Wednesday, March 19, 2014

Morris Number - Further Research (Morris Number 07) (PhD Ideas 06)


SOME PhD IDEAS RELATED TO THE MORRIS NUMBER

Graduate students in labor economics, sociology, political science, history, statistics and womens' studies who are looking for a research topic might want to explore Morris Numbers. Obtaining the data could, of course, be daunting.

Government agencies (see questions 10-12 below), may make public the salaries of their employees. For other kinds of public employers, some compensation data may be public by statute. The civil service, and some companies, also have a system of grades: entry level jobs are in a low grade, management jobs are higher. Among private employers, those with a genuine desire to improve their diversity might be willing to provide researchers with information about their workforce, including an organizational chart and title, grade or salary, and gender. If data is impossible to come by, then these ideas are for thought experiments and discussion.

1. Compare Morris Numbers for different industries.

2. Compare Morris Numbers for different regions of the country.

3. Compare the OMNs for employers with 100 or fewer employees to those with 1000 or more.

4. Tech companies young and old: Collect data to evaluate the two true/false statements in Morris Number 05.

5. Find businesses willing to participate in the study. This would not, of course, be a random sample but it would be a place to start. Graph the Morris Numbers as a function of number of employees, median salary, assets, annual budget, stock price, population of city in which the main office is located, etc. Which factors, if any, have a relationship, direct or inverse, with the Morris Number?

Note: The Morris Numbers, ordinary and weighted, do not factor in the size of the company at all. The underlying assumption is that the ordinary Morris Number of any company with more than 10 employees ought to be in the single-digits; size is no excuse either way. But once there is a body of data on Morris Numbers, PhD candidates and other researchers could investigate whether size is now, or ever was, a good predictor of Morris Number.

6. Find a variety of organizations willing to participate: corporations, partnerships, family-owned and employee-owned businesses, universities, colleges, private schools, foundations, government agencies, non-profits concerned with health, religion, social welfare, etc., etc., etc. As with question 5, you will not have a random sample if you use willing participants, just a place to start. Does the Morris Number predict whether the employer is for-profit or not? If for-profit, are the Morris Numbers on average different for private corporations v. public? Among privately-owned entities, are there any striking differences among the Morris Numbers (the median? the spread?) for sole proprietorships, partnerships, closely-held corporations, or employee-owned businesses? If non-profit, does the purpose of the organization make a difference to the Morris Numbers?

7. Have Morris Numbers declined over the last decade? The last 30 years? What events or conditions have accompanied sharp declines, plateaus, or even increases in Morris Numbers?

8. In 2013, what was the median Morris Number for the Fortune 500, the Ivy League universities, the executive branches of state governments?

9. Track the Morris Number over a 10 year period for organizations with a female CEO, starting with two years before the woman took office. One company where historical data might be available, at least anecdotally from old timers, would be the Washington Post. In 1972 Katharine Graham was the first female CEO to make the Fortune 500 list. Graham had attained the highest position in the company -- Publisher -- in 1969. The Post, however, was not large enough to be on the Fortune 500 list until three years later when it reached number 478 out of 500. Graham, like Indira Gandhi, had a father in the business. Which brings us to the Indira Phenomenon.

THE INDIRA PHENOMENON

As I thought about the question of female CEOs and whether women help other women, it occurred to me that sometimes in a highly male-dominated organization, a highly accomplished, intelligent and lucky woman rises to the top. Below her, however, it's men all the way down until the very bottom levels. The woman at the top is not the reason: the organization was like that before she came and will be like that after she leaves.

Consider Indira Ghandhi. Her becoming her country's leader did not signal that India had abandoned sexism. At least, however, it meant that the country had progressed far enough that Mrs. Gandhi, the daughter of a previous powerful leader (Nehru), could become Prime Minister.

10. Over the years when Indira Gandhi was in power (1966-77 and 1980-84), what was the lowest Morris Number in her government?

It would appear that entities dominated by men, whether governments or corporations, are more willing to have a woman at the top than anywhere else on the ladder except the bottom. The same could be said with whites/black substituted for men/women.
When Thurgood Marshall became a Supreme Court Justice in 1967, African-Americans in the federal judiciary were very few in number. Once Marshall was on the Supreme Court, there were 1 out of 9 justices = 11% Blacks. For the judiciary as a whole, the percentage was much worse: there were 455 judgeships in the federal courts, according to page 8 of tables available from uscourts.gov, and 13, or about 3%, filled by Blacks. (Both the 455 and the 13 include Marshall.) More than half of those judges were appointed by Lyndon Johnson. References: "Integration of the Federal Judiciary" on jtbf.org, Picking Federal Judges by Sheldon Goldman (1999), and Black Firsts by Jessie Carney Smith (2nd ed. 2003).
PhD students in sociology and social psychology probably have examined the Indira Phenomenon under another name. If not, it is worth examining.

