{"id":1114,"date":"2018-05-21T17:53:18","date_gmt":"2018-05-21T16:53:18","guid":{"rendered":"https:\/\/marriott-stats.com\/nigels-blog\/?p=1114"},"modified":"2025-01-23T13:22:32","modified_gmt":"2025-01-23T13:22:32","slug":"gender-pay-gap-and-life-on-mars","status":"publish","type":"post","link":"https:\/\/marriott-stats.com\/nigels-blog\/gender-pay-gap-and-life-on-mars\/","title":{"rendered":"Pay Gap Case Study #1 – Life on Mars"},"content":{"rendered":"

The UK is facing the challenge of interpreting the first round of gender pay gap data. I listed some of the challenges in my article “<\/span>the 7 ways to misuse gender pay gap data<\/a><\/em>“<\/span> where in statement 4, I concluded a lack of understanding of the laws of chance will result in unjustified allegations of gender discrimination against some organisations.\u00a0 In this article, I want to demonstrate the laws of chance using nothing more than some dice and coins, a process known as simulation.\u00a0 My simulation model is simple enough for you to repeat by yourselves and at the end, you will have a better idea of the extent to which median gender pay gaps can vary even when organisations do not discriminate in any shape or form.<\/p>\n

*** This article was edited on 25th January 2025 to bring it in line with my current style guide.\u00a0 There is no material change to the content.<\/em><\/span>
\n<\/p>\n

The Map of Mars<\/strong><\/span><\/h5>\n

I founded Marriott Statistical Consulting Ltd in 2006 but prior to that I worked at Mars UK Ltd for 9 years<\/a>.\u00a0 In the UK, Mars<\/a> are split into 4 businesses covering Chocolate (Mars, Galaxy, Maltesers, Snickers, Twix, etc), Petcare (Whiskas, Pedigree, Royal Canin, etc), Food (Uncle Ben’s, Dolmio, Seeds of Change, etc) and Drinks (Klix, Flavia, etc).\u00a0 If you visit the government’s gender pay gap data website<\/a>, you can find out what the pay gaps are for each of these businesses which are shown in the graphic below.<\/p>\n

\"\"<\/p>\n

For an explanation of the chart format, please read my post “the 7 ways to misuse gender pay gap data”<\/em><\/a>.\u00a0 You can also retrieve the same data by downloading my spreadsheet\u00a0Gender Pay Gap Data & Chart Tool v1.0.<\/a><\/p>\n

Update October 2018 – shortly after I wrote this article, Mars sold their Drinks business<\/a> and restructured their other businesses.\u00a0 That means you will not find the same employers on the government portal now.<\/em><\/span><\/p>\n

It is important to note the four businesses are different in size.\u00a0 Both the Chocolate and Petcare businesses are categorised as having 1,000-4,999<\/strong> employees whilst the Food and Drinks business are stated to have between 250-499<\/strong> employees.\u00a0 For the purposes of the simulation model I will be using, I will assume Food and Drinks each have 300<\/strong> employees (known as Associates within Mars) and Chocolate and Petcare each have 9<\/strong> times as many employees i.e. 2700<\/strong> employees\/associates.<\/p>\n

The median pay gaps among these four businesses could not better demonstrate the point I want to get out of this article.\u00a0 For the two larger businesses the median woman earns \u00a30.94<\/strong> & \u00a31.08<\/strong> for every \u00a31<\/strong> the median man earns and for the two smaller businesses, the median woman earns \u00a31.18<\/strong> and \u00a30.89<\/strong>.\u00a0 Notice how the variation in pay gaps is much smaller for the two larger businesses compared to the two smaller businesses.\u00a0 A statistical theory known as the Central Limit Theorem<\/a>\u00a0states that if you increase your sample size (i.e. number of employees) by a factor of 9<\/strong>, the margin of error in your results will fall by a factor equal to the square root of 9<\/strong> i.e. 3<\/strong>.\u00a0 Sure enough, the largest pay gap of 18p<\/strong> from the two smaller companies is 3<\/strong> times the smallest pay gap of 6p<\/strong> from the two larger companies.<\/p>\n

