qpair: A command for analyzing paired Q-sorts in Q-methodology

Abstract

In this article, we introduce qpair as a new command written in Stata for the analysis of paired Q-sorts in Q-methodology, which is used for studying subjective issues and is a combination of qualitative and quantitative techniques. The quantitative component of Q-methodology employs a by-person factor analysis technique. However, currently there is no systematic approach for analyzing paired Q-sorts or longitudinal data in Q-methodology. We introduce the only statistical command available for the analysis of paired Q-sorts. The qpair command employs the factor extraction and factor rotation techniques in Stata. The command is illustrated using a dataset representing perceptions of 50 information technology professionals on person–organization fit regarding their training and development priorities.

Keywords

st0694 qpair Q-methodology by-person factor analysis paired Q-sort person–organization fit

1 Introduction

The Oxford Dictionary defines subjectivity as “the quality of being influenced by personal ideas, opinions, or feelings, rather than facts”. It may be considered as judgment based on individual impressions, feelings, and opinions, rather than external facts (Akhtar-Danesh, Baumann, and Cordingley 2008). William Stephenson introduced Q- methodology as an option for studying subjectivity, which he conceptualized as a person’s self-referent internal experience (Stephenson 1935a, b). Stephenson demonstrated, using empirical methods of measurement and analysis, that a person’s subjective internal experience has structure that is operationalized by a factor analysis of a person’s Q-sorts (Stephenson 1953).

Accordingly, Q-methodology is appropriate for research about attitudes, feelings, values, life experiences such as stress and quality of life, and intraindividual concerns such as self esteem and body (Dennis 1986). For example, Q-methodology has been used for research about political science (Stevenson 2019), pain (Risdon et al. 2003), job satisfaction (Chinnis et al. 2001), clinical decision making (McCaughan et al. 2002), nurses’ attitude toward health promotion (Cross 2005), stress (O’Byrne et al. 2021; Yeun et al. 2016), course evaluation (Brewer-Deluce et al. 2020; Mackinnon et al. 2022), information systems (Wingreen and Blanton 2018), climate change (Lo 2015), and health economics (Baker, Thompson, and Mannion 2006).

In a Q-methodology study, the subjective data collected from each person are collectively called a Q-sort. A Q-methodology study comprises qualitative and quantitative components. The quantitative component includes a by-person factor analysis of Q- sorts that factorizes participants into different groups, which reveals the structure of people’s internal subjective experiences.

The qualitative component of a Q-method study involves an interpretation of the factor structure revealed by the data analysis and may also be preceded by a rotation of the factors whose purpose is to make the factors more interpretable (Thurstone 1947). In a factor rotation, the factor axes are rotated to highlight salient aspects of the factor structure to be interpreted. By analogy, it is something like rotating a sculpture to achieve a viewing angle that best invokes a desirable ambience or sensation.

Sometimes, it is desirable to study how people’s subjective responses, perceptions, and their associated factors change over time and from one circumstance to another (for example, Bilal, Wingreen, and Sharma [2020]; Klaus, Wingreen, and Blanton [2010]). However, this is a conspicuously underresearched topic in the literature of Q-methodology, partly because of the lack of supporting statistical tools and methodological procedures. Although there are several commands for the statistical analysis of cross-sectional Q-sorts, such as PQMethod (Schmolck 2014), PCQ (Stricklin and Lincoln 1996), qfactor (Akhtar-Danesh 2018a), KADE (Banasick 2019), and qmethod (Zabala 2014), there is no unified strategy or statistical command for the analysis of paired Q-sorts. Thus, we introduce qpair as a new community-contributed command in Stata for the analysis of paired Q-sorts.

2 Q-methodology

Philosophically speaking, people interact with the universe of their perceptions and inner life in every conscious moment: sights, sounds, smells, tastes, touch, the sensations and emotions evoked by their senses, and their thoughts about them. The boundaries of a person’s potential experience are infinite, so Q-methodology requires researchers to define a limited domain of subjective experience, which is called a concourse. But even within the restricted subdomain of a concourse, there are potentially infinite subjective experiences a person may have; therefore, Q-methodology operationalizes subjective beliefs, perceptions, and preferences by observing people’s interactions with a sample of the concourse in the empirically controlled procedure of the Q-sort.