11. Compare Indira Gandhi's government's lowest Morris Number with those of other female world leaders, such as, in chronological order: Golda Meir (1969), Maggie Thatcher (1979), Corazon Aquino (1986), Benazir Butto (1988), and Angela Merkel (2005).

12. Trace the Morris Numbers over time in the governments of India, Israel, Britain, the Philippines, Pakistan and Germany, starting with the male leaders who preceded each female head of state and ending five years after she left office (or in the present, in the case of Germany). Compare the numbers with those of male-led countries during the same time periods.
13. Female CEOs: Identify pairs of peer organizations who chose new CEOs at around the same time, one that chose a male and one a female. Evaluate whether or not "women don't help other women" by looking at how the Morris Number changed with time in each company, starting from a few years before each new CEO was hired.
THE MORRIS DECILES

The question of why I had chosen to look for the 5th highest ranking woman, rather than, say, 2nd or 10th, made me think about how the gender mix at different ranks might reflect (or not) the company as a whole, the population as a whole, etc. But ranks are hard to define. They are also hard to compare from one organization to another. I thought about a more objective way to compare companies and came up with compensation deciles:

THE CONCEPT

Find out how many employees there are in the organization and divide that number by ten. That is the number of people in each decile. Then comes the hard part. Obtain compensation (salary + benefits) paid to all employees, and order it from highest paid to lowest paid. No identifying information other than gender (or other demographic under study) would be needed.

Given the "Inequality for All" that infects so many US entities, we can expect that the range of compensation within each decile will be different for different deciles. The decile with the lowest salaries will have a narrow range. Within the decile with the highest salaries, however, the highest paid employee (the CEO in a company, the athletic director in some universities) might receive a compensation package that is 10 times - or many more than 10 times - that of the lowest paid person (who is still making more than 90% of the company's workforce).

The medical supply company McKesson, which according to Forbes, has had the highest paid CEO in the US for the last 13 years, currently pays him $131.2 million. At what compensation level does McKesson's top decile begin? If it is as high as $565,000, then the salaries in the top decile will differ by a factor of 200 (565K x 200 = 130M.) If it is lower than 565K, then someone in the top 10% of the company makes less than 1/200 of what the CEO makes. And it might be lower: McKesson's average [or do they mean median?] product manager, the title with the highest average salary according to this site makes 198K. Even adding a handsome benefits package and employer-paid social security and all the rest, the CEO probably makes 600 times more than that product manager.
14. Is the compensation spread in the top decile a predictor of the Morris Number?



Half the employees of an organization may be women but that does not tell us much about equal opportunity if all the women are at the bottom of the compensation scale. In the 1950s or 1960s (think Mad Men and How to Succeed in Business Without Really Trying), women in business were secretaries or file clerks and women in food services or hotels were waitresses and room cleaners. How much has that changed?

This may have been the subject of countless studies already. Here are some follow-up ideas.

15. For any organization, what is the percentage of women in each compensation decile? Is there any decile with gender equality? What is the highest of the compensation deciles at which the percentage of women is the same as it is for the company as a whole?

16. In a group of 100 organizations (businesses, law firms, nonprofits, etc.,) how often is the lowest compensation decile the one with the highest percentage of women? If that is the case for most entities in the sample, what characteristics, if any, are common to the outliers?

17. For any organization, identify the decile, if any, in which the compensation of the median woman equal to or better than the compensation for the median man. If none, in which decile is the median woman's compensation the closest to the median man's?

March 19, 2014; updated 20140331,0403

The Weighted Morris Number (Morris Number 06)


THE MORRIS NUMBER, WITH WEIGHTS

When I calculated the range of ordinary Morris Numbers (OMNs) for the five tech companies discussed in Julianne Pepitone's CNN Money article, I thought about adding weights. Weights help to discriminate (npi) between companies with the same OMN but a different ordering of females and males. Weights are a way to take account of the gender pattern above the fifth highest ranking woman.

A SIMPLE EXAMPLE

Two companies have an ordinary Morris Number (OMN) of 5: there are 5 men above the 5th highest ranking women. In one company the top 10 positions alternate between M and F. In the other company the top five positions are held by men, the next five by women.

To distinguish between such situations, we can use weights. Counting down from the top, the more men above each successive woman, the higher (worse) the metric will be.


The Weighted Morris Number (WMN) is calculated by using different weighting factors for the number of men whose position at the company is higher than one or more of the top five woman. The weights go down as you go down the hierarchy. The number of men higher than the top woman is multiplied by the biggest factor. Let us set it at 15. If the CEO is a woman, the contribution to the Morris Number for Female #1 is 0. If the top woman is 6th in the company, the contribution is 75 (5 x 15).

The set of multipliers might be:
     15 for the number of men above Female #1
     10 for the number of men between Female #1 and Female #2
       6 for the number of men between Female #2 and Female #3
       3 for the number of men between Female #3 and Female #4
       1 for the number of men between Female #4 and Female #5
The size of the steps between weights are 5-4-3-2.

