Social Science & Medicine 123 (2014) 90e95
Contents lists available at ScienceDirect
Social Science & Medicine journal homepage: www.elsevier.com/locate/socscimed
Social network analysis of public health programs to measure partnership Martin W. Schoen*, Sarah Moreland-Russell, Kim Prewitt, Bobbi J. Carothers Center for Public Health Systems Science, George Warren Brown School of Social Work, Washington University in Saint Louis, USA
a r t i c l e i n f o
a b s t r a c t
Article history: Received 7 July 2013 Received in revised form 30 August 2014 Accepted 29 October 2014 Available online 30 October 2014
In order to prevent chronic diseases, community-based programs are encouraged to take an ecological approach to public health promotion and involve many diverse partners. Little is known about measuring partnership in implementing public health strategies. We collected data from 23 Missouri communities in early 2012 that received funding from three separate programs to prevent obesity and/or reduce tobacco use. While all of these funding programs encourage partnership, only the Social Innovation for Missouri (SIM) program included a focus on building community capacity and enhancing collaboration. Social network analysis techniques were used to understand contact and collaboration networks in community organizations. Measurements of average degree, density, degree centralization, and betweenness centralization were calculated for each network. Because of the various sizes of the networks, we conducted comparative analyses with and without adjustment for network size. SIM programs had increased measurements of average degree for partner collaboration and larger networks. When controlling for network size, SIM groups had higher measures of network density and lower measures of degree centralization and betweenness centralization. SIM collaboration networks were more dense and less centralized, indicating increased partnership. The methods described in this paper can be used to compare partnership in community networks of various sizes. Further research is necessary to define causal mechanisms of partnership development and their relationship to public health outcomes. © 2014 Elsevier Ltd. All rights reserved.
Keywords: Social network analysis Obesity prevention Tobacco cessation Public health Collaboration Partnership Community research
1. Introduction Collaborative efforts among organizations with multiple programming and skill sets can result in higher levels of community impact (Kania and Kramer, 2011). An increasing number of public health initiatives use community-based approaches involving cross-sector partnerships (Roussos and Fawcett, 2000). Integrated efforts to address public health issues by involving multiple stakeholders are expected to result in better health outcomes than programs not using a network approach (Kwait et al., 2001). The rationale behind this is that no single organization has full control over all of the determinants of population health (Woulfe et al., 2010). By pooling resources, talents, and strategies, multiple sectors can more effectively carry out the responsibilities that affect the health of the targeted population (Martin et al., 2009).
* Corresponding author. Center for Public Health Systems Science, 700 Rosedale Avenue, Campus Box 1009, St. Louis, MO 63112-1408, USA. E-mail address: [email protected] (M.W. Schoen). http://dx.doi.org/10.1016/j.socscimed.2014.10.057 0277-9536/© 2014 Elsevier Ltd. All rights reserved.
While community-based health initiatives or collective action approaches are quite popular, there is a lack of substantive research on their effectiveness and impact (Roussos and Fawcett, 2000). A key reason for the shortage of evidence is that evaluating the structure and collaboration of coalitions or community partnerships is challenging (de Silva-Sanigorski et al., 2010a). These difficulties must be considered when evaluating collaborative efforts and further highlight the need for continued research on partnership formation using designs that measure activities, organizations, and social network development (Provan et al., 2003). Network analysis can measure partnership characteristics and can be used to predict collaboration and effectiveness in organizations (Honeycutt and Strong, 2011). Network metrics such as degree, density, and centralization can be used describe relationships among people and organizations and can reveal differences in communication and collaboration among coalitions (Scholz et al., 2008) and determine community capacity (Singer and Kegler, 2004). Social network methods are frequently performed on single networks at one time (Leischow et al., 2010) or over a period of time (Luque et al., 2011) to examine network characteristics. There are few examples of using whole networks as the unit of analysis
M.W. Schoen et al. / Social Science & Medicine 123 (2014) 90e95
(Fujimoto et al., 2009; Luke et al., 2010; Provan et al., 2007). When comparing multiple whole networks, network size has an inverse relationship with density and can have an effect on network characteristics such as average degree and centralization (Valente, 2010; Wasserman and Faust, 1994). Therefore, adjustment for network size can reveal additional relationships at the wholenetwork level. The purpose of this paper is to use social network analyses to measure partnership development and compare community networks of various sizes among different public health funding programs (Provan et al., 2004). 2. Methods The Missouri Foundation for Health (MFH) created the Social Innovation for Missouri (SIM) program in 2010 to address the public health goals of tobacco cessation and obesity prevention through the development of partnerships with key stakeholders in local municipalities, rural, and urban neighborhoods across Missouri (Goodman et al., 1998; Kendall et al., 2012). MFH funds several other community public health programs. Two of these programs, the Tobacco Prevention and Cessation Initiative (TPCI) and the Healthy and Active Communities Initiative (H&AC), focus on tobacco control and obesity prevention, respectively. SIM was distinct from these initiatives because of its goals of collaboration and the integration of tobacco and obesity strategies. It is not known