The first step in a Q-methodology study is to define the boundaries of the concourse of interest. The next step is to develop a sample from the concourse, which for most academic research is usually a set of verbal statements to represent the concourse in the same way that a sample of people represents a population of people; this sample is called a Q-sample or Q-set (Brown 1993). The concourse may be developed from different sources, including a literature review, interviews, expert opinions, focus groups, or related techniques.

In this section, we use a running example to explain the terminology and steps used in a Q-methodology study. This example includes the marijuana legalization (ML) dataset (known here as the ML study). The ML study evaluated views of 40 participants on ML. The dataset was collected in different workshops on Q-methodology presented in different countries (Akhtar-Danesh 2018a).

In the ML study, the concourse was sampled by searching the World Wide Web and published literature on the topic, which resulted in 51 statements that represented the pros and cons of marijuana legalization. The statements in the concourse were reviewed by the research team to ensure that it satisfies various desirable criteria, for example, for clarity, to eliminate repetition, and to provide balanced coverage of the domain of the concourse (Akhtar-Danesh, Baumann, and Cordingley 2008). The review produced a Q-sample composed of 19 statements to represent the concourse (listed in table 1). The statements in the Q-sample are then randomly numbered and printed on a deck of cards with one statement per card, or as a “virtual card” in an online Q-sort application.

Table 1.

List of complete Q-sample (19 statements) with their randomly assigned numbers used in the running example (ML study)

1.	The harms associated with marijuana are less than those associated with tobacco and alcohol, and they are not sufficient reason to justify making marijuana illegal.
2.	By legalizing marijuana, doctors may become part of the black market by handing out prescriptions to those who want it rather than those who need it.
3.	The reason that marijuana poses a health threat is because most people smoke it, and smoking anything is hazardous to your health.
4.	Taxpayers are forced to pay billions of dollars to persecute, prosecute, and lock up people for having marijuana. If marijuana were legal, this money, plus tax revenues from marijuana sales, could be used for other purposes such as education or health care.
5.	Marijuana does not cause violence. In fact, people who are high on marijuana tend to be relaxed, mellow, and too happy to want to fight.
6.	Marijuana legalization ensures that people who use the drug for medicinal purposes, such as pain control, have access to it.
7.	Certain people are able to function only with the aid of marijuana. If it is more difficult for them to access the drug, they may be unable to perform effectively in society.
8.	Education and regulation are better options than prohibition.
9.	Prohibition is not an effective solution to the problems associated with marijuana use.
10.	If we legalize marijuana, we reduce the black market and the violence associated with the sale of marijuana.
11.	It should become legal for those over the age of 18 because these individuals are considered adults and are able to make their own decisions regarding drug use.
12.	The use of marijuana as a pain control may cause patients to rely solely on the drug rather than medical treatment.
13.	Marijuana legalization would decrease the likelihood of younger children buying marijuana.
14.	By legalizing marijuana, more people will use the drug and thus become addicted, and more families will become dysfunctional.
15.	By legalizing marijuana, there will be an increase in people using the drug and therefore a need to increase rehabilitation programs that will come at the cost of taxpayers and the government.
16.	A decrease in the use of marijuana means fewer health risks, such as slowed brain function or risk of cancer.
17.	Individuals should be allowed to choose whether they use marijuana; individual liberty is a fundamental value.
18.	There is an abundance of anecdotal evidence, as well as some scientific research, indicating that marijuana can be effective as a treatment for some illnesses.
19.	If marijuana were legal, steps could be taken to reduce the health risks associated with its use by avoiding contamination.

Next a grid with a quasinormal distribution is developed (Q-sort table) that has the same number of cells as the number of statements in the Q-sample. The grid is printed (or designed online) to serve as the data entry form. This grid includes a rating scale that typically ranges between about −3 to +3 or −6 to +6. The range of the rating depends on the number of statements and the goals of the research; therefore, a wider range is usually required for a larger number of statements or greater precision.