ALTERNATING MEN AND WOMEN AT THE TOP

If men and women alternate in the top 10 positions, the ordinary Morris Number is either 4, if a woman is at the top, or 5, if a man is at the top. The difference between the OMNs for those two situations is 1. The difference between the two WMNs is more dramatic. With a man in the number 1 position, the weighted Morris Number is
     1 x 15
     1 x 10
     1 x   6
     1 x   3
     1 x   1
for a total of 35. If a woman is in the top position, the weighted Morris Number is 20.
The bonus for a female CEO might make the weighted Morris Number a less desirable metric: it could encourage companies to rely on the Indira Phenomenon rather than ending discrimination.


Company 1: There are 50 men before you reach any women. The next 5 positions are held by women. The OMN is 50.

Company 2: The CEO is a woman. Then there are 5 men between her and F2, 35 men between F2 and the next two women, F3 and F4, then 10 more men between F4 and F5. The OMN is 50.

In Company 1, the top 5 females are below the executive tier. (I say that because it is rare for an organization to have more than 50 people with substantial executive clout.) Company 2 has a female CEO and another female also within the top 10. So far so good, but the Indira Phenomenon may dominate after F2.

Now consider the WMNs for these two companies: Company 1:
     750 = 50 men above F1 x 15
         0 = No men between F1 and F5
     ------------------------------------------------
     750 = WMN

Company 2:
          0 = 15 x  0 men above F1
       50 = 10 x  5 men between F1 and F2
     210 =  6 x 35 men between F2 and F3
         0 =  3 x  0 men between F3 and F4
        10 = 1 x 10 men between F4 and F5
     ------------------------------------------------
     270 = WMN

Company 2's WMN is about a third of Company 1's. Imagine if that fact were publicized at job fairs and university career offices and in a tweet that went viral. Company 2 would attract more and better women job seekers and more and better women customers. It would be able to achieve a level of excellence that company 1 could only envy until its top management finally realized that quality women should replace mediocre men.

March 19, 2014; rev 1 20140331,0403

Morris Number Ranges for Some Tech Companies (Morris Number 05)


CALCULATING MORRIS NUMBERS FOR TECH COMPANIES

Employment data is not easy to come by. But almost exactly a year ago, Julianne Pepitone published an article in CNN Money entitled "Black, female, and a Silicon Valley 'trade secret'" and subtitled "Silicon Valley Boys' Club" in which she sought to answer the question "How diverse is Silicon Valley?" Pepitone had managed to obtain employment data from five tech companies willing to permit such information to be public: Cisco, Dell, eBay, Ingram Micro and Intel. I discussed the article, and its excellent interactive tables, here.
Pepitone had sought information from twenty tech companies. Only three, Dell, Ingram Micro and Intel, cooperated; Intel alone has a policy of making such data public. After a FOIA request was filed seeking employment information that government contractors have to give the government, information about two more companies, Cisco and eBay, was obtained. Final tally: 20 companies, 5 with data, 15 not. Ten of those fifteen, including Amazon, Facebook and Twitter, had no government contracts so the FOIA request did not touch them. The other five -- Apple, Google, Hewlett-Packard, IBM and Microsoft -- successfully petitioned to prevent disclosure on the grounds that it would cause "competitve harm," hence the 'trade secret' joke in the title of the article. Would a company with an excellent record of diversity want to make sure nobody saw the numbers? Hmmm. If you know of further developments in the quest for this kind of information, please let me know.
Pepitone's tables present the numbers of employees in six categories. She explains that these are averages over 5 years. [See "Methodology" below the interactive tables and click "Read More."] Those categories are related to a set of ten codes from an EEO-1 form that all companies with more than 100 employees must file with the EEOC. Those ten codes are aggregates from the 300 occupations the US census uses. See http://www.eeoc.gov/employers/eeo1survey/jobclassguide.cfm.
The EEOC, however, is prohibited by statute (subsection e of 42 USC 2000e-8) from divulging EEO-1 information, which is why the CNN Money investigators first asked the companies directly, and then used a FOIA request addressed to the Department of Labor. Unlike the EEOC, the Department of Labor is not subject to a gag rule but the contractors do have the right to petition to keep secret any trade secrets.
Pepitone reorganizes the data to focus more on upper level employees. She breaks out the subcategories of the EEO-1's top code (1.1: executive/senior officers and 1.2: First/Midlevel Officials and Managers), identifying the first as "Officers and Managers" and the second as "Midlevel Officer or Manager." She also collapses the lower five EEO-1 codes into a single "Admin/Other" category.

