Factorial designs: an overview with applications to orthodontic clinical trials.

Factorial designs for clinical trials are often encountered in medical, dental, and orthodontic research. Factorial designs assess two or more interventions simultaneously and the main advantage of this design is its efficiency in terms of sample size as more than one intervention may be assessed on the same participants. However, the factorial design is efficient only under the assumption of no interaction (no effect modification) between the treatments under investigation and, therefore, this should be considered at the design stage. Conversely, the factorial study design may also be used for the purpose of detecting an interaction between two interventions if the study is powered accordingly. However, a factorial design powered to detect an interaction has no advantage in terms of the required sample size compared to a multi-arm parallel trial for assessing more than one intervention. It is the purpose of this article to highlight the methodological issues that should be considered when planning, analysing, and reporting the simplest form of this design, which is the 2 × 2 factorial design. An example from the field of orthodontics using two parameters (bracket type and wire type) on maxillary incisor torque loss will be utilized in order to explain the design requirements, the advantages and disadvantages of this design, and its application in orthodontic research.

Using Factorial Surveys and Stated Choice Experiments to Investigate Discriminatory Attitudes and Preferences

Empirical research on discriminatory attitudes and behaviour grapples with the social undesirability of its object. In many studies using regular survey methods, estimates are biased, and the social context of discrimination is not taken into account. Several methods have been developed, especially to deal with the first problem. In this regard, the estimation of the ‘true value’ of discriminatory attitudes is at the centre of interest. However, methodological contributions focusing on the social context of attitude communication and discriminatory behaviour, as well as the correlation between both, are rare. We present two experimental methods which address those issues: factorial surveys and stated choice experiments. In a first study, the usefulness of factorial surveys is demonstrated with data on German anti-Semitism (N=279). We show that the rate of approval with anti-Semitic statements increases if (a) respondents are told that the majority of fellows agree with such statements, (b) the term “Jews” is replaced by the term “Israelis”, and (c) reference to the Holocaust is made. Apart from the main effects of these experimental factors, significant interaction effects regarding the political attitudes and social status of respondents are observed. In a second study, a stated choice experiment on the purchase of olive oil and tomatoes was conducted in Germany (N=440). We find that respondents prefer Italian and Dutch products (control treatment) compared to Israeli and Palestinian ones (discrimination treatments). There are no significant differences between preferences for a so called ‘Peace product’ (which is produced jointly by Israelis and Palestinians) and products from Italy as well as the Netherlands. Yet, taking discriminatory attitudes (anti-Semitic and anti-Arabic attitudes) into account, a strong correlation between those attitudes and stated behaviour (purchase of Israeli, Palestinian and jointly produced products) can be found. This adds support to the hypothesis that discriminatory attitudes hold behavioural consequences.

Predictors of healthcare professionals' attitudes towards family involvement in safety-relevant behaviours: a cross-sectional factorial survey study.

OBJECTIVES To investigate predictors of healthcare professionals' (HCPs) attitudes towards family involvement in safety-relevant behaviours. DESIGN A cross-sectional fractional factorial survey that assessed HCPs' attitudes towards family involvement in two error scenarios relating to hand hygiene and medication safety. Each survey comprised two randomised vignettes that described the potential error, how the family member communicated with the HCP about the error and how the HCP responded to the family member's question. SETTING 5 teaching hospitals in London, the Midlands and York. HCPs were approached on a range of medical and surgical wards. PARTICIPANTS 160 HCPs (73 doctors; 87 nurses) aged between 21 and 65 years (mean 37) 102 were female. OUTCOME MEASURES HCP approval of family member's behaviour; HCP reaction to the family member; anticipated effects on the family member-HCP relationship; HCP support for being questioned about hand hygiene/medication; affective rating responses. RESULTS HCPs supported family member's intervening (88%) but only 41% agreed this would have positive effects on the family member/HCP relationship. Across vignettes and error scenarios the strongest predictors of attitudes were how the HCP (in the scenario) responded to the family member and whether an error actually occurred. Doctors (vs nurses) provided systematically more positive affective ratings to the vignettes. CONCLUSIONS Important predictors of HCPs' attitudes towards family members' involvement in patient safety have been highlighted. In particular, a discouraging response from HCP's decreased support for family members being involved and had strong perceived negative effects on the family member/HCP relationship.

The impact of the position effect on the factorial structure of the Culture Fair Test (CFT)

The Culture Fair Test (CFT) is a psychometric test of fluid intelligence consisting of four subtests; Series, Classification, Matrices, and Topographies. The four subtests are only moderately intercorrelated, doubting the notion that they assess the same construct (i.e., fluid intelligence). As an explanation of these low correlations, we investigated the position effect. This effect is assumed to reflect implicit learning during testing. By applying fixed-links modeling to analyze the CFT data of 206 participants, we identified position effects as latent variables in the subtests; Classification, Matrices, and Topographies. These position effects were disentangled from a second set of latent variables representing fluid intelligence inherent in the four subtests. After this separation of position effect and basic fluid intelligence, the latent variables representing basic fluid intelligence in the subtests Series, Matrices, and Topographies could be combined to one common latent variable which was highly correlated with fluid intelligence derived from the subtest Classification (r=.72). Correlations between the three latent variables representing the position effects in the Classification, Matrices, and Topographies subtests ranged from r=.38 to r=.59. The results indicate that all four CFT subtests measure the same construct (i.e., fluid intelligence) but that the position effect confounds the factorial structure