The reason for designing a quasinormal distribution is that many scholars believe it is a better model of participants’ preferences when compared with uniform distributions where people sort equal numbers of items into each category or with “free” distributions where people may sort as many or as few items into any category as they desire, although this has been a topic of some debate among Q-methodology scholars (Brown 1985). Briefly, the scholarly debate on the issue revolves around the tradeoffs between methodological rigor and the desire to faithfully model the true distribution of people’s beliefs. Cottle and McKeown (1980) demonstrate that the shape of the distribution is of little relevance with regard to the statistical analysis of Q-sorts because different distributions result in nearly identical statistical results. In theory, the quasinormal model is a better fit for people’s true subjective beliefs because most people feel very strongly about a few things, feel strongly about a greater number of things, and are ambivalent or neutral about an even greater number of things. For these reasons, most Q-methodology research implements a quasinormal distribution, although it is not strictly necessary to do so. The Q-sort table for the ML study is shown in figure 1.

Figure 1.

The Q-sort table used for data collection in the running example (ML study)

Participants then sort the cards into the Q-sort table according to a “condition of instruction” by which to elicit their preferences. The condition of instruction is customized based on the objective of the study, the number of statements, the Q-sort table, and the participants. For instance, the instruction may differ based on the literacy level of participants or if the participants are adults or children. The purpose of the Q-sort statements, Q-sort table, and sorting exercise is to provide an empirically observable, replicable means by which the person may interact with the Q-sample. Table 2 presents the condition of instruction for the ML study.

Table 2.

Condition of instruction for the running example (ML study)

Condition of instruction: Please note that this section is a three-step process.
Step 1	In this step, you will sort 19 statement cards about marijuana legalization.
	You have been given a set of 19 statement cards. Please divide these statements into three categories: agree, disagree, and neutral (you are free to change your arrangement of statements at any step in this process). By the end of this step, you should have 7 statement cards in your “agree” category, 7 statement cards in your “disagree” category, and 5 statement cards in your “neutral” category.
Step 2	In this next step, you will distribute your statement cards under a series of markers, which are numbered from −3 (strongly disagree) to +3 (strongly agree).
	Remember that you are free to change your arrangement of statements at any step in this process.
	Example:
	Sorting from each of the categories,
	choose the one statement from the cards in the “agree” category that you most strongly agree with, and place it under the +3 marker; choose the two statements from the remaining cards in the “agree” category that you most strongly agree with, and place these under the +2 marker; choose the remaining four statements in the “agree” category, and place these under the +1 marker; choose the one statement from the cards in the “disagree” category that you most strongly disagree with, and place it under the −3 marker; choose the two statements from the remaining cards in the “disagree” category that you most strongly disagree with, and place these under the −2 marker; choose the remaining four statements in the “disagree” category, and place these under the −1 marker; and place the last five statements, from the “neutral” category, under the 0 marker.
Step 3	In this final step, you will record your responses.
	On the back of each statement card, a number is shown. Using the Q-sort table and the number assigned to each statement, record your responses.

Participants in the ML study first sorted each card from the Q-sample into three categories: agree, disagree, and neutral. Participants then selected the one card from the “agree” category that represented their greatest agreement and coded it +3; they did the same for the “disagree” category, selecting the one card that represented their greatest disagreement and coding it −3 (Akhtar-Danesh, Baumann, and Cordingley 2008). Participants next selected the two cards from those remaining in the “agree” category that represented their greatest agreements and coded them +2; they did the same for those cards remaining in the “disagree” category, selecting two cards to code −2. Participants then took the remaining four cards in each of the “agree” and “disagree” categories and coded them +1 and −1, respectively. Finally, participants took the last five cards, from the “neutral” category, and coded them 0. When finished sorting, participants recorded the statement numbers into the grid as their completed Q-sorts. A completed Q-sort table for the first participant in the ML study is shown in figure 2.

Figure 2.

The completed Q-sort table for the first participant in the running example (ML study)

In the next step, a factor analysis is conducted on the Q-sorts. For instance, table 3 shows the first five Q-sorts for the ML study. As seen in the table, the statement numbers in the Q-sort tables are transformed to the rating scale so that each Q-sort represents the view or preferences of one participant. In contrast to R-methodology, where variables are the object of factor analysis, Q-methodology subjects, represented by their Q-sorts, are factor analyzed. This is a by-person factor analysis, where each Q-sort is a field vector that represents one person’s coherent viewpoint on the topic of study (Akhtar-Danesh 2018a; Akhtar-Danesh, Baumann, and Cordingley 2008; Brown 1980). Similarly to ordinary factor analysis, the extracted factors are usually rotated to have simpler structures and to become more interpretable (Thurstone 1947).