91
whether grant design can influence social structure and network characteristics in coalitions. These three funding programs by the same funder in similar communities across Missouri provide an opportunity to assess differences in partnership and community capacity in public health programs using network analysis (Provan et al., 2004). All seven Missouri organizations selected by MFH to receive funding as a part of the SIM Program were included, and TPCI and H&AC (two other MFH funded programs) were chosen as comparison programs. The comparison programs had singular aims of either tobacco control or obesity prevention, and did not include the specific goal of community capacity building and partnership development that was part of SIM. These organizations were geographically distributed around the state and included both rural and urban areas. The lead agencies for all 7 SIM, 12 TPCI and 11 H&AC programs were contacted; seven SIM, eight TPCI and eight H&AC networks elected to participate in the study. A map of Missouri counties and program locations is displayed in Fig. 1. To define the members of each network, we asked the lead agency in for each network in November 2011 to complete a partner identification form to identify individuals with whom they collaborate as a part of their public health program. Each lead agency was then contacted by telephone to review the partner form selections and verify the contact information of each individual partner. The lead agency was notified when each partner survey
Fig. 1. Partnership evaluation location of grantees.
92
M.W. Schoen et al. / Social Science & Medicine 123 (2014) 90e95
would be distributed via email and was asked to inform partners of the upcoming network survey. Individualized e-mails were sent to each identified partner with a recruitment statement and link to the web-based questionnaire system (Qualtrics, Provo UT) during JanuaryeFebruary 2012. Reminder e-mails were sent to participants who did not respond to the original e-mail. Those who did not complete the online survey after the second e-mail reminder were contacted via phone and encouraged to complete the survey. Participants were given 21 days to complete the online survey. This study was approved by the Washington University in St. Louis Institutional Review Board, ID# 201109220 and was funded by the Missouri Foundation for Health and the Corporation for National and Community Service Social Innovation Fund. The funding sources had no role in study design, collection, and analysis of data, nor in writing of articles or decision to submit for publication. 2.1. Questionnaire components We used network analytic methods to examine several key variables including frequency of contact and level of collaboration (Luke and Harris, 2007). Participants were presented with a roster of names of other individual partners in their network, and reported on key variables for each person. Participants were first asked how often they had direct contact with each of the other people in their network on a six-point scale: no contact, yearly, quarterly, monthly, weekly, and daily. A network tie was defined as monthly or more frequent contact. Respondents who selected ‘no contact’ for any partner were not asked further questions about that partner. Collaboration was assessed with a scale adapted from established network analytic methods (Harris et al., 2008). Participants were asked to select the response that best describes the current relationship with each of the people or organizations on the roster. Response options ranged from not linked (do not work together), communication (share information only), cooperation (work together informally to achieve common goals), collaboration (work together as a formal team with specific responsibilities e.g. an MOU or other formal agreement), and fully linked (work together as a formal team; mutually plan and share staff or resources to accomplish goals). A network tie was defined as cooperation or higher. Any partner or organization that was identified as ‘not linked’ was removed from further network questions. 2.2. Data analysis Network manipulation and description were performed with Pajek version 3.06. SPSS was used to for statistical description and analysis across whole networks. Due to the reciprocal nature of the relationships, all network links were symmetrized by using the higher score for each dyad, before applying threshold levels that define a network tie. When one participant in a dyad did not respond, the score for the available node was used. All partners decided by the lead agency were included, regardless of response. We also assessed network descriptors including average degree (the average number of links each node in the network has), density (the proportion of possible links in the network that actually exist), betweenness centralization (the extent to which a network is dependent on one or a few nodes to serve as connectors between nodes that are not otherwise connected) and degree centralization (the extent to which only a few nodes have a large number of ties). Because they influence how interventions are implemented, density, degree centralization and betweenness centralization have been identified as potentially the most informative network measures when examining public systems (Valente et al., 2007).