Total employees for each company are not displayed, so I have calculated them here.
           Company
Category
Cisco
Dell
eBay
Ingram Micro
Intel
Officer/Manager
225
125
55
236
41
Mid-level
6,496
3,374
1,804
574
5,027
Professional
24,100
11,237
3,977
846
28,306
Technical
59
3,370
58
119
10,970
Sales
2,850
5,895
163
714
577
Administrative/Other
902
4,820
2,700
2,123
2,000
Total
34,632
28,821
8,757
4,612
46,921

Apparently the five companies give different interpretations to the EEO codes. For example, Intel, which I calculate has almost 47,000 employees, has only 41 "Officers and Managers," less than 0.1% of the workforce. By contrast, Ingram Micro has 236 "Officers and Managers", almost 6 times as many as Intel, out of a workforce of 4600, one-tenth the size of Intel's. That means Ingram Micro's Officers and Managers are 5% of its workforce. Is Ingram Micro that top-heavy and is Intel that lean? Or what?

The CNN Money interactive tables let you view the total number of people the company designated in each category, as well as how many are men or women, or your choice of any combination of gender -- all, men or women -- and ethnicity -- all, Asian, Black, Hispanic, White, or Other.

Because all five companies have at least five women in the top category, it is possible to calculate a range of Morris Numbers. We cannot determine the precise value without more information about people's actual positions. (See Part 03 of this series for a discussion of different ways to rank employees using objective data.) Sometimes the companies' webpages help, at least for the very top of the top. I analyze some of this information below.

A suspicious mind might suspect that companies use as broad a definition as they can for the top category in order to have as few zeroes in the non-white-male boxes as possible. The range for the Morris Number [LOW, HIGH] for each company does not prove or disprove that theory. The greater the overall number of employees in the top category, however, the higher (worse) the upper limit on the Morris Number range.

MORRIS NUMBER RANGES FOR THE FIVE TECH COMPANIES

If we do not know the precise rankings of the women in a company's top management, we can at least calculate the range. The best (lowest) Morris Number is obtained by assuming the first five woman are clustered at the top, above all the men, the highest (worst) Morris Number by assuming that the fifth and all lesser-ranked women in that category are clustered at the bottom. (The ordinary Morris Number is the same whether the first woman is in that bottom cluster, too, or is the CEO. I propose the weighted Morris Number to take into account the actual positions of the four women you pass on the way to finding the fifth highest ranking woman.

Let's take an example, first with numbers, then without, to understand how this works.
        Total people in the category Officer and Managers is 105.
        Number of women in that category is 5
        Number of men = 105-5 = 100

If we assume the least sexist (genderist?) case, the 5 women are all at the top, the 100 men come below them, and the Morris Number is 0. In the worst case, the 5th woman is ranked below the 100 men and the Morris Number is 100. We can write the range as [0,100].

We can derive a formula, too. If T = total and W = women, then the worst number is T-W. If there are 5 or more women in the category, the best number is 0. If there are less than 5, then the next category has to be included to get the Morris Number.

Now let's consider Pepitone's data.

MORRIS NUMBER RANGES FOR FIVE TECH COMPANIES


The Officers and Managers row of the interactive tables shows that
Cisco: Women are 44 of the 225. Morris Number Range: 0 to 181
Dell: Women are 27 out of 125. Morris Number Range: 0 to 98
eBay: Women are 10 out of 55. Morris Number Range: 0 to 45
Ingram Micro: Women are 47 of the 236. Morris Number Range: 0 to 189
Intel: Women are 6 out of 41. Morris Number Range: 0 to 35.

Conclusion: Intel looks the best. Ingram Micro looks the worst, with Cisco a close second.



CISCO: The senior management (according to http://newsroom.cisco.com/exec-bios, last viewed 3/14/14), has only 71 people, compared to the 225 that CNN Money reported was on Cisco's EEO-1. The top level is called the Executive Leadership Team. The 15 members, 11 men and 4 women, are listed alphabetically by last name. The women's titles are SVP and Chief Marketing Officer; Chief Technology and Strategy Officer; CIO and SVP; and SVP and Chief Human Resources Officer. We need only look for one more woman to calculate the Morris Number. Of the 56 people in the next level, the Senior Leadership Team, 6 are women, 50 are men. (The fact that there are more women proportionally in the top level (4/15 = 27%) than in the second level (6/56 = 11% )reminds me of the Indira Phenomenon.) If one of the six women in Senior Leadership is above all the males in the category, the (lowest) Morris Number is 11. If all the men are above F#5, the (highest) Morris Number is 61. Range for Morris Number: [11,61].

INGRAM MICRO: The webpage listing Ingram Micro's senior management (corp.ingrammicro.com/About-Us/Executive-Leadership.aspx, last visited 3/17/14) has only 20 people, compared to 236 on the company's EEO-1 filing as shown on the CNN Money table. Of those 20, apparently listed in rank order, there are 2 females and 18 males. F1 is 11th, F2 is 14th. That means F3, F4 and F5 are below the 20 Executive Leaders. If they are directly below, the Morris Number is lowest: 18. If not, they must be somewhere among the remaining 216 (236-20, consisting of 189-18=171 men and 47-2=45 women). If F3, F4 and F5 are at the bottom with the rest of the women and below the 171 men, the worst Morris Number iss 189. Range for Morris Number: [18, 189].