Table 3.

The first five Q-sorts from the running example (ML study)

Statement number	Q-sort 1	Q-sort 2	Q-sort 3	Q-sort 4	Q-sort 5
1	−1	−1	0	−1	1
2	−3	0	1	0	2
3	1	−1	0	−2	2
4	1	1	0	−1	−3
5	0	0	−2	0	−1
6	−2	−1	−1	0	1
7	−1	−2	−1	−1	0
8	−1	1	1	3	−1
9	0	−1	−1	2	0
10	0	1	3	1	−2
11	−1	−2	0	1	0
12	0	0	−2	−1	0
13	−2	2	−3	0	1
14	2	3	−1	−2	−2
15	2	1	1	−3	−1
16	0	0	0	0	0
17	1	−3	2	2	3
18	3	2	1	1	−1
19	1	0	2	1	1

Following the analysis of the Q-sorts, the final step is the factor interpretation, which is based on the estimated factor scores for each statement and the identification of distinguishing statements for each factor. A distinguishing statement for a factor is one with a factor score that is significantly different from its scores on all the other factors (Akhtar-Danesh, Baumann, and Cordingley 2008). The distinguishing statements define the uniqueness of each factor compared with the other factors and are used in factor interpretation. For the ML study, the following output from the qfactor command (Akhtar-Danesh 2018a) presents the distinguishing statements for factor 1 (F_1) based on a three-factor solution with principal axis factoring extraction and varimax rotation. The output also includes the number of participants loaded on factor 1 and factor scores for the other two factors for comparison. The factor scores for each statement were estimated using the score(regression) option. Instead of reporting the z scores for each factor, factor scores were rescaled to resemble a Q-sort.

In the manner described above, the infinite universe of people’s subjective experience becomes accessible to controlled, replicable empirical investigation. Before a condition of instruction is administered, all possible Q-sorts are equally probable and equally unpredictable. Each condition of instruction is an experimental treatment, and each Q-sort is an experiment in subjectivity. Analysis of Q-sorts reveals the structure of people’s subjectivity from which inferences and generalizations may be made about the concourse. Each factor represents its own coherent “theory” of subjective experience that is derived from the interpretation of the factor. For a complete review of Q- methodology, the readers are referred to Brown (1980) and Akhtar-Danesh, Baumann, and Cordingley (2008).

3 The qpair command

The qpair command uses Stata’s factor and rotate commands as well as the options in the qfactor command (Akhtar-Danesh 2018a) to identify and display changes in paired Q-sorts from two different time points or based on two comparable measurements. The command suggests two different approaches for measuring changes in paired Q-sorts and identifies the related distinguishing and consensus statements for each factor. It also accommodates bipolar factor solutions and the use of Cohen’s d (Akhtar-Danesh 2018b; Cohen 1988) for identifying distinguishing statements.

Until recently, Brown’s (1980) method has been the only option for estimating factor scores in Q-methodology. Similarly to the qfactor command (Akhtar-Danesh 2018a), qpair uses a suite of options from Stata, such as the regression, bartlett, and thompson methods. Each identified factor may have multiple distinguishing statements.

Historically, Stephenson’s (1978) method has been the only method for identifying distinguishing statements; however, the qpair command also uses Cohen’s effect size (Cohen 1988; Akhtar-Danesh 2018b) as a new option. In addition to the distinguishing statements, there might be a set of statements called consensus statements with factor scores that do not differ significantly between different factors.

3.1 Syntax

The command syntax is

qpair [if] [in], first(varlist) second(varlist) nfactor(#)

[approach(approach_options) extraction(extraction_options) rotation(rotation_options) score(score_options) esize(esize_options) bipolar(bipolar_options) stlength(#)]

The qpair command requires two sets of varlists (that is, Q-sorts): first() to include Q-sorts from time 1 (or baseline) and second() to include Q-sorts from time 2 (or follow-up) assessments. The order of Q-sorts in both sets must be the same so that the first Q-sort in both sets refers to the first person, the second Q-sort refers to the second person, and so on. For factor extraction, qpair employs principal axis factor (pf), iterated principal axis factor (ipf), and principal-component factor (pcf) extraction methods. It also uses different factor rotation techniques on the extracted factors. qpair displays the eigenvalues of the extracted factors, rotated and unrotated factor loadings, and the uniqueness and communality (h²) of each Q-sort. In addition, for each extracted factor it displays z scores and composite-ranks scores, distinguishing statements, and number of Q-sorts loaded on each factor. Furthermore, qpair displays the consensus statements for all participants in the study.

