Results of the Investigation

:date: 2002-07-02 :tags: values :Author: John Plumridge

.. contents:: Table of Contents :depth: 2 .. sectnum::

.. _Adapting Sacred Landscape: http://cms.nfshost.com/thesis_Q_landuse_interests.html .. |Fmax| replace:: F\ :sub:max

Results from Adapting Sacred Landscape_

Five factors were found, accounting for 56% of the total variance. Reliability coefficients and composite reliability scores are high. Factor ratios of statements and sorts were judged to be adequate for clear separation of factors. Reliability measures were high. Factors show separation at a maximum 0.5636 correlation.

Following interpretation of the array of statements scores for each factor, the five viewpoints were labelled’ Sacred Adaptive’, ‘Technologist’, ‘Sacred Protector ‘‘Protector’ and ‘Administrator’. These appellations represent viewpoints concerning environmental management and sacred beliefs.

Balance of the statements #

|Fmax| Between groups tests show balance was obtained in the four groups of statements, and thus responses were not contingent upon design and represent a point of view. Interactions across Levels and Effects were noted, and these indicate where improvements to the sample of statements might be made.

Demographic variables #

Factor loadings did not vary with within Wales or outside Wales, within the West. This indicates a comprehensive selection of participants and similar range of viewpoints in this concourse of views.

No effects of age were found upon factor loadings, which suggests that no viewpoint is age dependent. The age range of participants was from 20 to 64 (mean age = 29, median 33).

Factors Obtained & Salience of Statements #

Factors Obtained #

The 38 Q sorts were processed following the usual steps of Q methodology, of correlation and centriod factor analysis using MQMethod 2.0 (revised and maintained by Peter Schmolck, University of the Federal Armed Forces Munich, Germany).

Raw scores are shown in Appendix A.1; the correlation matrix in Appendix A.2; the unrotated factor matrix is shown in Appendix A.3.

An initial 8 factors were obtained using the centroid factor analysis model. Factors were rotated using the Varimax criterion, to produce Factor z scores are given in Appendix A.5. From Factor Z scores normalised factor statement scores were calculated, as given Appendix A.6., upon which interpretation was to be based. Standard errors for factor scores in Appendix A.7. The Varimax procedure rotates the factors to maximise the degree of difference between each factor. Five factors where participants had a factor loading of 0.45 or more were significant at the p = 0.01 level.

.. table:: Table 4: Eigen values and % variance for Factors 1-5

================= ======= ====== ====== ======= factors f1 f2 f3 f4 ================= ======= ====== ====== ======= Eigen Values 15.4654 3.0135 1.3056 1.0548 % explained var. 21 13 11 8 ================= ======= ====== ====== =======

From Table 4, Factor eigen values ranging from 15.4654 to 1.0340 accounted for 56 percent of the total variance

.. table:: Table 5: Factor characteristics for factors 1-5

========================= ======= ====== ====== ======= ======= factors f1 f2 f3 f4 f5 ========================= ======= ====== ====== ======= ======= No. of defining variables 12 6 2 2 2 Average Rel.Coef. 0.8 0.8 0.8 0.8 0.8 Composite Reliablity 0.98 0.96 0.889 0.889 0.889 S.E. of Factor Scores 0.143 0.2 0.333 0.333 0.333 ========================= ======= ====== ====== ======= =======

From Table 5, Factor characteristics reliability coefficients and composite reliability scores are all greater than 0.8 which was considered highly reliable. The number of defining variables for factors ranged from 12 to 2.

.. image:: http://cnrm.lilyralph.co.uk/images/dissrt7.jpg

Factor Ratios #

  • The ratios of Q-sorts to factors was 38/5 =7.6
  • The ratio of statements to factors was 56/5 = 11.2

Significance of Q-sort factor loadings #

A loading is statistically significant (i.e. significantly different from zero) if it is 2.58 times the standard error (Brown 1980:283,238), where SE=1/SQRT(N)N is the number of statements. SQRT means square root.

  • i.e. 1/SQRT(58) x 2.58 - 0.338 (where N=58).

    • Hence a loading was significant (p<0.1) if it exceeded 0.338.

  • All 38 Q-sorts load significantly across one factor or more (refer to Appendix A.4. Factor Matrix Loadings).

  • Number of mixed cases, scoring highly on two factors = 5

Salience of Statements #

Statements lack salience, and hence would not be useful in depicting any factors’ point of view, if all factor types sort the statement into the neutral range (Thompson, 2000). The neutral range is defined as a statement’s average absolute value (factor Z-score) of less than 0.5

A consensus statement is one where all factors agree pr disagree. Np statement’s Z-scores is in the neutral range for all factors.

