T Test, Anova & Regression Analysis of Node level Network Data

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1 T Test, Anova & Regression Analysis of Node level Network Data Definition: Node level T Test, Anova and regression analysis allow us to test whether the aggregated number of ties each individual has is associated with other variables. For example, does the hierarchical level or gender of an individual predict how many of their colleagues they seek for advice? It is also possible to see if the number of ties an individual has is associated with their level of performance. Note that this type of analysis uses total or aggregated ties as opposed to examining each tie individually (see the dyadlevel analysis handout for this option). Implications: Knowing the association between individual characteristics such as location or hierarchical level and advice seeking or other network behaviors helps managers develop the networks of their staff. For example, research suggests being higher in the hierarchy predicts being sought for advice but not necessarily advice seeking. Analysis: Standard T test, Anova and linear regression analysis are not appropriate for node level data because the aggregated measures for each node (i.e., people surveyed) are not independent of one another. This contravenes one of the basic assumptions of linear regression analysis. Therefore, we use a permutation test to generate the significance level, which accounts for the non independence of the cases. Node level analysis is different from tie level analysis. In node level analysis, we aggregate the number of ties each individual, rather than looking at each tie. For example, we can examine if being at a certain hierarchical level predicts the total number of ties an individual has. In the tie level analysis, using the quadratic assignment procedure (QAP), we are examining what predicts a tie between two nodes (individuals).

2 T Test Analysis Node level T Test analysis in UCINET In this analysis, we are going to examine whether men or women have more advice seeking (information) ties. Advice seeking are the outgoing ties from an individual. A T Test allows us to examine whether a binary variable (e.g., gender) is associated with a continuous variable (e.g., number of advice seeking ties). Please note that it is not possible to use a T Test to analyze a categorical variable of more than two categories. For that we need to conduct an Anova test. Creating the advice seeking and gender node level data files. Step 1. Load the information network into UCINET and call it info. Dichotomize your info network: Transform > dichotomize. Then select the info network and dichotomize at greater than or equal to 4. Step 2. Run the degree centrality routine: Network > Centrality and Power > Degree. Then in the input network box type info_ge_4 or click and select the info_ge_4 network. In the output file, which is called info_ge_4 deg, the advice seeking variable is column 1. Step 3. Load the attribute network into UCINET and call it attrib. The gender variable is column 2 in the attrib file. The variable is coded 0 for men and 1 for women. Running a T Test in UCINET Step 1. To run a T Test: Tools > Testing Hypotheses > Node level > T Test. Step 2. In the dependent variable box, select the info_ge_4 deg file. First, we will test for advice seeking ties, therefore select col 1. Step 3. In the independent variable box, select attrib, We are testing for gender, which is col 2. Then press ok. We could rerun this analysis using column 2 of our info_ge_4 deg file. This would allow us to see if there were a difference in being sought out for advice with regard to gender. The analysis could also be rerun with the other binary variable in the attribute file: Region.

3 T Test Analysis In our output file, Group 1 is men and Group 2 is women. The N of Obs indicates that there are 35 men and 11 women. The mean number of advice seeking ties for men is 4.143, and for women it is The significance test at the bottom of the output file indicates that the difference in means is Men on average seek advice from more people than women. The standard statistical decision point for significance is a two tailed test of below In our output, the two tailed significance is , and therefore not below 0.5. This suggests that while men on average seek advice more than women, the difference is not statistically significant.

4 Anova Analysis Node level Anova in UCINET In this analysis, we are going to examine whether being in a certain practice is associated with having more advice seeking (information) ties. The practice variable is categorical and an individual can be in one of seven practices. An Anova test allows us to examine whether a categorical variable (e.g., practice) is associated with a continuous variable (e.g., number of advice seeking ties). Running an Anova in UCINET Step 1. To run an Anova test: Tools > Testing Hypotheses > Node level > Anova. Step 2. In the dependent variable box, select the info_ge_4 deg file. First, we will test for advice seeking ties; therefore, select col 1. Step 3. In the independent variable box. select attrib. We are testing for practice, which is col 3. Then press ok. The standard statistical decision point for significance is a significance test of below In our output the significance is , and therefore is below 0.5. This suggests that people in some practices seek advice more than people in other practices. However, we cannot tell from the output which practices are different from each other. The analysis could also be rerun with the other categorical variables in the attribute file: Location and Hierarchy.

