Co-authorship network analysis of iMetrics researchers.

Khasseh, Ali Akbar ; Soheili, Faramarz ; Chelak, Afshin Mousavi 等

Introduction

Nowadays, scientific collaboration is prevalent in various scientific disciplines. Scientific collaboration has been resulted from knowledge complexity, increase in demand for more specialization, and interdisciplinary skills in research. It is a social phenomenon in research and has been studied systematically since the 1960s. Since then, some increase in the rate of scientific collaboration has been reported by various researchers.

Social network analysis is used for describing the scientific collaboration patterns identified by co-authorship relations (Stefano, Giordano & Vitale, 2011). Scientists included in the collaboration networks share their ideas, use similar methods and techniques for extracting and analyzing research data and influence each other's works. As one of the most documented and tangible forms of scientific collaboration and the most formal manifestation of intellectual share among authors in producing scientific works, co-authorship is the collaboration among two or more authors on producing a work that results in a production with higher quality and quantity than that produced by a single author (Hudson, 1996). Collections of such collaborations among researchers can construct a co-authorship network in which authors form nodes and the line between two nodes is considered as the co-authorship relation created in the papers. As a main category of social networks, the co-authorship network can be used for determining the structure of scientific collaboration and individual authors' research states (Liu et al., 2005).

On the other hand, one of the complex debates in bibliometrics is researchers' scientific influences. Since some authors relate a researcher's scientific influence to the citation rate of his/her works, scientific influence is not restricted to one's works and a researcher's interaction with other researchers in a field is at work when considering his/her scientific influence, i.e. his/her social influence. Social influence is one's ability to influence others by a means of social interaction processes (Truex et al. 2011). In other words, the expansion of a researcher's thoughts can be measured by studying his/her co-authorship trends in a certain scientific field (Cuellar et al. 2016). Three measures of centrality (degree, betwenness, and closeness) are often used for measuring the social influence. Centrality is one of the most important and common measures in analyzing social networks, especially for identifying main and powerful influencing actors.

Considering the above-mentioned points, this study aims at investigating the relationship between researchers' productivity and performance with their centrality measures among researchers in the iMetrics. Specifically, this study attempted to determine:

1. The rankings of iMetrics researchers based on their centrality (including degree, betweenness, and closeness) measures;

2. The possible relationship between productivity (the number of articles) and centrality measures; and

3. The possible relationship between performance (the number of citations) and centrality measures.

Literature review

Several scholars have directly applied centrality measures to co-authorship networks in different fields (Barabasi et al. 2002; Otte & Rousseau, 2002; Mutschke, 2003; Liu et al, 2005, Acedo et al, 2006; Krichel & Bakkalbasi, 2006; Liu et al, 2007; Hou et al, 2008; Gomez et al, 2008). On the other hand, the study of research productivity, citation impact and collaboration has a long-standing tradition in LIS research, and these three indicators have been employed in many disciplines to measure research success in terms of output (Abrizah et al. 2014). To be more specific, the relationship between social network structures in co-authorship network and research productivity and impact is studied in several studies (Newman, 2001; Egghe et al. 2007; Abbasi and Jaafari 2013; Yin et al. 2006).

Among them, Hou, Kretschmer and Liu (2008) investigated the structure of scientific collaboration networks in scientometrics at the level of individuals by using bibliographic data of all papers published in the international journal Scientometrics during 1978-2004. The result showed that Glanzel is the central author of the whole network in terms of the highest degree, betweenness and closeness centralities, which indicates that he is the most influential person in the network. With respect to sub-networks. Moreover, they found a positive and significant correlation between output of authors and the centrality measures, which revealed that most of the prolific authors were also active in collaboration network in the field of scientometrics.

Yan and Ding (2009) indicated that co-authorship centrality measures are significantly associated with citation counts, with betweenness centrality having the strongest association. Badar et al. (2012) examined the association of co-authorship network centrality (degree, closeness and betweenness) and the academic research performance of chemistry researchers in Pakistan. Results related to regression revealed a positive impact of degree and closeness and negative impact of betweenness centrality on research performance. Temporal analysis using node-level regression confirmed the direction of causality and demonstrated a positive association of degree and closeness centrality on research performance.

Guns et al. (2010) found that top authors in Scientometrics and Journal of Informetrics had the highest global collaboration network centrality measures. Moreover, Liao and Yen (2012) indicated that the degree of research collaboration had a strong positive relationship with research productivity.