At first sight, all this is what would be expected if Mars UK was a genuinely non-discriminating company when it comes to pay & promotion. In fact, this is the case since I know from my own experience, Mars has the same pay system<\/strong> in all four companies.\u00a0 This point is critical to my argument here so I want to use my inside knowledge (as of 2006 but I doubt if things have changed much) to describe the main features of the Martian pay system (and yes we did call ourselves Martians!).<\/p>\n

The Martian Pay System and Gender Equality<\/strong><\/span><\/h5>\n

My company is not large enough to need a pay system but if I ever did, I would have no hesitation basing it on the Martian system.\u00a0 A good pay system should be based on clear principles which are widely understood and pay progression should be based solely on criteria that are not directly or indirectly based on sex.\u00a0 What I experienced on Mars is the Martians come pretty close to this ideal so how does it work on Mars?<\/p>\n

    \n
  1. There are 13<\/strong> pay bands globally (known as zones on Mars) but in practice, Mars UK only uses about 10<\/strong> of these.<\/li>\n
  2. Each job is evaluated on a scale which weights the degree of responsibility and accountability entailed by the job and this evaluation determines which of the 13<\/strong> pay bands the job is allocated to.<\/li>\n
  3. Each pay band has a Base<\/strong> salary plus an Incremental<\/strong> scale up to a maximum increment in discrete steps.\u00a0 For example, band 8<\/strong> might start at \u00a330k<\/strong> and go up to a maximum of \u00a350k<\/strong> in steps of \u00a31,000<\/strong> e.g. you can earn \u00a333k<\/strong>, \u00a341k<\/strong>, etc but not \u00a336.5k<\/strong>.<\/li>\n
  4. The base salaries for each pay band will increase (or decrease in the case of management level bands) over time depending on sales performance and salary comparisons with other companies.<\/li>\n
  5. Pay progression within a pay band is based on performance evaluations and the outcome is that your salary goes up by 0, 1, 2<\/strong> or 3<\/strong> steps.<\/li>\n
  6. Crucially, the performance evaluations are pooled at a business\/site\/divisional level to see if any major anomalies are occurring before the pay progression is confirmed.\u00a0 For example department A might give everyone a 3-step increase and department B might give no-one any increases.\u00a0 This calibration exercise asks why is this the case and can be particularly helpful in identifying unconscious discrimination e.g. if dept A was mostly male and department B mostly female and these performance evaluations were confirmed, it could disadvantage women.<\/li>\n<\/ol>\n

    Mars was always conscious of gender disparities in my time there and whilst I will contend that they are near perfect when it comes to pay and progression, it should be noted that they still have some way to go on overall female employment.\u00a0 From the chart above, you can see the four businesses vary between 31%<\/strong> and 41%<\/strong> in terms of the percentage of employees who are women and the average is just under 37%<\/strong>.\u00a0 For the purpose of this article, I will assume that the gender ratio on Mars is 5 to 3<\/strong> male to female i.e. 37.5%<\/strong> female.<\/p>\n

    Perfectly Equal Simulation Ltd<\/strong><\/span><\/h5>\n

    This is the imaginary company I have created for my simulation model.\u00a0 It consists of seven pay bands where band 1<\/strong> is the lowest paid and band 7<\/strong> is the highest paid.\u00a0 \"\"Only the Managing Director is in band 7<\/strong>, everyone else is in bands 1 to 6<\/strong>.\u00a0 The chart here shows the base salary and the incremental scale for each pay band and also the expected distribution of base salaries within the company.\u00a0 On average, 42%<\/strong> of employees will be in band 1 and only 3%<\/strong> in band 6 but in practice due to employee turnover, reorganisations, etc, the actual percentage of employees in each band will vary.\u00a0 So our simulation model needs to allow for such variation and there is a statistical tool known as the binomial distribution<\/a> which I could have used but in order to keep things simple, I will be using coins and dice instead.<\/p>\n