Analysis of Balance in the Q Sample #

Variance Across Groups #

The Fischer |Fmax| test was chosen because it does not assume homogeneity of variance, unlike Anova. It is used to test the null hypothesis that the group variances are equal. Assumptions are: Within each group, the scores are independent, and identically normally distributed with the same mean and variance. (Zar, 1996). See Appendix B.1. for details of the F tests; see Appendix B.3. for Tables of means, medians, sums of scores.

Effects x Levels (AxB) interactions: Factor 1, 3 and 4 show significant interaction between Levels(A) and Effects (B).

  • F ratios = 3.70 (F1), 12.50 (F3), 4.50 (F4)
    • critical value (2,27)= 2.93 p < 0.01

Levels (A) interactions:

  • No significant effects occurred between two Levels Aa and Ab.
  • |Fmax| = 1.33 critical value (4,13) = 6.40

Effects (B) interactions Factor 3 only, shows significant interaction between the Effects Bc and Bd.

  • F ratio = 7.63 critical value (4,13) = 6.40 p < 0.01

.. image:: http://cnrm.lilyralph.co.uk/images/dissrt8.jpg

Between groups variance tests #

|Fmax| tests:

  • Group Interaction variances: No factor shows significant variability in response to the 14 statements of each topic in |Fmax| tests.
  • |Fmax| = 3.27 - Critical value (4,13)- = 4.45: p<05 (see appendix B.1. for data)

Unpaired t- tests by groups #

The unpaired t-test compares the means between two groups. A mean of zero was hypothesised, according to the balanced forced-choice Q sort employed with a mean of zero. Homogeneity between cells was not assumed. Normal, or quasi-normal distribution is assumed. (see appendix B.2. for data)

F3 alone shows significant variance. This occurs in the involvement group and the responsibility group - within Level Aa, as displayed in Fig.3, below

  • Involvement: mean= 1.071
    • T= +4.02 p = 0.0015
  • Responsibility: mean = -1
    • T= -2.463 p = 0.0285

.. image:: http://cnrm.lilyralph.co.uk/images/dissrt9.jpg

Median Values by Factor #

.. table:: Table 7: Summary of Trends in median for factors 1-5

============= ==== ==== ==== ==== ==== / f1 f2 f3 f4 f5 ============= ==== ==== ==== ==== ==== relationship + - 0 + 0 responsiblity - 0 - - 0 significance - 0 0 - 0 invovement 0 0 + + - ============= ==== ==== ==== ==== ====

Table 7 above gives the trends in scores for factors by group. (See appendix B.5.for median values and sums of scores).

  • Balance is achieved in 9 out of 20 cells.
  • ‘Relationship’ views are given positive emphasis by factors 1 and 4.
  • ‘Responsibility’ values are given negative emphasis by F1, and F2 and F3.
  • ‘Significance’ views are given negative emphasis by F1 and F and balance by F2, F3 and F5.
  • ‘Involvement’ values are given overall positive emphasis by F3 and F4, negative emphasis by F5, and are balanced by F1 and F2.
  • Trends in discriminations of strength of agreement, are indicated by sums of scores in Table 8. The stronger the feeling the higher the SS, whether the median score is low or not.

Sums of Squares #

.. table:: Table 8: Total Sums of Square scores by group for all five factors

========== ========== ================ ============== ============= / relation responsibility significance involvement ========== ========== ================ ============== ============= total SS 133 181 91 152 ========== ========== ================ ============== =============

Discussion of the Balance of Groups #

Variance analysis was to determine whether the a priori structure that was built into the Q sample is evident in the pattern of factor scores.

Interactive effects across groups, within Levels SS(A) and also, Effects SS(B) indicate that the mean scores of the four cells deviate from one another. The principle of randomisation has not operated during the judges’ self description and contingencies are involved between cells (Brown, S.R. & Melamed, L.E., 1990, p. 73). Technically, it indicates there is an “interaction” between main effect A and effect B (Sohn, 1991). This interaction is not a cause for alarm, the means being relatively close to the hypothesised mean of zero, with cell counts of 28. The comfort for the judges in completing the sort would be tolerable.

Interaction effects were observed across groups, and within the Level, interactions observed are not a cause for alarm, given a maximum mean of 1.071 and- the negative findings with |Fmax| tests between groups.

Observation of the medians shows considerable balance within item groups, realised in 9 cases out of twenty subgroup trails. Significant differences occurred for F3 within the level Aa. Cell interactions were expected; within the context of the whole sort, it was possible for judge’s to comfortably complete the sort from their viewpoint. Personal observation, and the reported experience, of judges’ comfort in performing the sorts, was encouraging. Such Interaction was expected because the heterogeneous sample of 56 items represented a- range of views, as well as values, and cannot be balanced as a set of attributes might be with ‘vices and virtues’/‘skills and non-skills’. Some people find more of the range of views acceptable, than others can.