In order to determine whether the networks in the SIM program were structurally different from non-SIM (H&AC and TPCI) networks, a MANOVA was conducted comparing SIM and non-SIM networks on network size, average degree, density, betweenness centralization, and degree centralization. Separate analyses were conducted for the contact and collaboration relationships. Network size can affect measures of density and centralization (Wasserman and Faust, 1994). Larger social networks tend to be less dense; for example, the number of close school friends one has does not increase with the number of classmates past a certain point. Therefore, it was important to account of the effects of network size when comparing between networks of different size, similar to how others have adjusted for the effects of network density (Fujimoto et al., 2009). Therefore, MANCOVA analyses using network size as a covariate (holding network size constant) were also performed. Although using p* (exponential random graph) models is likely a more rigorous method to compare model parameters (Gould, 1993; Harris et al., 2012), many of the networks examined here were too small and sparse for such models to converge, and no easily comprehensible analogs to betweenness and degree centralization exist for those modeling techniques.
3. Results Four hundred and five people were contacted to participate in the network assessment in 23 community groups among 3 different funding programs. Overall, there was an 83% response rate, with each average response rates of 81% for SIM, 85% for H&AC, and 85% for TPCI grantees (p ¼ ns). Characteristics of each of the funding groups are displayed in Table 1. Visual depiction of the variety of networks analyzed is available in Fig. 2. Means and standard deviations for network size, average degree, network density, betweenness centralization, and degree centralization for both the contact and collaboration relationships are reported in Table 2 for SIM and non-SIM networks. Adjustment for network size (holding network size constant) had the effect of decreasing the average degree, betweenness centralization, and degree centralization statistics while increasing the network density for the SIM networks and had the opposite effect on non-SIM networks. Significance testing of the non-adjusted and size adjusted SIM and non-SIM networks is available in Table 3.
Table 1 Grantee characteristics.
Number of networks Size of community served by each grantee (average, range) Duration of programs (yrs) Funding per year (average, range) % Rurala # of people (nodes) per network (average, range) # of organizations per network (average, range) Response rate (%) a
SIM
H&AC
TPCI
7 58,999 (4131e159,498)
8 79,021 (7139e319,294)
8 98,951 (4131e255,357)
3
3
2
$198,777 (105,367e242,664) 43 22.4 (14e28)
$95,150 (74,354e100,00) 50 16.5 (8e27)
$66,405 (16,607e99,938) 75 14.5 (7e21)
12.6 (5e20)
12.5 (6e21)
10.5 (3e17)
81
85
85
Rural/urban classification based on RUCC (Rural-Urban Continuum Codes) if grantee serves an entire county, or RUCA (Rural-Urban Commuting Areas) if grantee serves a city or if county code would not apply.
M.W. Schoen et al. / Social Science & Medicine 123 (2014) 90e95
93
Fig. 2. Example large and small networks from public health programs.
3.1. Contact On average, SIM contact networks were larger and had a higher average degree than non-SIM networks when not controlling for size. When controlling for size, there were no significant differences between SIM and non-SIM networks in other network characteristics. Effect sizes for average degree and density were moderate however, both of which were higher for SIM than nonSIM networks (Table 2, adjusted means). For the contact relationship, the multivariate F for comparing SIM and non-SIM networks not adjusting for network size was nonsignificant, Roy's Largest Root ¼ 0.69, F (5, 17) ¼ 2.36, p ¼ 0.08, h2p ¼ 0.410. The multivariate F when adjusting for network size was also non-significant, Roy's Largest Root ¼ 0.39, F (4, 17) ¼ 1.64, p ¼ 0.21, h2p ¼ 0.278. Given the large effect sizes and low levels of observed power (0.60 and 0.40, respectively) due to a small sample size (n ¼ 23), univariate effects were still examined, and are reported in Table 3.