    To begin with, let’s assume Perfectly Equal Simulation Ltd has 300<\/strong> employees and does not discriminate at all when it comes to pay and progression.\u00a0 However, it is not equal in terms of gender splits and on average 3<\/strong> out of 8<\/strong> employees are female.\u00a0 Our first employee will always be the band 7<\/strong> employee i.e. the managing director, but thereafter we will use coins and dice to determine the gender of the employee, the pay band they are in and where they are on the incremental scale.\u00a0 We therefore need a set of rules for interpreting our coin tosses and dice throws in order to make these decisions.<\/p>\n

    Rules for Coins and Dice in our Simulation Model<\/strong><\/span><\/h5>\n

    The rules are shown in the graphic.\u00a0 The three coins determine the gender of the employee, two die determine the pay band and another two die \"\"determine the increment.\u00a0 Let’s explore each in turn.<\/p>\n

    As you can see, when you toss 3<\/strong> coins, each coin can either be heads or tails and there are 8<\/strong> possible permutations that can arise.\u00a0 3<\/strong> permutations which have 2<\/strong> heads and 1<\/strong> tail and if I toss any of these, the simulated employee will be female<\/strong>.\u00a0 If I toss any of the other 5<\/strong> permutations, the simulated employee will be male<\/strong>.<\/p>\n

    For the pay band, two die are thrown, one of which is denoted to be the first dice and the other is the second dice.\u00a0 This time we have 6×6=36<\/strong> possible permutations which are laid out as a 6×6<\/strong> table in the graphic.\u00a0 I have then allocated each permutation to a pay band as shown.\u00a0 So only one permutation (6,6)<\/strong> will result in a band 6<\/strong> employee whilst there are 15<\/strong> permutations (e.g. 1 then 4) that result in a band 1<\/strong> employee.\u00a0 15\/36 = 42%<\/strong> and 1\/36 = 3%<\/strong> which is what we see in the chart in the earlier section.<\/p>\n

    For the pay increment, two die are thrown and the resulting two numbers are multiplied together.\u00a0 So 5<\/strong> and 4<\/strong> would give you 20<\/strong>.\u00a0 You then subtract 1<\/strong> to get 19<\/strong> in our example and divide this by 35<\/strong> to get 54%<\/strong>.\u00a0 The increment will then be 54%<\/strong> of the relevant maximum increment for the simulated pay band as shown in the earlier chart.\u00a0 I’ve chosen to use this system as most pay systems will not divide increments into equal sized steps but rather increase the step size by a certain percentage.\u00a0 This what the rules I have come up with here tries to mimic.<\/p>\n

    I am sure that you can see that it is possible with this system to come up with your own rules for deciding gender, pay bands and increments.\u00a0 By the way, my simulation model does not allow for any bonuses and the reported median gender pay gap is supposed to include (pro-rated) bonuses paid in the relevant pay period.\u00a0 In the case of Mars, their bonus system means nearly everybody receives a bonus of some kind.<\/p>\n

    Two Simulated Employees<\/strong><\/span><\/h5>\n

    \"\"Two simulations are demonstrated in the images below.\u00a0 Each image uses the rules shown above and arrives at the simulated genders and salaries shown.\u00a0 It is worth checking these are right.\u00a0 For the pay band, the orange dice is the first dice (rows in the table) and the blue dice is the second dice (columns in the table).\"\"<\/p>\n

    I will let you work out what THH<\/strong>, 3 then 2<\/strong> followed by 2 and 5<\/strong> would lead to.<\/p>\n

    5,000 Simulations of Perfectly Equal Simulation Ltd with 300 Employees<\/strong><\/span><\/h5>\n

