Boutique Sampling

Overview

Boutique Sampling refers to concepts in transverse or 'oblique' data analysis and explicit data parsing techniques designed to catechize and integrate observed instances of the categorical relations under study. The method intentionallly constructs a sample frame for diagnostic imputation and statistical interpolation in order to derive robust inferences about the census.

The MSI approach to boutique sampling is distinctively indicial featuring integrated procedures to identify regularities and autocorrelates prevalent throughout the sample frame via a synoptic process of sample stratification.

Administering boutique sampling is a two step process of: (1) line-intercept sampling (LIS), intended to establish probability function and density function markers, and (2) sample stratification (SS), concerned with analytical quantitisation.

Summary Methodology:

> Line-Intercept Sampling (Sampling Method)

> Sample Stratification (Analytical Method)

Sampling Method

The sampling method coordinates - organises and builds - the database in preparation for the analytical method.

Determine Sample Frame

The sample frame is defined by the categorical relation (research question) under study and is generally delimited by resource and time constraints. Therefore, the sample frame refers to all possible samples that qualify (fit) the categorical relation, meaning that they are sample elements or reference points selected for their attributes of interest and amenability for inclusion.

The sample frame is conditional to validation, and requires a conventional number of 'validation points' (data points) uniformly assigned to each 'instance' (measurement point) to assure research confidence. These 'nodes' configuring the sample frame constitute a Relational Matrix illustrated at the next section.

Build Data Point Matrix

The data point matrix is a relational database devised to measure 'instances' (tuples) of the categorical relation together with systematic 'validation points' (attributes) collected to validate observations and differentiate density structuration of the sample frame.

Table 1: Define Relational Matrix

Build Database

The relational matrix may be populated using line-intercept sampling (LIS), which simply means selectional sampling. As an indicative rule, boutique sampling should be conducted for a minimum count of 25-30 of reference points (instances).

Application: Survey of Newsmedia for Business Sentiments about Affirmative Action

Adopting the categorical relation of contemporary 'Business Sentiments about Affirmative Action', the MSI Boutique Sampling method interrogated available multi-media databases to build an n=30 database itemised at Table 2 below.

Table 2: Multimedia Survey Results

Analytical Method

The analytical method utilises the database constructed from the sampling method for diagnostic imputation and statistical interpolation. The analytical method is thus essentially a process of data stratification.

Summary Method:

> Qualitative Analysis

> Diagnostic Imputation

> Statistical Analysis

Qualitative Analysis

Inferential analysis may be deployed to ascertain qualitative dimensionalities of the sample observations. This is typically achieved by enumerating cardinal properties of the dataset.

Using the case study of 'Business Sentiments about Affirmative Action', the process of inferential analysis may proceed per the data classification guide provided at Table 3 below.

Table 3: Generic Classification Guide for Boutique Sampling Qualitative Analysis

The foregoing qualitative analysis is precursor to more in-depth inferential analysis that involves diagnostic imputation by professional judgment, discussed further at the next section.

Diagnostic Imputation

Contemporary professional practice increasingly ascribes a multi-disciplinary peer review approach to managerial decision-making.

Accordingly, MSI provides a pre-formulated regime for diagnostic imputation. As shown at Table 5 below, there are a range of modalities by which diagnostic imputation may be conducted to conform with differential cost, time efficiency and peer acceptance frameworks.

Table 5: Methodologies of Statistical Interpolation

While the Panel Methods (P1, P2) are most commonly used, these collegiate-style approaches may be enhanced by the Triangulation Methods (T1, T2) which ascribe an overlay of quantitative rigor. As illustrated at Chart 1 below, the Triangulation Methods are rated most practical, although market and peer acceptance is highest for P2 which includes endorsement by reputable expert/agencies.

Chart 1: Diagnostic Interpolation Methodologies Compared

Enlarge

Statistical Analysis

The Statistical Analysis is the expositional and declarative procedure of the boutique sampling approach. The statistical analysis is comprised of a three step process of categorical transposition, locating the transect maxima (centriole), and generating resolutions to the categorical relation under study.

