9.1 Introduction
The investigation had reached the stage where a series of computations and analysis thereof, was required that would permit the current researcher to convert sampled statistical data into noteworthy scientific evidence and present these to the global scientific community for critical evaluation (refer to Graziano & Raulin, 1989, p. 2). Research of excellence, however, requires more than scientific evidence: it mandates conversion of captured statistical data into plausible, convincing, and realistic evidence that supports various assumptions and commitments that the researcher had made in the course of the study. The statistical information that is presented in Chapter 9 is derived from three data sources: the intact main data set and the two condensed versions thereof (refer to Subsection 6.6.2 in Chapter 6). In presenting and analysing calculations, the researcher takes cognisance of scientific implications of essential comments that he has made in earlier Sections of the dissertation:
1. The researcher’s resolve (refer to Section 1.3 of Chapter 1). 2. The problem statement (see Section 3.2 of Chapter 3). 3. The thesis statement (see Section 3.3 of Chapter 3). 4. The research question (refer to Section 3.4 of Chapter 3). 5. The practical question (refer to Section 3.5 of Chapter 3).
6. The 6 proximal and 5 distal scientific objects (these are stated in Section 3.6 of Chapter 3).
7. The 10 research objectives that are set and substantiated in Section 3.7 in Chapter 3).
9.2 Descriptive Statistics
The minimum and maximum scores, arithmetic means, standard deviations and standard errors of estimate were descriptive statistics that were generated during the course of the study. These statistics appear in Appendix C of the dissertation. Section C1 of this Appendix contains descriptive statistics for the Total Sample. Sections C2 and C3, respectively, provide similar statistics for participants who either held Long- or Short-Term Employment
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Contracts with their employers. Descriptive statistics in Sections C4 and C5, respectively, are derived from a Male-Female split of condensed data set 1. The descriptive statistics that appear in Sections C6 to C10, respectively, required a data-set split according to six Age Cohort Groups. The sample of executives were bracketed as follows: Age Cohort Group 1, 21-30 years; Age Cohort Group 2, 31-40 years; Age Cohort Group 3, 41-50 years; Age Cohort Group 4, 51-60 years; Age Cohort Group 5, 61-70 years; and Age Cohort Group 6, 71-80 years. Fellow-scientists and readers are reminded that the six Age-Cohort Groups, for the purposes of multivariate analysis of variance, were recoded into three categories. Age Cohort Groups 1 and 2 were combined into the revised Age Cohort Group 1. The original Age Cohort Group 3 was kept unchanged but renamed Age Cohort Group 2. Finally, Age Cohort Groups 4, 5, and 6 were combined to form Age Cohort Group 3. The bracketing produced three revised Age Cohort Groups: the age categories 21-40 years, 41-50 years, and > 50 years. The descriptive statistics that are reported in Sections C11 and C12 are those of the revised Age Cohort Groups 1 and 3. The descriptive statistics for Age Cohort Group 2 are that of the original Age Cohort Group 3 that are reported in Section C8 of Appendix C. If necessary, refer to Subsection 6.6.2 in Chapter 6.
The sets of arithmetic means, standard deviations, and subsample sizes that were used in the assessment of one-, two, and three-way analysis of variance of the 20 dependent variables appear in Subsections 19.4.1 to 19.4.20 immediately after presentation of the analysis of variance tables. The sheer volume of calculations generated by three-way interaction required a different approach to presentation and reporting of outcomes. Comprehensive analyses and reporting were limited to those three-way contrasts that generated statistically significant F ratios: the attributes Executive Capability, Regular Organisation Evaluation, and Individual Consideration were the only dependent variables that met this criterion. Similarly, comprehensive descriptive statistics and protected t values were provided in these instances but only significant computations were analysed and reported in detail. All insignificant F ratios for three-way interactions were reported but were not subjected to in-depth analysis.