INTEL: The webpage identifying senior management (http://www.intel.com/newsroom/assets/bio/CorpOfficers.htm , last viewed 3/14/14) has the same number of employees, 41, as Intel had reported to the EEOC. The Chairman of the Board, a non-employee, brings the page's total to 42. Within each title -- Executive Vice President, Senior VP, Corporate VP -- people are listed alphabetically by last name so no ranking is revealed. The President, listed after the CEO so overall ranked #2, is female. There is also a female EVP (1 of 4), a female SVP (1 of 6) and six female Corporate VPs (6 of 29). F#5 is thus among the Corporate VPs, but we do not know her rank within that group. If she is top-ranked, Intel has the lowest Morris Number: 9. If she is below all the male Corporate VPs, Intel has the highest Morris Number: 32. Range for Morris Number: [9,32].

Conclusion: Intel still looks best, Cisco looks better, Ingram Micro looks about the same.


I also looked on the web for information about the younger tech companies with high profile women, Facebook (Sheryl Sandberg) and Yahoo (Marissa Mayer). The result was: they like to keep secrets. The Indira Phenomenon may be present at both companies.

Facebook lists only 4 executives on its main company information page, Sandberg and 3 men. The Board of Directors has the same ratio: 2 women and 6 men. A 2012 article in the Business Insider has a photo of 18 people from Facebook who had visited Walmart, 13 men and 5 women. Author Owen Thomas points out that the picture includes some "junior [Facebook] staffers who work closely with Walmart" which seems to include at least one of the women, a customer marketing manager involved with the Facebook-Walmart relationship. The other four women are COO Sandberg, her executive assistant, a (the?) director of design, and the VP for Human Resources (so often the only high level job for someone outside the homosocial reproduction group). If these are the four highest ranking women at Facebook, who and how far down is F5? Is Facebook better than Intel or Cisco?

Yahoo's Proxy Statement filed in 2013 has a table showing the ten most highly compensated current or former executives. Two are women, one with the highest compensation on the list, CEO Marissa Mayer, and one with the lowest. Other than the Proxy Statement, I was unable to find anything from Yahoo with any executive leadership biographies or other information from which to calculate a Morris Number range.

True of false? 1. The younger the tech company, the more secretive about diversity data. 2. The younger the tech company, the worse the Morris Number. (Two more PhD ideas there.)
March 19, 2014; rev 1 20140330,0403

Calculating the Morris Number - Hypotheticals (Morris Number 04)


The ordinary Morris Number, described here, is the number of men you pass, starting at the top of an organizational chart, on your way to finding the fifth highest ranking woman. 

Here are some illustrative examples.  A note on notation:  Female #3 or F3 means the 3rd highest ranking female.

A.  WOMEN'S ORGANIZATIONS

In a nunnery, the Morris Number is probably 0. If the Mother Superior is not really the top person but reports to a male Priest, the Morris Number is 1.

Note:  I thought the Girl Scouts might have a Morris Number of 0 but then I found the senior leadership here and realized I was wrong.  There is one man on that page and six women: Is the Morris Number 0 or 1?  We can infer that it is 1. The man apparently ranks third overall. This is suggested by the fact that the various Chiefs below the CEO and Chief of Staff are not in alphabetical order by title nor last name.  Mr. Boockvar, Chief Customer Officer, is listed above Chief Officers for Development, Information, and Financial, and the General Counsel (named, respectively, Taft, Miller, Olden and Rochon). If we were to use weights in calculating Morris Numbers, we would need to know M1's rank vis-a-vis F1 through F5. See Part 06 of this series.
Is a female as highly placed in the Boy Scouts organization? No. Their leadership team consists of eight men: three holding positions called "National" and designated volunteer -- the President, Commissioner and President-Elect, then four Scout Executives of different ranks and last the Chief Financial Officer.

B.  SOME POWERFUL FEMALES

This hypothetical organization has
    - one CEO, a female (F1)
              Contribution to Morris Number =   0
    - a COO, CFO and CTO, all reporting to the CEO; the first two are male and the CTO is female (F2): 
              Contribution to Morris Number =   2
    - five Executive Vice Presidents (EVPs); one is female (F3):
              Contribution to Morris Number =   4
    - eleven Senior Vice Presidents (SVP); one is female (F4): 
               Contribution to Morris Number = 10
    - one Associate Senior Vice President, a female (F5, so we can stop looking)
               Contribution to Morris Number =   0
                               The Morris Number is 16

Note that in this example we do not have to know the standing of Female #3 or Female #4, the lone female EVP and SVP, respectively, relative to the men with the same title because all those males are above Female #5. 