In a more recent study, Abrizah et al. (2014) investigated the field of informetrics to identify publication strategies that have been important for its successful researchers. They used a micro-analysis of informetrics researchers from 5,417 informetrics papers published in 7 core informetrics journals during 1948-2012. Findings revealed that the 30 most productive informetrics researchers of all time span several generations and seem to be usually the primary authors of their research, highly collaborative, affiliated with one institution at a time, and often affiliated with a few core European centres. Their research usually has a high total citation impact but not the highest citation impact per paper. Moreover, results indicated that the most cited authors also tend to be the most productive authors: 20 of the 30 most cited authors are also in the most productive 30. Based on betweenness centrality, Glanzel, Rosseau, and Leydesdorff gained the highest scores, respectively.

Results of Soheili, khademi and mansouri (2015) showed that there is a significant correlation between Journal Impact Factor (JIF) and all centrality measures except closeness centrality at P= 0.001. Results also showed that there is a significant correlation between productivity of authors and all centrality measures scores at P> 0.001. Also, regression reports direct relationship of degree, closeness and flow betweenness and inverse relationship of betweenness as well as Eigen vector centrality on productivity of researchers.

Methodology

This research applied co-authorship analysis and social networking analysis. The research population consisted of the iMetric papers that were indexed in the Web of Science (WoS) during 1978-2014. It worth nothing that in research on fields such as bibliometrics, informetrics, webometrics and in general, iMetrics, the lack of a justified and appropriate statistical population can be seen. However, the selection of primary data is important in every iMetrics study as it directly affects consequent results and findings. Therefore, it is better to include comprehensive primary data. Considering this main point, following the methodology innovated by Milejeciv and Leydesdorff (2013), the statistical population of this research included all papers published in Scientometrics and the Journal of Informetrics, as well as iMetrics papers published in the six journals including the Journal of American Society for Information Science and Technology (JASIST), Information Processing and Management, Journal of Documentation, Journal of Information Science, Research Evaluation and Research Policy. The reason for selecting these journals was that they published most papers in the field of iMetrics (Milejeciv and Leydesdorff, 2013). In addition, the journal Scientometrics is the first specialized journal in iMetrics field that has been published since 1987 and developed the field (Milejeciv and Leydesdorff, 2013; Leydesdorff, et al., 2014). Therefore, the time spam of 1978-2014 was selected for this research.

Data collection

A relatively comprehensive method was used for data collection. This method introduced by Milejeciv and Leydesdorff (2013). At first, all scientific productions in the WoS that were published in the eight above-mentioned journals were extracted. Then, documents labeled under "article" or "proceeding" were selected. The papers irrelevant to iMetrics field in the six journals including Journal of American Society for Information Science and Technology (JASIST), Information Processing and Management, Journal of Documentation, Journal of Information Science, Research Evaluation, and Research Policy were excluded. All papers published in Scientometrics and the Journal of Informetrics were included, however. The preposition of exclusion was that every paper published in Journal of American Society for Information Science and Technology (JASIST), Information Processing and Management, Journal of Documentation, Journal of Information Science, Research Evaluation, and Research Policy which cited one of papers published in the Scientometrics or the Journal of Informetrics were included. In other words, citation to papers published in Scientometrics and the Journal of Informetrics as main journals of iMetrics field was the criterion for separating the papers published in the other six journals in iMetrics field from those of non-iMetrics field. The software isi.exe was used for records screening. Many related papers were retrieved by applying this method. However, it was probable that some related papers published in these journals had no citation to Scientometrics or the Journal of Informetrics. For retrieving such papers, some commonly-used and highly-frequent keywords in the field extracted from previous researches were used in the following search strategy that resulted in some other related items:

TITLE= ("informetric*" OR "bibliometric*" OR "scientometric*" OR "webometric*" OR "citation*" OR "cite" OR "*citation" OR "indicator*" OR "productivity" OR "mapping" OR "h-index" OR "h index" OR "Hirsch index" OR "*index" OR "co-autho*" OR "coautho*" OR "impact factor*" OR "link analys*" OR "link structure" OR "patent analys*" OR "Zipf*" OR "Bradford*" OR "Lotka*" OR "collaboration network*" OR "scientific collaborat*")

Finally, considering the attempt to achieve a complete statistical population, 5944 papers in iMetrics field were identified and analyzed. As shown in Table 1, most of these papers were published in the journals of Scientometrics, JASIST and Informetrics, respectively.