3.2 Options

first(varlist) includes Q-sorts from time 1 or baseline assessments. first() is required.

second(varlist) includes Q-sorts from time 2 or follow-up assessments. second() is required.

nfactor(#) specifies the number of factors to be extracted. nfactor() is required.

approach(approach_options) identifies which method to use for assessing the change between two sets of Q-sorts. approach(I) indicates the analysis to be conducted on the differences of Q-sorts between the first and second sets. Using this approach, one Q-sort of differences is assigned to each person (Akhtar-Danesh and Wingreen 2022). Therefore, the factor analysis is performed on the Q-sorts of differences. In approach(II), the Q-sorts from the first set (time 1) are considered as a baseline or reference. Therefore, the baseline factors are identified using the Q-sorts in the first set. Then an analysis is conducted to show the changes in factor scores for participants loaded on each factor at time 1 using the Q-sorts from time 2. The default is approach(I).

extraction(extraction_options)specifies the factor extraction method to be used. The current extraction methods include the principal component (pcf), principal axis factor (pf), and iterated principal axis factor (ipf). The default is extraction(ipf).

rotation(rotation_options) identifies the factor rotation techniques. This option can accommodate all orthogonal and oblique rotation techniques available in Stata, including varimax, quartimax, equamax, promax(), oblimin(), and target() (for theoretical rotation) techniques. rotation(none) can be used if no rotation is desired. The default is rotation(varimax).

score(score_options) specifies how the factor scores are to be calculated. The choices include score(brown), which indicates that scores are to be calculated as described by Brown (1980). The other choices are score(regression), score(bartlett), and score(thompson). The default is score(brown).

esize(esize_options) specifies how distinguishing statements for each factor are to be identified. The options 0 or Stephenson indicate that distinguishing statements are identified based on Stephenson’s (1978) formula. This is the default. For any other number between (0, 1], distinguishing statements are identified based on Cohen’s (1988) effect size.

bipolar(bipolar_options) identifies a bipolar factor and regroups it into two separate factors. The default is bipolar(0) or bipolar(no), which indicate that no factor is to be regrouped into two factors. For any other integer number, bipolar() identifies the minimum number of negative factor loadings needed for each factor to be regrouped. For instance, bipolar(3) indicates that at least three significant negative factor loadings are needed for each factor to be considered a bipolar factor. Currently, the bipolar() option works only with Brown’s (1980) factor scores.

stlength(#) identifies the maximum length of characters for each statement to be displayed. The default length is stlength(50) for 50 characters.

3.3 Stored results

In addition to the displayed results, qpair stores two matrices in r(). The first matrix is r(fctrldngs), whose columns include variables, such as Qsort (Q-sort number); unrotated and rotated factor loadings; unique (for the uniqueness and communality of each Q-sort); and Factor. The Factor column indicates which Q-sort was loaded on what factor. The second matrix is r(fctrscrs), which stores factor scores for all statements. This matrix is generated only when approach(II) is used and contains z scores and ranked scores for the extracted factors.

These matrices can be retrieved and used in subsequent analysis, for example, to compare factor scores based on different factor extraction techniques, to compare demographic and other background variables among the extracted factors, or to graphically display rotated and unrotated factor loadings.

4 Example

qpairdata.dta includes data for 50 information technology (IT) professionals with their views assessed on person–organization (PO) fit regarding training and development priorities using a Q-methodology study. This dataset includes a random sample of 50 IT professionals from a larger group (n = 218) of IT participants on a PO fit study (Wingreen and Blanton 2018). Although the larger dataset has already been analyzed using a preliminary version of qpair (Akhtar-Danesh and Wingreen 2022), in this article we intend to demonstrate application of qpair as a command. Each participant in the study provided his or her views (using Q-sorts) regarding training and development priorities based on his or her own PO fit priorities and his or her understanding of the organization’s priorities. The Q-sample includes 27 short statements on the topics, venues, and resources relevant to IT professional training and development priorities. The data were collected using a Q-sort table with 27 cells (figure 3). We demonstrate the two approaches of analysis to highlight change in the IT professionals’ perceptions using the PO dataset.

