98, p = .08). Concerning the fourth dimension, social interaction, shopping behavior intentions of participants with hedonic and with functional motivational traits were significantly different in the paratelic state scenario (F = 29.898, p <.000) as well as in the telic state scenario (F = 9.559, p = .003). However, the interaction effect showed that this behavioral difference was significantly stronger in the paratelic scenario. All these results support our research hypothesis. Discussion and Implications Our study provides consistent support for our hypotheses saying that there is an interaction effect between shopping motivational states and shopping motivational traits. The generalization of the results is strengthened by the study of four different shopping traits: social interaction, novelty/utility seeking, bargain hunting and browsing. As we proposed, when shopping in a goal-oriented state (telic state), behaviors of hedonic and functional shoppers do not differ significantly. Conversely, when shopping for a recreational reason (paratelic state), hedonic and functional shoppers behave significantly different. These results could explain why some previous studies concluded that shopping motivational traits had no impact on shopping behavior: they did not take into consideration the interaction between motivational trait and motivational state. Moreover, our study shows that marketing surveys performed by store managers to draw the personal profile of their customers must be crossed with contextual motivations in order to accurately forecast shopper behavior. Future Developments Our results can be explained by the self-control process, which pushes hedonic-trait shoppers to behave in a rather functional way in utilitarian situations. However, to be certain that this is the very process that occurs, we plan to add self-control perception scales to our existing measures. This is obviously the next step of this research.

Theory and data for area summation of contrast with and without uncertainty:evidence for a noisy energy model

Contrast sensitivity improves with the area of a sine-wave grating, but why? Here we assess this phenomenon against contemporary models involving spatial summation, probability summation, uncertainty, and stochastic noise. Using a two-interval forced-choice procedure we measured contrast sensitivity for circular patches of sine-wave gratings with various diameters that were blocked or interleaved across trials to produce low and high extrinsic uncertainty, respectively. Summation curves were steep initially, becoming shallower thereafter. For the smaller stimuli, sensitivity was slightly worse for the interleaved design than for the blocked design. Neither area nor blocking affected the slope of the psychometric function. We derived model predictions for noisy mechanisms and extrinsic uncertainty that was either low or high. The contrast transducer was either linear (c1.0) or nonlinear (c2.0), and pooling was either linear or a MAX operation. There was either no intrinsic uncertainty, or it was fixed or proportional to stimulus size. Of these 10 canonical models, only the nonlinear transducer with linear pooling (the noisy energy model) described the main forms of the data for both experimental designs. We also show how a cross-correlator can be modified to fit our results and provide a contemporary presentation of the relation between summation and the slope of the psychometric function.

The antecedents and consequences of anticipatory identification

The aim of this thesis was to investigate anticipatory identification: newcomers’ identification with an organisation prior to entry; in particular by exploring the antecedents and consequences of the construct. Although organisational identification has been frequently investigated over the past 25 years, surprisingly little is known about what causes an individual to identify with a new organisation before entry and whether this has an impact on their relationship with the organisation after formally taking up membership. Drawing on a Social Identity approach to organisational identification, it was hypothesised that newcomers would more closely identify with an organisation prior to entry when the organisation was seen as a source of positive social identity and was situationally relevant and meaningful to the newcomer, i.e. salient, during the pre-entry period. It was also hypothesised that anticipatory identification would have post-entry consequences and would predict newcomers’ post-entry identification, turnover intentions and job satisfaction. An indirect relationship between anticipatory identification and post-entry identification through post-entry social identity judgements (termed a “feedback loop” mechanism) was additionally proposed. Finally anticipatory identification was also predicted to moderate the relationship between post-entry social identity judgements and post-entry identification (termed a “buffering” mechanism). Four studies were conducted to test these hypotheses. Study One served as a pilot study, using a retrospective self-report design with s sample of 124 university students to initially test the proposed conceptual model. Studies Two and Three adopted experimental designs. Each used a unique sample of 72 staff and students from Aston University to respectively test the hypothesised positive social identity motive and salience antecedents of anticipatory identification. Study Four explored the relationship between anticipatory identification, its antecedents and consequences longitudinally, using an organisational sample of 45 employees. Overall, these studies found support for a social identity motive antecedent of anticipatory identification, as well as more limited evidence that anticipatory identification was associated with the salience of an organisation prior to entry. Support was inconsistent for a direct relationship between anticipatory identification and post-entry identification and there was no evidence that anticipatory identification was a significant direct predictor of turnover intention and job satisfaction. Anticipatory identification was however found to act as a buffer in the relationship between post-entry social identity judgements and post-entry identification in all but one of the four samples measured. A feedback loop mechanism was observed within the experimental designs of Studies Two and Three, but not within the organisational samples of Studies One and Four. Overall the findings of these four studies highlight key ways through which anticipatory identification can develop prior to entry into an organisation. Moreover, the research observed several important post-entry consequences of anticipatory identification, indicating that an understanding of post-entry identification may be enriched by attending more closely to the extent to which newcomers identify with an organisation prior to entry.

The role of self-regulation as a meta-competency in developing leaders: a longitudinal field experimental study

The question of how to develop leaders so that they are more effective in a variety of situations, roles and levels has inspired a voluminous amount of research. While leader development programs such as executive coaching and 360-degree feedback have been widely practiced to meet this demand within organisations, the research in this area has only scratched the surface. Drawing from the past literature and leadership practices, the current research conceptualised self-regulation, as a metacompetency that would assist leaders to further develop the specific competencies needed to perform effectively in their leadership role, leading to an increased rating of leader effectiveness and to enhanced group performance. To test this conceptualisation, a longitudinal field experimental study was conducted across ten months with a pre- and two post-test intervention designs with a matched control group. This longitudinal field experimental compared the difference in leader and team performance after receiving self-regulation intervention that was delivered by an executive coach. Leaders in experimental group also received feedback reports from 360-degree feedback at each stage. Participants were 40 leaders, 155 followers and 8 supervisors. Leaders’ performance was measured using a multi-source perceptual measure of leader performance and objective measures of team financial and assessment performance. Analyses using repeated measure of ANCOVA on pre-test and two post-tests responses showed a significant difference between leader and team performance between experimental and control group. Furthermore, leader competencies mediated the relationship between self-regulation and performance. The implications of these findings for the theory and practice of leadership development training programs and the impact on organisational performance are discussed.

Approximately optimal experimental design for heteroscedastic Gaussian process models

This paper presents a greedy Bayesian experimental design criterion for heteroscedastic Gaussian process models. The criterion is based on the Fisher information and is optimal in the sense of minimizing parameter uncertainty for likelihood based estimators. We demonstrate the validity of the criterion under different noise regimes and present experimental results from a rabies simulator to demonstrate the effectiveness of the resulting approximately optimal designs.

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.