Data Analysis

First, all the authors of the documents were extracted. The authors were then edited and modified and those authors whose name were written in several ways changed to the preferred name. In order to show the main structure of the network, each author must published 4 papers or more to be included in this study. This threshold resulted in a total of 626 prolific authors publishing 4 or more papers during 1978 to 2014, among them there are 609 authors published co-authorship papers, accounting for 97.28% of the prolific authors. It is necessary to mention that some authors such as Vinkler (34 papers), Sangwal (11 papers), Haitun (10 papers), and Kosmulski (10 papers) have published no co-authored paper. In the next step of the co-authorship square matrix consisting of 609 researchers was created and imported to the UCINet. Using UCINet, the matrix was converted into a correlation matrix, centrality indicators were calculated by UCINet, and the network visualized using NetDraw.

Results

In total, 13,258 authors' frequency were involved in authoring 5,944 papers in the iMetrics that represented 2.23 authors per paper. The number of unique author names in the studied sample was 5,476. The rate of productivity based on the number of published papers revealed that "Leydesdorff L" with 146 papers and "Rousseau R" with 136 papers were in the first and second ranks, respectively. "Egghe L" and "Glanzel W", each with 134 papers were in the next rank and "Thelwall M" with 113 papers was in the fifth rank. As table 2 shows, the difference in the number of papers produced by these five authors is much more than that of other authors. It is worth noting that these authors may have other papers in the fields other that the iMetrics that are not included in this study, however.

The primary analysis of records by Publish or Perish Software revealed that out of 5,944 papers, 2,048 papers (34.46%) were authored by one author, as a prevalent authorship pattern in iMetrics and the remainding papers (65.54%) were authored by two or more authors, as the co-authorship pattern. As shown in table 3, 2-author pattern with 1911 papers, 3-author pattern with 1911 papers and 4-author pattern with 487 papers were in the second to fourth ranks, respectively. Only one paper was authored by 11, 15, 23 or 26 authors in the field.

Top iMetrics researchers based on three centrality measures

The iMetrics researchers' ranking is shown in table 4 based on three centrality measures (including degree, betweenness, and closeness centralities). The highest degree centrality belonged to "Glanzel W". "Rousseau R" and "Thelwall M" were in the second and third ranks, respectively. Considering the rate of betweenness centrality, "Leydesdorff L", "Rousseau R" and "Glanzel W" were in the first, second and third ranks, respectively. As table 4 shows, the highest closeness centrality measures belonged to "Leydesdorff L", "Rousseau R" and "Rafols I", respectively. Researchers appearing in all columns are highlighted in bold and those in two of the columns are shown in underline.

The relationship between productivity and centrality measures

Regression analysis was used for exploring the possible relationship between authors' productivity and centrality measures. The results of analysis of variance (ANOVA) for regression analysis are depicted in table 5.

Based on the results of regression analysis (F= 591.517, p [less than or equal to] 01), the centrality measures explain 74% of variance of productivity ([R.sup.2] = .74). Considering the significant effect of productivity on the centrality measures, the coefficients of prediction equation was shown in table 6.

The regression coefficients of each predicting variable showed that each centrality measure can significantly explain the variance of productivity variable (p [less than or equal to] 0.01). The effect coefficient of degree centrality showed that 1 unit increase in degree centrality can increase 0.692 rate in productivity (B= 0.692, p [less than or equal to] 0.01). The effect coefficient of betweenness centrality showed that 1 unit increase in betweenness centrality can increase 0.256 rate in productivity (B= 0.256, p [less than or equal to] 0.01). However, the effect coefficient of closeness centrality showed that 1 unit increase in closeness centrality can decrease 0.092 rate in productivity (B= - 0.092, p [less than or equal to] 0.01).

The relationship between performance and centrality measures

Regression analysis was used for exploring the possible relationship between performance and centrality measures. The results of ANOVA for regression analysis are depicted in table 7.

Based on the results of regression analysis (F= 288.628, p [less than or equal to] 0.01), the centrality measures explain 58% of variance of performance ([R.sup.2] = 0.582). Considering the significant effect of performance on the centrality measures, the coefficients of prediction equation was shown in table 8.