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9.3 Pearson Correlation Matrices
Three matrices of Pearson product-moment correlations were generated with two of the three data sets that are discussed in detail in Subsection 6.6.2 of Chapter 6. The matrices appear in Appendix B. The matrix in Section B1 of Appendix B contains intercorrelations among the original 29 Executive Tasks. The matrix in Section B2, similarly, describes correlations among the original set of 29 Executive Behaviours. The matrix that appears in Section B3 of Appendix B, reflects intercorrelations between the 20 dependent variables. The 20 variables included (a) the two latent constructs labelled Inspiring Subordinates and Interpersonal Sensitivity that were extracted by principal component analysis of the original 29 executive behaviours, (b) the six new latent constructs Executive Capability, Future- Oriented Actions, Other-Directedness, Up- and Downward Communication, Coaching and Motivating Subordinates, and Regular Organisation Evaluation that were extracted by principal component analysis of the original 29 executive tasks, and (c) 12 Leadership Styles, as assessed by the Multifactor Leadership Questionnaire, or MLQ. The four unaccounted variables are the subject identification number and the three main-effect variables Length of Contract Term, Gender, and Age Cohort Group. Participants’ scores on the 24 variables were the core contents of condensed data set 1. The computations in Matrix B3 were derived from the latter data set which was not standardized.
9.4 Three-Way Analysis of Variance
The computations of the three-way classification analysis of variance involved the respective categories of the primary, secondary, and tertiary variables Length of Contract Term, Gender, and the revised Age Cohort Group categories, as well as their effects on 20 dependent variables: the two latent executive behaviours, six latent executive tasks, and the 12 MLQ styles of leadership. The chosen method was appropriate for examination of statistical interactions between the three main effect variables and the 29 dependent variables. The researcher was optimistic that the method of data analysis was appropriate for achievement of the objectives of the prospective study.
Conduct of one-, two-way and three-way analysis of variance requires advanced statistical knowledge of the F test and multiple comparison procedures, such as Fishers protected t test, and adherence of dedicated research conventions and assumptions that underlie their application. Fellow-researchers and students, therefore, need to note the three critical statistical values that figured regularly in the interpretations and discussions of the outcomes
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of the one-way, two-way, and especially three-way interactions that are reported in the rest of Chapter 9: (a) the F critical value of 3.91 for the main effect variables Length of Contract
Term and Gender, with 1 and 127 degrees of freedom and p = 0.05, (b) a F critical value of
3.06 for the main effect variable Age Cohort Groups, with 2 and 127 degrees of freedom and p = 0.05, and (c) the t critical value of 1.645 that figured in applications of Fisher’s LSD
test, or the protected t test as prerequisite for multiple comparison procedures, with 116 degrees of freedom and p set at 0.05 (if necessary, refer to Sections 6.7.7 and 6.7.10 in Chapter 6 of this dissertation).
9.4.1 Executive Behaviour I: Inspiring Subordinates
Executive behaviour I was derived from items 1 to 15 as well as items 17 to 20 of the original set of twenty-nine executive behaviours. This complex executive trait, designated as
Inspiring Subordinates included the following subconstructs:
Developing Others; Building Partnerships with Others; Flexibility; Persuasiveness; Empowering Others; Inspiring Others; Communicating the Vision to Others; Instilling Moral Principles; Advising Others; Envisioning the Future; Coaching Others; Evaluating the Performance of Subordinates; Frequent Communication; Implementing the Vision; Delegating Authority to Subordinates; Live the Values of the Organisation; Motivating Others; Employing the Best Talent; and Empowering Others.
The results of the 2 x 2 x 3 analysis of variance of the executive behaviour Inspiring Subordinates are included in Table 9.1.