Table 3 MANOVA and MANCOVA results comparing SIM and Non-SIM networks. Variable
Non-adjusted
Contact Size 4.69 Average degree 6.99 Network density 0.01 Betweenness centralization 0.07 Degree centralization 0.38 Collaboration Size 4.69 Average degree 12.89 Network density 0.16 Betweenness centralization 0.92 Degree centralization 0.20
Size-adjusted h2p
F (1, 20) p
h2p
Contents lists available at ScienceDirect
Social Science & Medicine journal homepage: www.elsevier.com/locate/socscimed
Social network analysis of public health programs to measure partnership Martin W. Schoen*, Sarah Moreland-Russell, Kim Prewitt, Bobbi J. Carothers Center for Public Health Systems Science, George Warren Brown School of Social Work, Washington University in Saint Louis, USA
a r t i c l e i n f o
a b s t r a c t
Article history: Received 7 July 2013 Received in revised form 30 August 2014 Accepted 29 October 2014 Available online 30 October 2014
In order to prevent chronic diseases, community-based programs are encouraged to take an ecological approach to public health promotion and involve many diverse partners. Little is known about measuring partnership in implementing public health strategies. We collected data from 23 Missouri communities in early 2012 that received funding from three separate programs to prevent obesity and/or reduce tobacco use. While all of these funding programs encourage partnership, only the Social Innovation for Missouri (SIM) program included a focus on building community capacity and enhancing collaboration. Social network analysis techniques were used to understand contact and collaboration networks in community organizations. Measurements of average degree, density, degree centralization, and betweenness centralization were calculated for each network. Because of the various sizes of the networks, we conducted comparative analyses with and without adjustment for network size. SIM programs had increased measurements of average degree for partner collaboration and larger networks. When controlling for network size, SIM groups had higher measures of network density and lower measures of degree centralization and betweenness centralization. SIM collaboration networks were more dense and less centralized, indicating increased partnership. The methods described in this paper can be used to compare partnership in community networks of various sizes. Further research is necessary to define causal mechanisms of partnership development and their relationship to public health outcomes. © 2014 Elsevier Ltd. All rights reserved.
Keywords: Social network analysis Obesity prevention Tobacco cessation Public health Collaboration Partnership Community research
1. Introduction Collaborative efforts among organizations with multiple programming and skill sets can result in higher levels of community impact (Kania and Kramer, 2011). An increasing number of public health initiatives use community-based approaches involving cross-sector partnerships (Roussos and Fawcett, 2000). Integrated efforts to address public health issues by involving multiple stakeholders are expected to result in better health outcomes than programs not using a network approach (Kwait et al., 2001). The rationale behind this is that no single organization has full control over all of the determinants of population health (Woulfe et al., 2010). By pooling resources, talents, and strategies, multiple sectors can more effectively carry out the responsibilities that affect the health of the targeted population (Martin et al., 2009).
* Corresponding author. Center for Public Health Systems Science, 700 Rosedale Avenue, Campus Box 1009, St. Louis, MO 63112-1408, USA. E-mail address: [email protected] (M.W. Schoen). http://dx.doi.org/10.1016/j.socscimed.2014.10.057 0277-9536/© 2014 Elsevier Ltd. All rights reserved.
While community-based health initiatives or collective action approaches are quite popular, there is a lack of substantive research on their effectiveness and impact (Roussos and Fawcett, 2000). A key reason for the shortage of evidence is that evaluating the structure and collaboration of coalitions or community partnerships is challenging (de Silva-Sanigorski et al., 2010a). These difficulties must be considered when evaluating collaborative efforts and further highlight the need for continued research on partnership formation using designs that measure activities, organizations, and social network development (Provan et al., 2003). Network analysis can measure partnership characteristics and can be used to predict collaboration and effectiveness in organizations (Honeycutt and Strong, 2011). Network metrics such as degree, density, and centralization can be used describe relationships among people and organizations and can reveal differences in communication and collaboration among coalitions (Scholz et al., 2008) and determine community capacity (Singer and Kegler, 2004). Social network methods are frequently performed on single networks at one time (Leischow et al., 2010) or over a period of time (Luque et al., 2011) to examine network characteristics. There are few examples of using whole networks as the unit of analysis
M.W. Schoen et al. / Social Science & Medicine 123 (2014) 90e95
(Fujimoto et al., 2009; Luke et al., 2010; Provan et al., 2007). When comparing multiple whole networks, network size has an inverse relationship with density and can have an effect on network characteristics such as average degree and centralization (Valente, 2010; Wasserman and Faust, 1994). Therefore, adjustment for network size can reveal additional relationships at the wholenetwork level. The purpose of this paper is to use social network analyses to measure partnership development and compare community networks of various sizes among different public health funding programs (Provan et al., 2004). 2. Methods The Missouri Foundation for Health (MFH) created the Social Innovation for Missouri (SIM) program in 2010 to address the public health goals of tobacco cessation and obesity prevention through the development of partnerships with key stakeholders in local municipalities, rural, and urban neighborhoods across Missouri (Goodman et al., 1998; Kendall et al., 2012). MFH funds several other community public health programs. Two of these programs, the Tobacco Prevention and Cessation Initiative (TPCI) and the Healthy and Active Communities Initiative (H&AC), focus on tobacco control and obesity prevention, respectively. SIM was distinct from these initiatives because of its goals of collaboration and the integration of tobacco and obesity strategies. It is not known