The regression coefficients of each of these predicting variables showed that two centrality indicators (degree and betweenness) can significantly explain the variance of performance as the dependent variable (p [less than or equal to] 0.01). The effect coefficient of degree centrality showed that 1 unit increase in degree centrality can increase 0.569 rate in performance (B= 0.569, p [less than or equal to] 0.01). The effect coefficient of betweenness centrality showed that 1 unit increase in betweenness centrality can increase 0.272 rate in productivity (B= 0.272, p [less than or equal to] .01).

Discussion

Recently, various researchers applied the centrality as a measure for analyzing co-authorship networks (Mutschke, 2003; Yin et al. 2006; Liu et al. 2007). These researchers believe that the centrality is an effective indicator of scientific influence. In this study, the iMetrics researchers' co-authorship network was studied based on common centrality measures. The possible relationship between productivity and performance on one hand and centrality measures on the other hand were investigated, as well.

The findings showed that the average number of authors per paper was 2.23. In a similar vein, Egghe (2012) found that the average number of authors per paper in the Journal of Informetrics was 2.28. The one-author pattern (with 34.46%) was the most common approach to authoring in iMetrics. For example, as a famous top researcher, Vinkler is a researcher in the field who inclusively published his works under the one-author pattern. Two-author and three-author patterns were in subsequent ranks. A paper published in the Research Policy in 2011 entitled "The European university landscape: A micro characterization based on evidence from the Aquameth project" owned the highest number of authors (26 authors).

The results related to co-authorship centrality measures revealed that researchers such as "Glanzel", "Rousseau", "Leydosdorff", "Thelwall" and "Bornmann" were five top authors based on degree centrality. Such researchers with higher degree centrality have more opportunities and alternatives in comparison with others. This findings is largely in accordance with that of Erfanmanesh et al. (2012). Including the papers published in the Scientometrics, they found "Glanzel", "Schubert", "Rousseau", "Braun" and "Debackere" as top researchers based on degree centrality in scientometric studies.

Based on betweenness centrality measure, "Leydesdorff", "Rousseau", "Glanzel", "Ye" and "Zitt" were five top researchers. The high betweenness centrality gives the actor an opportunity to mediate the contacts among other actors. The actors who access other actors with a shortest path or ones accessible in a short path by other actors have appropriate position in the network. This structural advantage could be interpreted as "power" and ones with such posiotions in the network are more powerful researchers than others. In a research by Erfanmanesh et al. (2012), the higher betweenness centrality belonged to "Glanzel", "Rousseau", "Leydesdorff", "Meyer" and "Zitt", respectively. Moreover, Abrizrah et al. (2014) found "Glanzel", "Rousseau", "Leydesdorff", "Kretschmer" and "Liang" as authors with higher betweenness centrality, respectively.

Regarding the closeness centrality, "Leydesdorff", "Rousseau", "Glanzel", "Rafols" and "Ye" were among five top researchers. There are more connection between these authors and others and their connections are made with few mediators. As a result, the distribution and dissemination of information is speedy among them. Of these top researchers, "Rousseau" and "Glanzel" are among the five top researchers in the study by Erfanmanesh et al. (2012). They found "Glanzel", "Rousseau, "Meyer", "Debackere" and "Kretschmer" as five top researchers, respectively. The difference may be due to the sample studied in their research, i.e. the papers published in the Scientometrics.

After identifying prolific and highly-cited authors in iMetrics, regression analysis showed a significant relationship between productivity and performance. Therefore, it can be concluded that iMetrics researchers considered both quantity (the number of papers) as well as quality (the number of citations). In other words, the more the paper published by the researchers in the field of iMetrics, the more the citation their papers received. This finding is in line with that of Rumsey-Wairepo (2006) that found positive relation between productivity and performance. However, this finding is not accorded with that of Abrizah et al. (2014) that found that highly-productive authors are not necessarily highly-cited ones.

After measuring the indicators involved in social influence (degree, betweenness and closeness centralities), the relationship between these indicators (as independent variables) and the authors' productivity as well as performance (as a dependent variables) was investigated by applying a multivariate regression analysis. The results showed that there was a significantly positive relationship between degree centrality and betweenness centrality (as independent variables) on one hand and performance (as the dependent variable) on the other hand. This was so in the case of all three indicators (as independent variables) and productivity (as a dependent variable). Such relationships have been found in other studies, such as Glanzel and Schubert (2001), He, Geng and Campbell-Hunt (2009). Stringer (2009) found that researchers with higher centrality in a co-authorship network have better research performance (productivity and performance).

