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Sections:
10.1 Results of the citation study
10.2 Results of the reference study
10.3 Discussion
10.4 Other patterns related to the Barnett curves
The results of each distribution have been tabulated (Tables 1-8, 9ff) and graphed (Graphs 1-8ff)
Hypothesis 1-A is confirmed. A Barnett curve may be generated for H citations that does fit the distribution data better than any straight line.
Hypothesis-1B is confirmed. A Barnett curve may be generated for SS citations that does fit the distribution data better than any straight line. In fact hypothesis-1 also holds true for each of the six subjects.
Hypothesis-2 is rejected, since t*SS = 4 = t*H = 4
Hypothesis-3 is upheld, since Umax,SS = 8.41% > Umax,H = 7.49%
Performing the analysis (as per Table 11) we may further conclude that:
Hypothesis-4 was upheld. As µ increases, the skew is statistically proven to decrease (with at least a 90% confidence level).[127]
Hypothesis-5: was not upheld. As µ increases, the kurtosis was not proven to decrease.
Hypothesis-6: was not upheld. As the skew decreases, the kurtosis not proven to decrease.
Using the data as a reference study (Tables 1A-8A, 9Aff) and graphed (Graphs 1A-10A).
Hypothesis 1 is again confirmed for H, SS, and all subjects.
Hypothesis-2 is again rejected, since t*SS = 6 = t*H = 6
Hypothesis-3 is again upheld, since Umax,SS = 7.31 % > Umax,H = 5.43 %
Hypothesis-4 was again upheld, this time perfectly (at least 99.9% confidence).
Similarly Hypotheses-5 and Hypotheses-6: again were not upheld.
Looking at the experimental citation distributions (comparing between H and SS), and their Barnett curves, we notice that Barnett et al. were correct about the following interrelated points:
However, Hypotheses 2, 4, and 5 failed because of the unsubstantiated assumption that:
From the data, I conclude that there is not a significant difference between the H and SS adoption rates since both have an experimental modal citation age of 4 years. Indeed, given modern abstracting and indexing resources, why should Humanities be slower to adopt valid innovations?[128] Actually, examining the Barnett curves which the experimental distributions are compared against, we may note that TSS = 5.09 is indeed less than TH = 4.47, but this is barely perceptible in the corresponding graph (Graph 10). Similar results are seen in the reference study Barnett curves (TSS = 5.44 > TH = 4.71 see Graph 10A).
There is a good correlation between the increasing number of total citations and the decreasing curve error --- with more than 95% confidence (Table 12).[129]
This "Total-citations:Curve-error" trend supports the supposition that the various Barnett curves are valid descriptions of the respective subject distributions. Furthermore, the sundry coefficients of alienation for the subject curves indicate the suitability of the corresponding Barnett curves,[130] particularly Education and Psychology.
To summarize the six subject distributions fall into 3 groups: [131]
The reference study data is generally similar (compare Tables 10 & 12 with 10A & 12A).[132]
126. In this and subsequent sections, the following abbreviations may be used:
| H= humanities | h. = held |
| SS = social sciences | n.h. = not held |
127. Because we do not know that the Skew must decrease (rather than increase) as µ increases, the two-tailed t-distribution applies; hence the confidence is only over 90%, not over 95%.
128. The cliché dichotomy is of a stick-in-the-mud humanities fossil versus the fickle, fad-following social scientist.
129. Almost 99.9% confidence in the reference study (Table 12A).
130 . The coefficient of alienation = (1 - r²) is the "amount of variation in the dependent variable not attributed to the independent variables in the model," i.e., an indication of measurement error or unknown variables --- Donald M. Pilcher, Data Analysis for the Helping Professions: A Practical Guide, Sage Sourcebooks for the Human Services Series, no. 10 (Newbury Park: Sage, 1990), 136, 226.