Table 9.1. Factorial Analysis of Variance for the Variable Inspiring Subordinates
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Selected descriptive statistics that were essential for assessing homogeneity of variance and analy sing intera ction amon g the subs ets of score s of the attrib ute Inspir ing Subo rdinat es that was extracted through statistical manipulation of the main effect variables, were:
Executives with Long-Term Contracts: 49.14 ± 18.00, and n = 76 Executives with Short-Term Contracts: 43.44 ± 18.08, and n = 52
Male executives: 47.67 ± 17.54, and n = 86 Female executives: 45.09 ± 19.52, and n = 42
Executives in the Age Cohort Group 21-40 years: 48.80 ± 18.37, and n = 54 Executives in the Age Cohort Group 41-50 years: 43.65 ± 16.06, and n = 41 Executives in the Age Cohort Group > 50 years: 47.55 ± 20.25, and n = 33 Male executives with Long-Term Contracts, 50.18 ± 17.51, n = 53
Female executives with Long-Term Contracts, 46.75 ± 19.25, n = 23 Male executives with Short-Term Contracts, 43.65 ± 17.09, n = 33 Female executives with Short-Term Contracts, 43.08 ± 20.17, n = 19
Executives with Long-Term Contracts in Age Cohort Group 21-40 years: 53.63 ±15.32, n = 29
Executives with Long-Term Contracts in Age Cohort Group 41-50 years: 45.37 ± 16.23, n = 27
Executives with Long-Term Contracts in Age Cohort Group > 50 years: 47.73 ± 22.79, n = 20
Executives with Short-Term Contracts in Age Cohort Group 21-40 years: 43.19 ± 20.26, n = 25
Type III Sum Degrees of Mean Level of
Source of Squares Freedom Square F Ratio Significance
Corrected Model 3 852.332 11 350.212 1.066 0.395 Intercept 158 220.735 1 158 220.735 481.539 0.000
Contract Term 95.614 1 95.614 0.291 0.591
Gender 110.535 1 110.535 0.336 0.563
Age Cohort Group 857.487 2 428.744 1.305 0.275 Contract * Gender 446.228 1 446.228 1.358 0.246 Contract * Age 1 488.846 2 744.423 2.266 0.108
Gender * Age 315.351 2 157.675 0.480 0.620
Contract * Gender *
Age Cohort Group 1 622.749 2 811.374 2.469 0.089 Error Factor 38 114.447 116 328.573
Total Sum of
Squares 322 638.264 128 Corrected Sum of
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Executives with Short-Term Contracts in Age Cohort Group 41-50 years: 40.33 ± 15.77, n = 14
Executives with Short-Term Contracts in Age Cohort Group > 50 years: 47.28 ± 16.47, n = 13
Male executives in Age Cohort Group 21-40 years: 49.58 ± 17.72, n = 25 Male executives in Age Cohort Group 41-50 years: 46.35 ± 15.29, n = 33 Male executives in Age Cohort Group > 50 years: 47.53 ± 20.18, n = 28 Female executives in Age Cohort Group 21-40 years: 48.12 ± 19.20, n = 29 Female executives in Age Cohort Group 41-50 years: 32.50 ± 15.11, n = 8 Female executives in Age Cohort Group > 50 years: 47.69 ± 23.08, n = 5
The arithmetic means varied considerably from 32.36 to 53.63 while the standard deviations fell within the range of 15.11 to 23.08. The later distribution pointed to potential heterogeneity of variance. Examination of the arithmetic mean-standard deviation ratios suggested overestimation of the parameters of dispersion.
The main effects were compared and analysed. Contrast 1: The F ratio of 0.291 for the two categories of the independent variable Length of Contract Term was less that the F critical
value while its probability of 0.591 exceeded the p value of 0.05. This result was
insignificant; Contrast 2: The variable Gender yielded a F ratio of 0.336 that was less than the F critical value, with a level of significance of 0.563 that exceeded the 0.05 level. This result was insignificant; and Contrast 3: The F ratio of 1.305 for The Age Cohort Group comparison, too, was less than the F critical value with a probability of 0.275 in excess of p =
0.05; This result was insignificant. Interpretation: The three main effect variables did not
have any statistical effects of note on the dependent variable.
The two-way interactions were next assessed. Contrast 4: The observed F ratio of 1.358 for the Length of Contract Term x Gender comparison was insignificant. It was less than the F
critical value while its probability of 0.246 was greater than the probability level of 0.05;
Contrast 5: The Length of Contract Term x Age Cohort Group comparison yielded a F ratio