In addition, Borgman and Furner (2002) believe that higher rates of collaboration are usually associated with higher productivity. Egghe et al. (2007) gave three explanations for this reality: (a) authors involved in co-authored papers have more time to write additional papers since part of the work is done by the other co-authors; (b) collaboration could be higher between the better researchers, which then leads to higher production; and (c) collaboration is higher in fields with highly productive large research laboratories.

The relationship between co-authorship centralities and citation performance showed that higher centrality in the network results in higher citation absorption capacity. Yang and Ding (2009) and Li, Liao and Yen (2013) found that the more the betweenness centrality is, the more the citations an author receives. In a co-authorship network, the researcher with higher closeness centrality has speedy access to all researchers in the network and receives needed resources as soon and appropriate as possible. Appropriate access to resources can result in an increase in the quality of publications. As the high quality of publications can increase the number of received citations, it can be concluded that in a co-authorship network, researchers who are closer to other researchers (who have higher closeness centrality) can receive more citations.

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Ali Akbar Khasseh

Payame Noor University, khasseh@gmail.com

Faramarz Soheili

Payame Noor University, Iran, fsohieli@gmail.com

Afshin Mousavi Chelak

mousaviaf@gmail.com

Ali Akbar Khasseh (1); Faramarz Soheili (2); Afshin Mousavi Chelak (3)

(1.) Assistant Professor, Department of Library and Information Science, Payame Noor University; Tehran, Iran, khasseh@gmail.com (correspondence author)

(2.) Assistant Professor, Department of Library and Information Science, Payame Noor University; Tehran, Iran, F_soheili@pnu.ac.ir