5 Regression Analysis Node level regression analysis in UCINET In this analysis, we are going to examine whether gender, hierarchy, region and number of friendship ties are associated with having more advice seeking (information) ties. Adviceseeking ties are the outgoing ties from an individual. A regression analysis allows us to estimate whether various different variables are associated with advice seeking. This is different from the T Test and Anova analysis which only allowed us to examine if one variable was associated with advice seeking. Creating the friendship, gender, hierarchy and region node level file. To do the regression analysis we need two different files. First, we need a file that includes our outgoing friendship ties, gender, hierarchy and region data. Second, we need a file for advice seeking. We can use the info_ge_4 deg file that we created earlier for advice seeking (column 1). Step 1. Open the attrib file using the Excel matrix editor in UCINET and delete the columns for practice and location. Save the file using the save active sheet as UCINET dataset command and call it indep variables. Step 2. Load the friendship network into UCINET and call it friend. Dichotomize your friend network. Transform > dichotomize. Then select the friend network and dichotomize at greater than or equal to 4. Step 3. Run the degree centrality routine: Network > Centrality and Power > Degree. Then in the input network box type friend_ge_4 or click and select the friend_ge_4 network. In the output file, which is called friend_ge_4 deg, the outgoing friendship variable is column 1. Step 4. Open the friend_ge_4 deg file using the Excel matrix editor in UCINET. Copy the first column of data. Then open the indep_variables file in the Excel matrix editor. Paste the data into the file. Name the column header friend, then save the file. Running a regression analysis in UCINET Step 1. To run a node level regression: Tools > Testing Hypotheses > Node level > Regression. Step 2. In the dependent dataset box, select the info_ge_4 deg file. First, we will test for advice seeking ties; therefore, the dependent column # should be set to 1. Step 3. In the independent dataset box, select f. The independent column #s should be set to all. Then press ok. We could rerun this analysis using column 2 of our info_ge_4 deg file. This would allow us to see if there were a different result with regard to being sought out for advice.

6 Regression Analysis At the top of the output file is the correlation matrix detailing the correlation coefficients between each pair of variables. Notice that the correlation between outdegree (which is our advice seeking variable) and friend is relatively high, with a coefficient of Under model fit, the first thing to notice is the Adjusted R square value, which is This suggests that our model accounts for 64.8% of the variance in the advice seeking network. This is also a relatively high value. The next thing to examine is the regression coefficients table. The proportion as large column works in a similar way to the significance tests in the earlier analysis. Any value under 0.05 indicates that an independent variable is significant. In this output, only friend is significant, with The unstandardized coefficient is positive ( ), indicating that the number of friendship ties a person has positively predicts the number of advice seeking ties they will have.

7 Bibliography Methodological papers and books: Borgatti, S. P., Everett, M. G., & Johnson, J. C Analyzing social networks. Los Angeles, CA: Sage. Freeman, L. C Centrality in social networks conceptual clarification. Social Networks, 1(3), Hanneman, R. A., & Riddle, M Introduction to social network methods. University of California, Riverside. Published in digital form at Scott, J Social network analysis. London: Sage. Wasserman, S., & Faust, K Social network analysis: Methods and applications. Cambridge, United Kingdom: Cambridge University Press. Empirical papers and review papers: Brass, D. J., Galaskiewicz, J., Greve, H. R., & Tsai, W Taking stock of networks and organizations: A multilevel perspective. Academy of Management Journal, 47(6), Cross, R., & Cummings, J. N Tie and network correlates of individual performance in knowledge intensive work. Academy of Management Journal, 47(6), Kilduff, M., & Brass, D. J Organizational social network research: Core ideas and key debates. The Academy of Management Annals, 4(1), Klein, K. J., Lim, B. C., Saltz, J. L., & Mayer, D. M How do they get there? An examination of the antecedents of centrality in team networks. Academy of Management Journal, 47(6), Mehra, A., Kilduff, M., & Brass, D. J The social networks of high and low self monitors: Implications for workplace performance. Administrative Science Quarterly, 46(1), Sparrowe, R. T., Liden, R. C., Wayne, S. J., & Kraimer, M. L Social networks and the performance of individuals and groups. Academy of Management Journal, 44(2), Andrew Parker, PhD, is a visiting professor at the University of Kentucky. He has conducted network analysis in over 100 multinational organizations and government agencies. He was a Senior Consultant at IBM s Institute for Knowledge Management and a research fellow at the Network Roundtable at the University of Virginia as well as an advisor to the Knowledge and Innovation Network at Warwick Business School. His research has appeared in Science, Organization Studies, Journal of Applied Psychology, Journal of Applied Behavioral Science, Social Networks, Management Communication Quarterly, Sloan Management Review, Organizational Dynamics and California Management Review. He is also the co author of The Hidden Power of Social Networks. He received his PhD from Stanford University.