91
whether grant design can influence social structure and network characteristics in coalitions. These three funding programs by the same funder in similar communities across Missouri provide an opportunity to assess differences in partnership and community capacity in public health programs using network analysis (Provan et al., 2004). All seven Missouri organizations selected by MFH to receive funding as a part of the SIM Program were included, and TPCI and H&AC (two other MFH funded programs) were chosen as comparison programs. The comparison programs had singular aims of either tobacco control or obesity prevention, and did not include the specific goal of community capacity building and partnership development that was part of SIM. These organizations were geographically distributed around the state and included both rural and urban areas. The lead agencies for all 7 SIM, 12 TPCI and 11 H&AC programs were contacted; seven SIM, eight TPCI and eight H&AC networks elected to participate in the study. A map of Missouri counties and program locations is displayed in Fig. 1. To define the members of each network, we asked the lead agency in for each network in November 2011 to complete a partner identification form to identify individuals with whom they collaborate as a part of their public health program. Each lead agency was then contacted by telephone to review the partner form selections and verify the contact information of each individual partner. The lead agency was notified when each partner survey
Fig. 1. Partnership evaluation location of grantees.
92
M.W. Schoen et al. / Social Science & Medicine 123 (2014) 90e95
would be distributed via email and was asked to inform partners of the upcoming network survey. Individualized e-mails were sent to each identified partner with a recruitment statement and link to the web-based questionnaire system (Qualtrics, Provo UT) during JanuaryeFebruary 2012. Reminder e-mails were sent to participants who did not respond to the original e-mail. Those who did not complete the online survey after the second e-mail reminder were contacted via phone and encouraged to complete the survey. Participants were given 21 days to complete the online survey. This study was approved by the Washington University in St. Louis Institutional Review Board, ID# 201109220 and was funded by the Missouri Foundation for Health and the Corporation for National and Community Service Social Innovation Fund. The funding sources had no role in study design, collection, and analysis of data, nor in writing of articles or decision to submit for publication. 2.1. Questionnaire components We used network analytic methods to examine several key variables including frequency of contact and level of collaboration (Luke and Harris, 2007). Participants were presented with a roster of names of other individual partners in their network, and reported on key variables for each person. Participants were first asked how often they had direct contact with each of the other people in their network on a six-point scale: no contact, yearly, quarterly, monthly, weekly, and daily. A network tie was defined as monthly or more frequent contact. Respondents who selected ‘no contact’ for any partner were not asked further questions about that partner. Collaboration was assessed with a scale adapted from established network analytic methods (Harris et al., 2008). Participants were asked to select the response that best describes the current relationship with each of the people or organizations on the roster. Response options ranged from not linked (do not work together), communication (share information only), cooperation (work together informally to achieve common goals), collaboration (work together as a formal team with specific responsibilities e.g. an MOU or other formal agreement), and fully linked (work together as a formal team; mutually plan and share staff or resources to accomplish goals). A network tie was defined as cooperation or higher. Any partner or organization that was identified as ‘not linked’ was removed from further network questions. 2.2. Data analysis Network manipulation and description were performed with Pajek version 3.06. SPSS was used to for statistical description and analysis across whole networks. Due to the reciprocal nature of the relationships, all network links were symmetrized by using the higher score for each dyad, before applying threshold levels that define a network tie. When one participant in a dyad did not respond, the score for the available node was used. All partners decided by the lead agency were included, regardless of response. We also assessed network descriptors including average degree (the average number of links each node in the network has), density (the proportion of possible links in the network that actually exist), betweenness centralization (the extent to which a network is dependent on one or a few nodes to serve as connectors between nodes that are not otherwise connected) and degree centralization (the extent to which only a few nodes have a large number of ties). Because they influence how interventions are implemented, density, degree centralization and betweenness centralization have been identified as potentially the most informative network measures when examining public systems (Valente et al., 2007).
