Appendices
Question 1: “Please rate the following tasks according to what you spend most of your time on
1 should represent the most”
Surveys were sent to all women in the months January, February, March 2016 40/55 replies Survey: CFO work responsibilities
Question 2: “Please rate the following tasks according to what you consider the most important for a CFO. 1 should represent the task you consider most important”
Surveys were sent to all women in the months January, February, March 2016 40/55 replies
Appendix B2: Questions 3 and 4 Survey: Evidence of Homophily
“Do you know any of the following women?”
Surveys were sent to all women in the months January, February, March 2016 33 Replies
Survey: Evidence of Homophily
“Do you discuss important matters with any of the following women?”
Surveys were sent to all women in the months January, February, March 2016 24 Replies
Appendix C: Optimal Matching Explained
Optimal matching provides the researcher with a tool to explore similarities in the data by calculating distances between sequences. Consider the following five simple hypothetical career sequences A, B, C, D and E:
Years
Sequences 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19
A bs bs bs bs 1 1 2 2 2 2 3 3 4 4 4 4 4 5 5
B 1 1 1 1 2 2 2 2 3 3 3 3 3 3 5 5 5
C bs bs 1 1 1 1 1 2 2 2 3 3 3
D bs bs bs bs 1 2 2 2 2 2 2 3 3 4 4 5 5 5 5
E 1 1 1 1 1 1 1 2 2 4 4 4 4 4
Hypothetical example of 5 women’s careers (A, B, C, D, E) with the alphabet or career categories: business school (bs), first-entry level position (1) following occupational hierarchy: position level 2, 3, 4 and 5 observed over 19 years.
It is clear that the careers develop in an upward-looking manner, they all move through clear hierarchical position levels ranging from 1 to 5. Each entry represents one year which means Woman A’s career or sequence is observed over 19 years with 19 events and Woman B 17 years.
Subject A, C, D begin their sequences in business school (bs) while B and E start their career at position level 1. Subject B and E stand out, because they both skip certain position levels. Subject B advances after 14 years from level 3 to 5, while subject E advances after 10 years from level 2 to 4. Consider again the first two sequences from the above table:
Woman A bs bs bs bs 1 1 2 2 2 2 3 3 4 4 4 4 4 5 5 Women B 1 1 1 1 2 2 2 2 3 3 3 3 3 3 5 5 5
By first look, it is difficult to conclude what career looks more similar to what career. In the following let “–“ indicate a match that is costless, “I” stands for insertion costs and “S” for substitution costs, while “D” represents deletion.
D D D D I I S S S S Woman A bs bs bs bs 1 1 2 2 2 2 3 3 4 4 4 4 5 5
- - - - - -
5 - 5
Women B 1 1 1 1 2 2 2 2 3 3 3 3 3 3
In the above example it costs 11 to turn A into B; four deletions, two insertions and 5
substitutions = 11. It is also clear that where insertion costs have been used, it would have been just as correct to delete the entries to turn the two sequences into each other. Which is why insertion and deletion costs are often combined and referred to as “indels”. In this example I moved the sequence two events to the right by inserting to “1”’s, this also makes the two sequences of same lengths. By inserting these two, it was possible to match many of the
following events. Using optimal matching, the researcher can decide to assign the same costs to all transitions like in the above example, where each transition regardless of the tool used had a cost of 1. Usually such approach only leads to satisfying results under very restrictive empirical conditions (Blanchard 2011:10) and is only used here in order to exemplify. Go to chapter 7.3.
for costs estimates and considerations for this particular study.
Relaxing the importance of sequence length
With optimal matching the researcher have the ability to relax the importance of the lengths of sequences or at least its weigh in the analysis by changing the value of insertion and deletion costs (Abbott 1999, Blair-Loy 1999). Consider again the simple example of the two hypothetical women from before
Woman A bs bs bs bs 1 1 2 2 2 2 3 3 4 4 4 4 4 5 5 Women B 1 1 1 1 2 2 2 2 3 3 3 3 3 3 5 5 5
For simplification purposes I sat the costs of both substitution and deletion and insertion costs to 1 in the previous example, and ended up with a final costs of 11 for transforming sequence A into B. If I choose to set deletion and insertion costs to half of substitution costs, I get other results. Practically this means insertion or deletion will in this example cost 0.5 while substituting events costs 1. Consider the following example again but now with different costs:
D D D D I I S S S S
Woman A bs bs bs bs 1 1 2 2 2 2 3 3 4 4 4 4 5 5 Costs 0.5 0.5 0.5 0.5 - - 0.5 0.5 - - - 1 1 1 1 -
5 - 5
Women B 1 1 1 1 2 2 2 2 3 3 3 3 3 3
Setting the deletion and insertion costs differently than the substitution costs gives a final cost of:
= 4∗ 0.5 +2∗ 0.5 +4∗ 1 = 7
If sequences are of equal length, and indels are set to any cost greater than half the largest substitutions, then indels will never be used since it will take two indels to replace a substitution.
But if the sequences are of unequal length, then the size of such indels costs can help prevent the algorithm from using any more indels than needed to offset the difference in length (Blair-Loy 1999, Abbott 2000, Blanchard 2011).
Appendix D: Optimal Matching Distance Matrix Optimal Matching Distance Matrix
Total Sample
The Optimal Matching algorithm calculates distances between all women based on the determined substitution and indel costs. Go to 7.3. for further explanations.
The Distance Matrix illustrates the distances with values form 0 to 2.
Appendix E: Optimal Matching Frequency Plots Optimal Matching Total Sample Frequency Plots
Variables: Position levels, Organisation size and industry type
Optimal Matching applied to sample in R. Total sample 47.
Organisation Sizes: Small-medium (M), Large (L), Very Large V
Industry Type: Finance & Conglomeerates (FC), Trade & Services (TS), Pharmaceuticals (PH), Industry, Energy and Construction (IEC)
Position Levels: business school (bs), non-finance position (nf), 1, 2, 3, 4, 5, 6, 7.
Go to 7.2 for further explanation
Appendix F: Optimal Matching Position Level Index Plot Optimal Matching Total Sample
Index Plot Position Levels
Optimal Matching applied to sample in R. Total sample 47.
Ordered by sequence length
Position Levels: business school (bs), non-finance position (nf), 1, 2, 3, 4, 5 (CFO), 6 (CEO), 7. Go to 7.2 for further explanations
Appendix G: Optimal Matching Organisation Size Index Plot Optimal Matching Total Sample
Index Plot Organisation Size
Optimal Matching applied to sample in R. Total sample 47.
Ordered by sequence length
Organisation Sizes: Small-medium (M), Large (L), Very Large (V) Go to 7.2 for further explanations
Appendix H: Optimal Matching Industry Type Index Plot Optimal Matching Total Sample
Index Plot Industry Type
Optimal Matching applied to sample in R. Total sample 47.
Ordered by sequence length
Industry Type: Finance & Conglomeerates (FC), Trade & Services (TS), Pharmaceuticals (PH), Industry, Energy and Construction (IEC)
Go to 7.2 for further explanations
Appendix I: Cluster Analysis Position Levels Frequency Plots