Analysis of Q sort data

The data analysis in Q methodology involves the application of correlation, factor analysis, and the computation of factor scores. Q methodology employs a by-person correlation and factor analytic procedure, as the analysis involves persons in place of variables. It is the overall configurations produced by the participants that are inter-correlated and factor analysed indicating segments of subjectivity that exist. Initially the correlation matrix of all the participants’ Q sorts is calculated. The correlation matrix reflects the extent of the relationships that pertain between all the Q sorts in the group and demonstrates the

relationship of each Q sort with every other Q sort configuration.

matrix is subject to factor analysis to determine a set of factors onto which the participants load, based on the item configurations they created in their Q sort. The objective is to identify the natural groupings of Q sorts by virtue of being similar or dissimilar to one another. Factor analysis is looking for groups of persons who have rank ordered the stimulus items in a very similar fashion (Brown, 1980). People with similar views will share the same factor.

A factor loading is determined for each Q sort, which expresses the extent to which each Q sort is associated with each factor and can be said to exemplify the factor pattern. The factor loading captures different item configurations that are shared by and characteristic of the participants who load onto that factor. The factors obtained from the analysis “indicate clusters of persons who have ranked the statements in essentially the same fashion” (Brown, 1980, p. 6). Fundamentally, factor analysis examines the correlation matrix and determines how many basically different Q sorts are in evidence and how many factors exist. The idea is to identify groups of participants who sorted their Q sorts in a similar way and thus can be seen to share similar viewpoints.

Several dedicated Q methodology packages allow appropriate analysis to be conducted. Such packages facilitate data input, generate the by-person correlation matrix, and make the processes of factor extraction, rotation, and estimation straightforward. Different types of factor analyses exist and so do different methods of factor rotation. The type of analysis used depends on what theories might exist prior to analysis. In a Q methodological context, the oldest of factor techniques, centroid is the extraction method generally preferred as it offers a potentially infinite number of rotated solutions. This openness and indeterminacy is appealing as it gives freedom to consider the data set and select the solution considered most appropriate and theoretically informative. Factor rotation should shift the perspective and ensure each factor offers the most meaningful vantage point from which to view the subject matter. Q sorts whose position and viewpoint closely approximate that of a particular factor are identified. Rotation does shift the perspective as it examines the Q sorts from different angles but it does not affect the consistency in sentiment throughout the individual Q sorts or the relationship between the Q sorts. Rotation may be

either objective according to some statistical principle (like Varimax rotation) or theoretical whereby the rotation is guided by abductory principles of the

investigator. Theoretical or by-hand rotation allows the rotation of factors

manually based on some theory or substantive knowledge of the subject matter or data. An objective rotation is usually an automated procedure, such as varimax, that will rotate the factors and position them according to statistical criteria to arrive at a final set of factors. In practice, many Q methodologists use modern factor rotation techniques, such as varimax, as the simplicity and

reliability of the procedure is preferred. The varimax procedure is also

consistent with one of the typical aims of Q methodology, which is to reveal the range of viewpoints that are favoured by the participant group. Given this aim, a rotated solution that maximises the amount of variance explained by the

extracted factors should be pursued. The technique of rotation employed is dependent “on the nature of the data and the aims of the investigator” (Brown, 1980, p. 238).

An important step is to decide which factors should be selected for analysis. In Q methodology there are no firm rules on how many factors should be

extracted from the analysis. A variety of statistical and theoretical criteria can be employed in making that determination. An important characteristic of the final set of factors is that they should account for as much of the variability in the original matrix as possible (Brown, 1980). Eigenvalues are indicative of factors’ statistical strength and explanatory power. A standard requirement is to select only those factors with an eigenvalue in excess of 1.00; a generally accepted means of safeguarding factor reliabilities. A second standard requirement is that an interpretable Q method factor must ordinarily have at least two Q sorts that load significantly upon it alone. These are called ‘factor exemplars’ as they exemplify the shared item pattern that is characteristic of that factor. Another useful parameter to guide the decision-making is to extract one factor for every six to eight participants in the study. It is important to distinguish between the statistical and theoretical significance of factors in Q methodology (Brown, 2008; McKeown & Thomas, 1988; Stenner et al., 2008). The importance of a factor cannot be determined by statistical criteria alone and common sense

may offer the best counsel when determining their theoretical and contextual significance.

In Q methodology, interpretations are primarily based on factor scores as they enable statistical means to be used to assess the significance of different statement locations within the factor arrays. To probe the character of these viewpoints a factor score or estimate is then generated via a weighted

averaging of all the Q sorts that load significantly on a given factor and on that factor alone. In effect, Q sorts of all participants that load significantly on a given factor are merged to form a single, composite Q sort, which serves as an interpretable ‘best estimate’ of the pattern or item configuration that

characterises that factor. For the sake of convenience, the statements are returned to the original Q sort format. The composite Q sort of the factor represents how a hypothetical respondent with a 100 percent loading on that factor would have ordered all the statements in the Q set. When a respondents loading exceeds a certain limit (usually p < 0.01) this is called a defining variate (Van Exel & De Graaf, 2005). To understand distinguishing statements, the concept of a difference score needs to be understood. The difference score is the magnitude of difference between a statement’s score on any two factors that is required for it to be statistically significant. When a statements score on two factors exceeds this difference score, it is called a distinguishing statement (i.e., placed in the composite sort in locations that are significantly different) for that point of view. A statement that does not distinguish between any of the identified factors is called a consensus statement.

Factor scores and different scores on a factors composite Q sort point out salient statements that deserve special attention in describing and interpreting that factor. The statements ranked at both extreme ends of the composite sort of a factor are called characterising statements, and are used to produce the first description of the composite point of view presented by that factor. The distinguishing and consensus statements can be used to highlight the differences and similarities between factors.

Q sorts that do not load significantly on any factor or those that load

weighted averaging procedure (Akhtar-Danesh et al., 2008). Exclusion of confounding participants’ Q sorts ensures that there is the maximum difference between each factor (McKeown & Thomas 1988). The endpoint of the statistical analysis is reached when each of the selected factors is represented by its own ‘best estimate’ or ‘factor array’. A factor array is a single Q sort configured to represent the subjective viewpoint of a particular factor. These factor arrays are subjected to interpretation. The computation of factor arrays is one of the

analytical strengths of the methodology.