(3.) Assistant Professor, Department of Library and Information Science, Payame Noor University; Tehran, Iran, mousaviaf@gmail.com Table 1. Distribution of iMetrics papers published in the studied journals Journal name No. of No. of No. of iMetrics papers articles articles (after applying citation and keyword filters) Keyword Citation filters filters Scientometrics 4003 3556 3556 JASIST 5194 3503 758 87 Journal of Informetrics 510 463 463 Research Policy 2680 2248 327 26 Research Evaluation 429 384 213 18 Journal of Information 1941 1434 146 28 Science Information Processing 2965 1968 145 43 and Management Journal of Documentation 2714 866 91 43 Total 20436 14422 5944 Table 2. 30 highly-productive authors in the iMetrics Rank Author Name #Papers Rank Author Name #Papers 1 Leydesdorff L 146 16 Tijssen RJW 39 2 Rousseau R 136 17 Ding Y 35 3 Glanzel W 134 18 Lewison G 35 4 Egghe L 134 19 Chen DZ 34 5 Thelwall M 113 20 Guan JC 34 6 Bornmann L 83 21 Vinkler P 34 7 Schubert A 81 22 Burrell QL 33 8 VanRaan AFJ 76 23 Cronin B 33 9 Moed HF 62 24 Gupta BM 33 10 Braun T 60 25 Bar-Ilan J 31 11 VanLeeuwen TN 58 26 Bordons M 31 12 Abramo G 50 27 Waltman L 31 13 D'Angelo CA 50 28 Lariviere V 30 14 Daniel HD 44 29 Kretschmer H 29 15 Huang MH 44 30 Small H 29 Table 3. The frequency of authorship patterns in iMetrics research Rank Authorship Frequency % Pattern 1 1-author 2048 34.45 2 2-author 1911 32.15 3 3-author 1170 19.68 4 4-author 487 8.19 5 5-author 203 3.42 6 6-author 62 1.05 7 7-author 26 0.44 8 8-author 16 0.27 9 9-author 12 0.2 10 10-author 5 0.08 11 Other 4 0.07 Total 5944 100 Table 4. iMetrics researchers' ranking based on the centrality measures Ranking by betweenness centrality Rank Researcher's Betweenness Name centrality 1 Leydesdorff 1166792 2 Rousseau 837081 3 Glanzel 409985 4 Ye FY 329995 5 Zitt 259213 6 Chen CM 246140 7 Thelwall 240091 8 Rafols I 222711 9 Park HW 219092 10 Kretschmer 197871 11 Chen DZ 189957 12 Aguillo 181172 13 Zhu DH 180924 14 Dina Y 179148 15 Lepori B 174288 16 Porter AL 170769 17 Zhang J 160646 18 Moed HF 154330 19 deMoya- 147512 20 Liang LM 140705 21 Li J 136029 22 Zuccala A 130648 23 vanLeeuwen 129590 24 Okubo Y 129311 25 Probst C 119397 26 Su XN 119215 2 Oppenheim C 118055 28 Meyer M 116494 29 ZHU J 113275 30 Bornmann 112952 Ranking by closeness centrality Rank Researcher's Closeness Name centrality 1 Leydesdorff 0.085788 2 Rousseau 0.085273 3 Rafols 0.0846535 4 Glanzel 0.0846444 5 Ye FY 0.084483 6 Kretschmer 0.084345 7 Egghe 0.084326 8 Meyer 0.084267 9 Bornmann 0.084259 10 deMoya-Anegon 0.084217 11 Liang 0.084067 12 Persson 0.084062 13 Jin 0.083929 14 Zuccala 0.08389 15 Zhou 0.083803 16 Wouters P 0.08376 17 Van den Besselaar 0.083751 18 Aguillo IF 0.083737 19 Chen CM 0.083679 20 Thelwall M 0.08362 21 Moed HF 0.083562 22 Cronin B 0.083524 23 Milojevic S 0.083486 24 Porter AL 0.083480 25 Thiis B 0.083404 26 Park HW 0.083382 2 vanLeeuwen 0.083374 28 Debackere K 0.083332 29 Guerrerobote VP 0.083312 30 Zhang J 0.083299 Ranking by Degree centrality Rank Researcher's Degree Name centrality 1 Glanzel 215 2 Rousseau 179 3 Thelwall 159 4 Leydesdorff 158 5 Bornmann 133 6 SCHUBERT 125 7 vanLeeuwen 123 8 Van Raan 121 9 Huang 116 10 Moed HF 110 11 Chen CM 109 12 Braun 102 13 Abramo 95 14 D'Angelo 95 15 Daniel 80 16 Ding Y 79 17 deMoya-Anegon 78 18 Debackere K 76 19 Gomez I 68 20 Lariviere V 66 21 Bordons M 62 22 Lepori B 62 23 Waltman L 61 24 Porter AL 60 25 van Eck NJ 59 26 Thiis B 58 2 Zhang J 57 28 Egghe 53 29 Sugimoto CR 53 30 Visser MS 49 Table 5. ANOVA for regression analysis of productivity and centrality measures Variation Sum of df Mean F p source squares square Regression 461.96 3 487.32 591.515 p [greater than or equal to] .01 * Residual 493.33 622 224.54 Total 954.01 625 Variation R 2R SE source Regression 0.86 0.74 7.364 Residual Total Table 6. The coefficients of prediction equation in the model of effect of the centrality indicators on productivity Model Co-efficient Std Error Beta (Standardized coefficients) Constant 7.198 7.198 1.371 Betweenn 0.0000512 0.000 0.256 Degree 0.447 0.018 0.692 closeness -82.406 18.948 -0.092 Model t P Constant 5.244 p [less than or equal to] .01 * Betweenn 9.463 p [less than or equal to] .01 * Degree 25.242 p [less than or equal to] .01 * closeness -4.349 p [less than or equal to] .01 * Table 7. ANOVA for regression analysis of performance and centrality measures Variation Sum of df Mean F p source squares square Regression 57800000 3 487.32 288.628 p [less than or equal to] .01 * Residual 41520000 622 224.54 Total 99320000 625 Variation R R2 SE source Regression 0.76 3 0.582 258.35 Residual Total Table 8. The coefficients of prediction equation in the model of effect of centrality indicators on performance Model Co-efficient Std Error Beta (Standardized coefficients) Constant 56.60 48.097 Betweennes 0.002 0.000 0.272 Degree 10.16 0.621 0.569 closeness 1251.251 664.79 0.051 Model t P Constant 1.177 p [less than or equal to] .01 * Betweennes 7.934 p [less than or equal to] .01 * Degree 16.357 p [less than or equal to] .01 * closeness 1.882 0.06