Figure 3.

The Q-sort table used in the PO study for data collection

4.1 Approach I, factorizing change in perception

If we want to extract three iterated principal axis factors (ipf) with varimax rotation from the 50 pairs of Q-sorts using approach(I), we use the following command:

. use qpairdata, clear

. qpair, first(qsort*_1) second(qsort*_2) nfactor(3) (0 real changes made)

The most important sections of the output produced by the above command are described below. First, as shown below, Stata displays the approach, the factor extraction and rotation techniques, the extracted factors with their eigenvalues, the differences between consecutive eigenvalues, the proportion of each eigenvalue to the total (number of Q-sorts), and the cumulative eigenvalues.

Second, each diff variable in the following section indicates the difference between each pair of Q-sorts. Table entries also show the factor loadings and the uniqueness of each difference (diff) variable. The Uniqueness for each difference shows how much of the variance for each variable is not explained by the extracted three factors, which is equal to unity minus communality of the variable.

Third, qpair displays the extracted factors with the number of Q-sorts loaded on each factor, their distinguishing statements, and the ranked factor scores. For instance, the following table indicates that 12 participants loaded on factor 1 (F_1). The distinguishing statements for factor 1 are shown with their ranked factor scores contrasted with the factor scores for the other factors. The results indicate that 12 participants who loaded on factor 1 scored their own perceptions 3 points higher compared with their organizations’ views on statement number 25 (time off from work for training), which indicates that the participants view their perception on this statement much more positively compared with their organization. On the other hand, these participants scored their own perceptions on Distance-based/Internet training (statement number 19) three points lower (−3) compared with their organization; however, subjects who loaded on factors 2 and 3 had only a difference of 1 between their own perceptions and their organization perceptions on this statement. For brevity, the results for factors 2 and 3 are omitted.

Finally, the consensus statements are shown below. There were only two statements (numbers 27 and 12) with factor scores that were not significantly different between the three factors. In other words, the ranking of differences for these statements was the same among all participants. For instance, all participants on average felt almost the same level of importance between their own views and the views of their organizations on Peripherals (maintenance/configuration) (statement number 27). The same applies for Information sharing between peers (statement number 12).

4.2 Approach II, measuring change from baseline

In the following, approach(II) is used, where the factors extracted from the first set of Q-sorts are regarded as baseline and the aim is to investigate the change in each factor with regard to the distinguishing statements. To identify factors from the first set of Q-sorts, we used a principal component factor, extraction(pcf), with varimax rotation and used a Cohen’s effect size of 0.8 to identify distinguishing statements for each factor, executed by the following command:

. qpair, first(qsort*_1) second(qsort*_2) nfactor(3) approach(II)

> extraction(pcf) stlength(23)

(14 real changes made)

The output regarding the unrotated and rotated factors are omitted, and sections of most interest to Q-methodologists are presented below.

First, the following section shows the approach and the factor extraction and rotation techniques.

Second, the following table indicates that 15 participants were loaded on factor 1 from the first set of Q-sorts (baseline). The statements that distinguish between this group and the other two factors are also shown in the table. For instance, participants who loaded on this factor ranked programming languages (statement number 1) as the highest priority compared with factor 2, which was ranked quite low (−2), or factor 3, which was neutral (0). On the other hand, members of factor 1 were neutral on Distance-based/Internet training (statement number 19) in contrast to members of factor 3, who ranked this statement with the lowest priority (−3).

Third, the following table compares the scores between the first and second sets of Q-sorts for the distinguishing statements among the 15 participants who loaded on factor 1. The score from the first set is shown under the F1_1 column (for factor 1 time 1), and the scores from the second set are shown under the F1_2 column (for factor 1 time 2). The scores from the second set were calculated by averaging the scores for each statement for those 15 participants who loaded on factor 1 at the baseline. The mean values of the statements were then rescaled to the original scale (from −3 to +3) so that the two statements with the largest values ranked as +3, the next three largest as +2, etc.