Summary method:

> Categorical Transposition

> Formulate Centriole

> Statistical Interpolation

Categorical Transposition

Categorical transposition integrates the categorical relation as a function of the research question and incorporates observations drawn from the qualitative analysis by creating an evaluative transposition. This is scheduled for the case example 'Business Sentiments about Affirmative Action' at Table 6 below.

Table 6: Categorical Transposition

Formulate Centriole

The 'centriole' or sampling focus equates to a density function of the categorical transposition (transect maxima). The centriole is denoted by the recombinant equation form as follows.

f [ X1(α), X2(b) ] = Y

In order to accurately constitute the centriole (Y), professional expertise is required to instigate semantic generalisation of the sampling objective function (SOF). This is typically manifested by a form of explicative analysis based on observed deviations from the group mean, commonly term 'advanced centering'.

For the 'Business Sentiments about Affirmative Action' case study, the recombinant equation-form is of a second-order derivative 'bounded center' logic which generalises to the sample foci of 'Absolute Disturbance Disjunct' which is considered to occur within the theoretical frame of estimated 'cognitive dissonance'.

Table 7: Recombinant Equation-Form ('centriolisation')

Isolation of the centriole effectively prepares the database for higher-order statistical interpolation.

Statistical Interpolation

Statistical Interpolation derives estimates for the centriole, theorised as an 'Absolute Disturbance Disjunct' (ADD) according to the geometric formula:

ADD = [Gd(a)] + [Gd(b)],

simplified

ADD = Geometric Distance (a,b)

For the purposes of statistical interpolation, a panel committee comprised of a selection of business executives (from Melbourne, VIC Australia) were invited to conduct the diagnostic analysis. Using the eliminative triangulation method (T2) discussed above, the Melbourne group returned a T2 statistical report for the n=30 multimedia sample and ADD estimates which is fully detailed at Table 8 below.

Table 8: Statistical Interpolation for Multi-Media Survey of Business Sentiments about Affirmative Action.

Boutique Sampling Illustrated

Graphical Compactness

Chart 2: Irregular Polygon (Radar) Chart of Business Sentiments about Affirmative Action

Diagnostic Contextualisation

Internalisation (reflexivity)

The internalisation of Affirmative Action is a reflexive process that entails both: (i) Business Constructivism, embodying an internal and individualistic locus of control of the manager as agent; and at the same time, (ii) Business Constructionism, being the instrumentality of exogenous perspectives on manager sentiment; an analytical framework consistent with larger (individualistic/structural) theorisation of the gendered global society.

The foregoing case example is demonstrated to derive an Absolute Disturbance Disjunct (ADD) as a centriole measure of cognitive dissonance and human distress, and is further applied to elicit the following dispositional schema of business sentiments about affirmative action.

Business Constructivism

Drawing on the ADD dimensionality, business constructivism may be interpreted as an intrinsic function of ‘intensity of sentiment’ (about a given topic) and the associated ‘urgency to act’ (concerning the same topical matter). The survey reveals that Low ADD Score Samples relate to general sentiments, broadly embracing: (i) Cognition, of the need to act (s11) considering the utility and good practice character of Affirmative Action (s13) in spite of delimiting conditionalities such as observed hazards of quotas (s12); (ii) Program Endorsement, to remove unfair bias (s2; s5), to service minority groups (s6), and to merit deserving candidates (s3) including by means of quotas (s19) and (iii) Systemic Reform, such as peer leadership (s9), removing structural barriers (s15) and attending to other retrogressive aspects of the system (s19).

Business Constructionism

The survey also apprises that High ADD Score Samples are specific to major social cleavages and intense politically-laden opinions, nominally: (i) Catalytic events, that incite disorderly conduct (s1); (ii) Quotas, which are argued to be unnecessary (s14, s17); (iii) Formal Procedures; such as Stock Market Listing Reporting Requirements (s18); (iv) Endemic Discrimination; that maintains the status quo (s16) extending to unconscious bias against female equality (s20) and market entry barriers of minority enterprises (s30); and (v) Personalistic Assertions, about equality of applied effort (s24) compared to overt admissions of affirmative discrimination (s21).