C.  ALL-MALE TOP MANAGEMENT

In this hypothetical organization:
    - The highest ranked woman is an Account Representative (AR).  Above her, there are 100 positions, all filled by males. 
            Contribution to Morris Number = 100.
     - There are 420 ARs, 20 of whom are women.   Without reliable information to know about the rank of the 5th women among the 420 ARs, we can nevertheless make some educated guesses.

       1. We can estimate the Morris Number assuming that the women and men in this organization have the same range of abilities. 
This may not be the case, especially given the absence of women in the first 100 positions and the widely accepted belief that people who do not conform to homosocial reproduction, which in this hypothetical means women, have to be better than men to attain the same level. Here is one citation for that proposition from thirty years ago: "Neutralizing Sexism in Mixed-Sex Groups: Do Women Have to Be Better Than Men?" by M. D. Pugh and Ralph Wahrman, American Journal of Sociology, 88:746-782 (Jan. 1983), available at http://www.jstor.org/stable/2779483, which references a study by the same authors from 1974 ("Sex, Noncomformity and Influence," Sociometry 37:137-47) in which they found that "[M]ale groups refused to be influenced by an obviously competent female despite the fact that without her they clearly failed at their task and lost money." Forty years later, how much has changed?
The 5th woman out of 20 is above 3/4 of the women.  She should therefore also rank above 3/4 of the men and therefore below 1/4 of them.
            Contribution to Morris Number:  1/4 of 400 = 100
            Morris Number assuming equal gender abilities:  200.
OR
        2. We can caculate the range of Morris Numbers, and the average within that range, obtained by calculating the lowest and highest possible numbers:
    - the Lowest Morris Number is obtained if the first five women are above all the men: 
            Contribution to Morris Number: 0 
            and
            the Morris Number is at least 100
    and
    - the Highest Morris Number:  all 400 men are above the first five women: 
            Contribution to Morris Number: 400
            and
            the Morris Number is at most 500

Morris Number Range: [100,400]. Average: 250

March 19, 2014; rev 1 20140328,0403

The Morris Number and Determining Rank (Morris Number 03; PhD Ideas 05)


 COUNTING HOW MANY MEN YOU PASS
ON THE WAY TO FEMALE #5:
WHEN THE ORG CHART IS NOT ENOUGH

To calculate the Morris Number of an organization, count the men above the fifth highest ranking female ("F5").  Sounds simple. But if several people have the same title as F5, and some of them are male, how many of those men should be counted?

One approach would be to assume that F5 is average:  half the men with the same title are above her, half below.  If F5 is not the only woman at that rank, we could guess that she is above the same percentage of men as she is above women. See this example. Or we might calculate the best and worst Morris Numbers, assuming that the woman is at the top or bottom of the rank, respectively.  That range may be useful for comparison to other companies or to the same company at a different time.

But maybe we can do better.  People with the same title, say, Senior Vice President, may not in fact have the same rank and they may not have the same power within the organization.   Assessments of relative power are likely to be subjective, but objective information may be available.  If the company website lists the management team, we may be able to guess who is above whom when the listing is not alphabetical.  (See the example here based on the Girl Scouts' public information.) If the job holders are high enough up in their organization, the company's Executive Leadership webpages or SEC filings may provide some answers as discussed here.

Other employees within the organization, or researchers granted limited access to employment data including title and gender (but no names, please), could use these proxies of true rank, alone or in combination:
       1st choice: compensation package, if available,
       2nd choice: median compensation of direct reports
       3rd choice: budget
       4th choice: seniority
       5th choice: number of direct and indirect reports. 
to calculate the Morris Number. Perhaps someone has already analyzed how accurately each of those predicts a manager's power within an organization.  If not, it seems like a good subject for some PhD research.

I choose direct/indirect reports last because a supervisor of lower-paid workers, compared to one who supervises higher-paid workers such as professionals (engineers, lawyers or accountants), may have
       - more people to supervise, and
       - the same or even a higher budget, but
       - less power or influence.
Seniority might indicate power within the organization, or it might be a sign of dead wood left in place because of strong social or family connections.  How many people you supervise may be less of a clue to your power than your own salary is.  The median salary of the people you supervise may be an even better clue.  Another PhD Idea there.
March 19, 2014; rev 1 20140328,0403

The Morris Number - A Few Questions and Answers (Morris Number 02)


Here are answers to some questions that came up during early discussions of the Morris Number.

"IN A PERFECT WORLD"

Q. How do you define "in a perfect world"?

A. In a perfect world, we can assume that
        1.  men and women receive equal treatment in education and employment,
        2.  the pool of people qualified for top-ranking jobs is half men, half women, and
         3.  women and men are equally likely to hold the top position in any organization.