As can be seen, these participants ranked statement number 1 the highest (3) based on their own views (baseline) and their organizations’ views (follow-up); they do not think that there is any difference in their views and their organizations’ views regarding this statement. However, they indicated large differences between their views and their organizations’ views on Network administration (statement number 13).

Finally, the following table presents all statements with factor scores for all three factors at baseline and the average factor score for each statement from the second set of Q-sorts.

4.3 Some other options with qpair

The other options that can be used with both approach(I)and approach(II)in qpair are briefly explained here.

4.3.1 score() option for factor scores

Historically, factor score in Q-methodology is calculated as suggested by Brown (1980). In addition, qpair allows calculating factor scores based on options available in Stata, including the regression, bartlett, and thompson options, although the brown option is used as the default. The following command calculates the factor scores using the score(regression) option:

. qpair, first(qsort*_1) second(qsort*_2) nfactor(3) score(regression)

4.3.2 esize() option for identifying distinguishing statements

In all Q-methodology commands except qfactor (Akhtar-Danesh 2018a), the distinguishing statements are identified using Stephenson’s (1978) approach. In qpair, similarly to qfactor, we included the esize() option (for effect size), which is based on Cohen’s suggestions for calculating effect size (Akhtar-Danesh 2018b; Cohen 1988). However, the Stephenson method remains as the default. For instance, the following command identifies distinguishing statements using a moderate effect size of 0.5:

. qpair, first(qsort*_1) second(qsort*_2) nfactor(3) approach(II) esize(0.5)

4.3.3 bipolar() option to identify factors with negative loadings

A factor might be bipolar, in which case it represents two opposing viewpoints. A bipolar factor can be easily identified by its negative factor loadings. qpair can divide a bipolar factor into two factors so that all Q-sorts with positive factor loadings are included in one factor and all Q-sorts with negative factor loadings are included in another factor. For instance, the following command separates each factor with at least two negative loadings into two separate factors:

. qpair, first(qsort*_1) second(qsort*_2) nfactor(3) approach(II) bipolar(2)

4.3.4 stlength() option to customize length of statement in the output

Sometimes, because of some lengthy statements or a large number of factors, the common output including the statement number (StatNo), statement, and factor scores may not fit on one line of the output. In such cases, the stlength() option allows for shortening the default length of the statement, that is, 50 characters, to a desired length. For instance, the following command allows a maximum of 25 characters for each statement as seen in the output.

5 Conclusions

In this article, we introduced qpair as a command for the analysis of paired Q-sorts. To the best of our knowledge, this is the only statistical command that offers a systematic analysis for paired Q-sorts. We introduced two approaches: Approach I is used when we are interested in factorizing the changes across the two related sets of Q-sorts. This is similar to a paired t test, where the differences between two related measurements are compared between two groups. Approach II investigates changes that occurred in each factor of the first set of Q-sorts to the second set or from baseline to follow-up; it explains how the perceptions of each group of participants loaded on each factor in the baseline have changed in the second set of Q-sorts (follow-up).

The qpair command is the first statistical tool to support the underresearched topic of changes that happen in Q-sorts over time and across circumstances. Many practitioners of Q-methodology also might point out the importance of factor interpretation rather than our emphasis on the statistical procedures employed. We agree; however, we refrained from the interpretation of the factors because our objective was to focus on the statistical component of the paired Q-sorts and to introduce the qpair command as a statistical tool. The qpair command is merely another tool to place in the Q-methodologist’s tool chest. How to interpret the factors derived by qpair presents itself as an opportunity for future research.

Finally, although the qpair command might look similar to the qfactor command in presenting the outputs, the difference is that qpair is used only when there are paired Q-sorts for each participant, but qfactor is only for the analysis of one time or cross-sectional Q-studies.

6 Programs and supplemental materials

Supplemental Material, sj-zip-1-stj-10.1177_1536867X221141002 - qpair: A command for analyzing paired Q-sorts in Q-methodology

Supplemental Material, sj-zip-1-stj-10.1177_1536867X221141002 for qpair: A command for analyzing paired Q-sorts in Q-methodology by Noori Akhtar-Danesh and Stephen C. Wingreen in The Stata Journal

Footnotes

6 Programs and supplemental materials

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