The strong responses overall to ‘Responsibility’ items, observed in the group total sums of squares, is potentially less a function of balance, and instead due to the ‘hot’ nature of the issues involved. Here is one example (factor scores in brackets):

“An environmental policy based on loss and profit accounting procedures should work.” (-2 -2 -2 -2 0 )

Perhaps people chose to disagree more strongly with responsibility items. A count reveals 29 negatives (see Appendix A.5. ‘Ranks statement totals’) in the low-scoring ‘significance’ group, when 28 would achieve true balance. Responsibility has 40 negatives, showing strength of disagreement. In this then, lies an explanation for the Interactive effects between Levels SS(A) and Effects SS(B). A search for more balance to the views represented in the Responsibility and involvement set would be fruitful.

The effects and levels do not function as independent variables; the judges are not under test. The subsequent factorisation has no critical dependency on test ‘construction’ effects’ (Stephenson, 1977, p. 8), “and the design is not used in interpretation because it is the subject’s understanding that is being measured” (Stephenson, 1963, p. 270). These groupings are determined by hierarchy. They are designed to achieve balance in the sample, and determine whether judge response is contingent upon design.

Balance has not been a problem, and is obtained through the four categories, as determined by |Fmax| tests. Overall balance for the judge in a forced choice Q sort was achieved through careful scrutiny of the range items presented across the hierarchies.

Discussion of Factor Results #

High factor-score interrelations usually indicate the forcing of too many factors. A maximum of 0.5636 correlation indicates a factor that can be considered meaningful, and is therefore not excessive. Reliability coefficient are high.

Five factors were found, accounting for 56% of the total variance. “Whereas reporting eigen values (EV) and percent of variance (%Var) may appear innocent enough, their reporting conveys the impression that they have some meaning and importance. I would therefore be inclined not to report them unless there is some overriding reason to do so” (Brown, 2002).

In fact they are relatively unimportant in Q. The eigen values are the sum of the squared factor loadings, and the the %VAr is given by dividing EV by the number of Q sorts: the more Q sorts, the higher the EV. Hence, if you happen to have included more factor A type persons than factor B in the P set, then the EV does not say anything about the real world. Participants in Q are usually selected for theoretical reasons, not randomly. EV is also relatively unimportant in R methodology, where type 1 trait may have more test items that type 2.

Both factor ratios of statements to factors are to be judged to be adequate for clear separation of factors.

The number of defining variables- refers to the Q sorts marked with high factor loadings used to define a factor. A minimum of two Q sorts (i.e. people) is sufficient to define a factor. actor matrix loadings are given in Appendix A.4.

No statement lacks salience. Where a consensus statement (where all factors agree, or disagree), consists in either strong agreement or strong disagreement, it would nevertheless be salient and relevant from each factor’s point of view.

Demographic Variables - Age and Region #

Demographic variables: age and region #

See Appendix B.6. for data table of demographic variables.

Region #

In a test of Anova, nominal variable region- (within Wales / outside the Wales) was tested for variance with respondents’ loadings on factors 1-5.

H0: The null hypothesis is that the mean of the dependent variable, factor loadings, is the same regardless of region.

No effects of region upon factor loadings were observed at the significance level p < 0.05. Therefore the null hypothesis is accepted. (See appendix B.7. for details)

Age #

The age range of participants was from 20 to 64 (mean age = 29, median 33). In a test of Anova, the continuous variable age- was tested for variance with respondents’ loadings on factors 1-5.

Assumptions homogeneity of variance, a linear or plateau relationship, normal distributions.

H0: The null hypothesis is that the mean of the dependent variable, factor loadings, is the same regardless of region.

No effects of age upon factor loadings were observed at the significance level p < 0.05. Therefore the null hypothesis is accepted (see Appendix B.8 for details.)

Implications of these findings are discussed in sections: Adapting Sacred Landscape_

Appendices #

======== ======================================================= ====== Appendix Table Page ======== ======================================================= ====== A.1. Data table: Statement scores by Q sort i-iii A.2. Correlation matrix between sorts iv-v A.3. Unrotated Factor Matrix showing factor loadings by sort vi A.4. Factor Matrix Loadings vii A.5. Normalised factor z scores viii A.6. Factor Q-sort values for each statement ix-xi A.7. Factor characteristics xii B.1. F-tests for variance by effect and level: Factors 1-5 xiii B.2. Unpaired t-tests: Factors by Groups. xiv B.3. Descriptive Statistics: Cell categories for factors 1-5 xv B.4. Demographic Variables xvi B.5. Analysis of factors by demographic variables: Region xvii B.6. Analysis of factors by demographic variables: Age xviii ======== ======================================================= ======

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