In order to determine whether the networks in the SIM program were structurally different from non-SIM (H&AC and TPCI) networks, a MANOVA was conducted comparing SIM and non-SIM networks on network size, average degree, density, betweenness centralization, and degree centralization. Separate analyses were conducted for the contact and collaboration relationships. Network size can affect measures of density and centralization (Wasserman and Faust, 1994). Larger social networks tend to be less dense; for example, the number of close school friends one has does not increase with the number of classmates past a certain point. Therefore, it was important to account of the effects of network size when comparing between networks of different size, similar to how others have adjusted for the effects of network density (Fujimoto et al., 2009). Therefore, MANCOVA analyses using network size as a covariate (holding network size constant) were also performed. Although using p* (exponential random graph) models is likely a more rigorous method to compare model parameters (Gould, 1993; Harris et al., 2012), many of the networks examined here were too small and sparse for such models to converge, and no easily comprehensible analogs to betweenness and degree centralization exist for those modeling techniques.
3. Results Four hundred and five people were contacted to participate in the network assessment in 23 community groups among 3 different funding programs. Overall, there was an 83% response rate, with each average response rates of 81% for SIM, 85% for H&AC, and 85% for TPCI grantees (p ¼ ns). Characteristics of each of the funding groups are displayed in Table 1. Visual depiction of the variety of networks analyzed is available in Fig. 2. Means and standard deviations for network size, average degree, network density, betweenness centralization, and degree centralization for both the contact and collaboration relationships are reported in Table 2 for SIM and non-SIM networks. Adjustment for network size (holding network size constant) had the effect of decreasing the average degree, betweenness centralization, and degree centralization statistics while increasing the network density for the SIM networks and had the opposite effect on non-SIM networks. Significance testing of the non-adjusted and size adjusted SIM and non-SIM networks is available in Table 3.
Table 1 Grantee characteristics.
Number of networks Size of community served by each grantee (average, range) Duration of programs (yrs) Funding per year (average, range) % Rurala # of people (nodes) per network (average, range) # of organizations per network (average, range) Response rate (%) a
SIM
H&AC
TPCI
7 58,999 (4131e159,498)
8 79,021 (7139e319,294)
8 98,951 (4131e255,357)
3
3
2
$198,777 (105,367e242,664) 43 22.4 (14e28)
$95,150 (74,354e100,00) 50 16.5 (8e27)
$66,405 (16,607e99,938) 75 14.5 (7e21)
12.6 (5e20)
12.5 (6e21)
10.5 (3e17)
81
85
85
Rural/urban classification based on RUCC (Rural-Urban Continuum Codes) if grantee serves an entire county, or RUCA (Rural-Urban Commuting Areas) if grantee serves a city or if county code would not apply.
M.W. Schoen et al. / Social Science & Medicine 123 (2014) 90e95
93
Fig. 2. Example large and small networks from public health programs.
3.1. Contact On average, SIM contact networks were larger and had a higher average degree than non-SIM networks when not controlling for size. When controlling for size, there were no significant differences between SIM and non-SIM networks in other network characteristics. Effect sizes for average degree and density were moderate however, both of which were higher for SIM than nonSIM networks (Table 2, adjusted means). For the contact relationship, the multivariate F for comparing SIM and non-SIM networks not adjusting for network size was nonsignificant, Roy's Largest Root ¼ 0.69, F (5, 17) ¼ 2.36, p ¼ 0.08, h2p ¼ 0.410. The multivariate F when adjusting for network size was also non-significant, Roy's Largest Root ¼ 0.39, F (4, 17) ¼ 1.64, p ¼ 0.21, h2p ¼ 0.278. Given the large effect sizes and low levels of observed power (0.60 and 0.40, respectively) due to a small sample size (n ¼ 23), univariate effects were still examined, and are reported in Table 3.
Table 3 MANOVA and MANCOVA results comparing SIM and Non-SIM networks. Variable
Non-adjusted
Contact Size 4.69 Average degree 6.99 Network density 0.01 Betweenness centralization 0.07 Degree centralization 0.38 Collaboration Size 4.69 Average degree 12.89 Network density 0.16 Betweenness centralization 0.92 Degree centralization 0.20
Size-adjusted h2p
F (1, 20) p
h2p