Q. Why would the average Morris Number in a perfect world be 4.5 rather than a whole number?

A. I state the average Morris Number as 4.5 rather than a whole number to highlight how the number changes depending on Assumption 3. Assume that men and women alternate. If the top person is a woman, the fifth highest ranking woman is at position 9 and the Morris Number is 4. If the top person is a man, then the fifth highest woman is at position 10 and the Morris Number is 5. The average of many companies in the perfect world would be 4.5.


Q. What if the applicant pool is not 50-50?

A. If the applicant pool for top-ranking positions has more men than women, then we would expect the average Morris Number for a group of perfectly non-discriminatory entities to be more than 5. But there is no reason for the applicant pool to be other than 50-50 because in a perfect world there is no sex discrimination: men and women have equal educational and employment opportunities.

The Morris Number was created as a way to measure
        (a) the imperfections of the world, or some subset of it, with regard to gender neutrality, and
        (b) the progress toward perfection as the years go by.

WHY 5: WHY FIFTH HIGHEST RANKING?

Q. Why look for the fifth highest woman, not the third, say, or the tenth?

A. I hope that the choice of five follows the Goldilocks principle: neither too few nor too many but just right. Using two or three might be affected by the Indira Phenomenon: there might be as many as three women at the power table in some organiations, but the rest of the women would be in the bottom ranks. A number like eight or ten might be a problem in smaller organizations. A metric based on five will, I hope, give useful information about almost all employers.

Q. What about employers with less than five women employees?

A. Employers with less than five women employees and more than ten total employees have a Morris Number of infinity. (Below ten total, we can skip that employer until there are a few more hires.)

WHERE ARE THE BEST (LOWEST) MORRIS NUMBERS

Q. Where do I expect to find lower Morris Numbers?

A. Not in Silicon Valley, I'm afraid. Some of the reasons for my low expectations for tech companies are here.
I recently came across the phrase 'homosocial reproduction.' It fits Silicon Valley to a T, or rather it fits Silicon Valley's HR practices to an HR.
My guess is that the best (lowest) Morris Numbers are to be found in companies whose products in the bad old days would have been featured on the women's pages of newspapers: cosmetics, fashion, food, things for children. For a century or more, women started their own companies in those industries. 
         - Coco Chanel opened her first shop in 1910.
         Madame C J Walker began her own hair products business in Indiana in 1910.
In 1945 Ruth Handler co-founded Mattel, a picture-frame company that became a maker of doll-house furniture a year later and then a toy company (and, yes, introduced Handler's invention, the Barbie doll, in 1959).
        Estee Lauder founded the company that bears her name in 1946.
   In the "women's pages" industries, as compared to "man's world" industries (finance, heavy industry, agribusiness) and regardless of the gender of the founder, women were hired more often and more readily, and that, in turn, improved the odds that a woman could rise to a higher position.
In 2013 there were 23 companies in the Fortune 500 that had female CEOs. See below. By my count, six of those companies are in women's pages industries (four in food, one in cosmetics and one in fashion). Five are in tech (software, hardware or both). In 2010, there were 15 companies in the Fortune 500 with female CEOs; by my count, four were in women's pages industries and two in tech. In 2000, the Fortune 500 companies with female CEOs numbered two, three or four, depending on when the count was made, and five different women were involved Three of them headed companies that make products heavily marketed to women: Mattel (toys: Jill Barad), Avon (cosmetics: Andrea Jung) and Walmart (retail: Jeanne Jackson). The other two were Carly Fiorina at HP and Marion O. Sandler at Golden West Financial.
Second, among the "man's world" companies, the best (lowest) Morris Numbers are more likely to be in older, rust-belt industries rather than 21st century ones.  The older companies, after all, have spent the last half century with the threat of affirmative action lawsuits forcing them to discriminate a little less and a little less openly. Those companies also hire from top business and law schools, and those schools have graduated plenty of women by now. Tech companies may hire fewer lawyers and B-school grads. I have heard that the tech world excuses its failure to hire women on the grounds that women don't get degrees in computer science. Assuming they are correct that women haven't pursued computer science in large enough numbers to make a dent in the Boys' Club culture of Silicon Valley, I can think of some solutions that the biggest employers - Google, Apple, Facebook - could easily afford that would make a dramatic difference pretty quickly. Just ask.


In the post that led to my developing the Morris Number I wrote:
We all know about Carly Fiorina and Meg Whitman at HP, and Marissa Mayer formerly at Google now at Yahoo, and Sheryl Sandberg at Facebook. What happens, though, if you look in those companies for the next highest ranking female? How many men do you pass on the way down?
Q. Do you mean that women who get to the top do not help other women?

A. No. That was not my point. The only reason I referred to those famous ladies is to illustrate that a female in the top position does not prove that the company is an equal opportunity employer.

Women do not have to hire and promote *only* women. And the fact is that any new leader has only limited opportunity to create new positions or to replace incumbents. It takes time to create an optimal management team. Sometimes, too, filling positions with outside candidates may not be an option for corporate-cultural reasons. If the company has not promoted women into positions within a few levels of the top, then the internal candidates will all be male.
The 23 Fortune 500 companies with female CEOs, see http://management.fortune.cnn.com/2013/05/09/women-ceos-fortune-500, last updated December 10, 2013, would be interesting to study with regard to the blame question. See number 13 of my PhD ideas. We do not know those companies' Morris Numbers but we can come up with a Morris-style Number that tells us something about the Fortune 500. If we consider the CEOs of the Fortune 500 as part of a single organization and give them their companies' Fortune 500 rankings, the Morris Number is 38: you pass 38 men on the way to finding the fifth highest company with a woman CEO, 43rd ranked Pepsico's CEO Indra K. Nooyi.
Maybe some women who get to the top are as blind as the men around them to the excellence of women. Maybe not. But until those female CEOs have had their titles for several years, and until the top women are at companies that in the past have consistently promoted women into upper management, the presence or absence of women in other important positions does not prove much about whether women help women.
March 19, 2014; rev 1 20140328;0401

The Morris Number - Introduction (Morris Number 01)


I propose a new metric I'm calling the Morris Number.  It is a way to quantify how gender-neutral an organization really is. It makes it possible to compare employers -- businesses, non-profits, universities, governments -- with regard to their equal opportunity characteristics.  I thought of the concept when I wrote about Silicon Valley: Boys Club last year.  Whatever the organization, the Morris Number answers the following question:
How many men do you pass on the way to finding the fifth highest ranking woman?
Other discriminatory behavior can also be evaluated with Morris Numbers.  Instead of men and women, any two demographic categories can be compared, e.g., whites and non-whites (or, for tech companies, TECMYs and non-TECMYs).
In a perfect world, the Morris Number averaged over many organizations would be 4.5. Assumptions behind the phrase "in a perfect world" are discussed in Part 02. That post also includes questions raised by friends when I first mentioned the Morris Number.

In the real world, almost all employers have a Morris Number above 4.5, often far above. Perhaps if we start calculating and publicizing Morris Numbers we can start to see them change.

The Morris Number may remind some readers of the Bechdel Test, which evaluates movies on a scale from 0 (bad) to 3 (good) depending on the presence of female characters and what they do. Both the Morris Number and the Bechdel test are metrics concerning unequal opportunities for women. They differ, however, in that
  • the Morris Number is for all employers, not just movie producers,
  • unlike Bechdel, and instead like golf and cholesterol, a lower Morris Number is better than a high one, and
  • the Morris Number can be much higher than 3, and almost never, alas, is that low.
A Morris Number in the single digits means that the employer's hiring and promotion practices today are what I would have predicted back when I was in law school.  A Morris Number above 10 reminds me that change sometimes takes a long time.

In the Fortune 500, is the average Morris Number below 30? What about in Silicon Valley?  Among major nonprofits? At the top research universities?  Wouldn't you like to know? I would.

HOW TO CALCULATE THE MORRIS NUMBER

You may be wondering how to identify the fifth highest ranking woman in an organization.  For a start, we can use the employer's organizational chart. 

Starting from the top person in the hierarchy, usually the CEO, count all the men you have to pass before you get to the fifth woman.  That is the Morris Number in its ordinary form.

True, there is an obvious problem with org charts.  If several people have the same title, how do you determine who has a higher rank?  You might want to base your answer on how much power each person has. To evaluate that, you might try objective indicia of power such as salary, budget, or direct reports.  Ideas about going beyond the org chart are discussed in Part 03.

EXAMPLES

In Part 04 I calculate ordinary Morris Numbers for some hypothetical entities and discuss a way to deal with the same-title-different-power problem.  Morris Numbers calculated from the tech company data presented in Julianne Pepitone's 2013 CNN Money article can be found in Part 05.

SAME MORRIS NUMBER, DIFFERENT REALITY

Part 06 presents a comparison of the ordinary Morris Number, which we  might call the OMN, with a weighted Morris Number, WMN.  The reason to add weights is to distinguish between two companies with identical OMNs but different distributions of the sexes. For example, a company with a Morris Number (OMN) of 5 might have men and women alternating in the top 10 positions, or it might have men in the top 5 positions and women in the next 5.  The WMN quantifies the difference.

MORE PhD IDEAS

Comparing Morris Numbers among companies, times, or regions, would be interesting. So would looking at how a company's Morris Number changes when it has a female CEO. We might also use Morris Numbers to examine what I call the Indira Phenomenon. (It probably has a name already but I am not aware of it.)

Another metric for gauging equal opportunity would be to identify the compensation deciles with a 50/50 gender ratio or an ethnic ration similar to the population in the area.

Those and other ideas for PhD dissertations in Economics, Political Science, Statistics, Sociology, Gender Studies or American Studies are in Part 07.
RJM 3/19/2014; rev 1 20140321;0401