    Having decided the rules for your coins and dice, you can then apply these to create a single simulation where our company has 300<\/strong> employees.\u00a0 This would be our first company simulation and the 300<\/strong> simulated employees can then be analysed to calculate the median gender pay gap and the gender splits by income quartile.\u00a0 Of course, one cannot draw conclusions solely from one simulation but a computer can rapidly replicate the coin and dice throws and create many company simulations.\u00a0 The graphic shows six such simulations, three where the median woman is paid more than the median man and three where the median woman is paid less than the median man.<\/p>\n

    \"\"<\/p>\n

    It is worth comparing these simulations with the actual results for Mars Food and Drinks.\u00a0 The percentage of employees that are women varies between 34%<\/strong> and 41%<\/strong>, a difference of 7%<\/strong> which is similar to the difference between Food and Drinks.\u00a0 One simulation has a 27p<\/strong> pay gap which just goes to show how much variation can be expected purely through the laws of chance even when a company has no discriminatory practices at all.<\/p>\n

    Obviously, even six company simulations are not enough and I ended up doing 5000<\/strong> company simulations in all.\u00a0 For each of these, I calculated the median gender pay gap and the chart below shows the distribution of these 5000<\/strong> simulated median gender pay gaps for an organisation with 300<\/strong> employees in a 5:3<\/strong> male:female gender ratio.\u00a0 Of these, 80%<\/strong> result in the median woman being paid between \u00a30.93<\/strong> and \u00a31.08 <\/strong>per hour, 95%<\/strong> result in the median woman earning between \u00a30.81<\/strong> and \u00a31.17<\/strong> and 99%<\/strong> of the simulations result in the median woman earning between \u00a30.73<\/strong> and \u00a31.32<\/strong>.\u00a0 When I compare these simulations with Mars Food’s median woman of \u00a31.18<\/strong> and Mars Drinks’ median woman of \u00a30.89<\/strong>, I find that Food is in the top 3%<\/strong> and Drinks in the bottom 3%<\/strong> of simulations.<\/p>\n

    \"\"<\/p>\n

    If you didn’t know these two companies had the same pay system, you might think whilst their pay gaps are plausible with non-discrimination under the laws of chance, they are towards the extreme end of plausibility and perhaps there might be an issue to look at.\u00a0 But when you factor in that my simulation model does not include any simulation of bonuses whereas the reported figures do, you can immediately see there is an extra element of chance which will increase the range of plausible median gender pay gaps.\u00a0 That and the fact both Food and Drinks use the same pay system means to my mind, there is no evidence, based solely on the reported gender pay gap figures, the Mars pay system is discriminatory with respect to gender.<\/p>\n

    5,000 Simulations of Perfectly Equal Simulation Ltd with 2700 Employees<\/strong><\/span><\/h5>\n

    If I repeat my company simulation model but this time for an organisation of 2,700<\/strong> employees (to represent Mars Chocolate and Petcare), I will end up with simulated examples as shown in the six charts below.\u00a0 This time, we see the degree of variation in possible gender pay gaps looks to be considerably smaller.<\/p>\n

    \"\"<\/p>\n

    Once again, I undertook 5000<\/strong> such simulations and the distribution of possible median gender pay gaps is shown in the histogram here.\u00a0 80%<\/strong> of the time, the median woman earns between \u00a30.98<\/strong> and \u00a31.03<\/strong>, 95%<\/strong> of the time she earns between \u00a30.96<\/strong> & \u00a31.04<\/strong> and 99%<\/strong> of the time, she earns between \u00a30.95<\/strong> and \u00a31.06<\/strong>.<\/p>\n

    \"\"Therefore, Mars Chocolate’s median woman’s earning of \u00a31.08<\/strong> put them in the top 1%<\/strong> of plausible median pay gaps and Mars Petcare’s median woman’s earning of \u00a30.94<\/strong> puts them in the bottom 1%<\/strong> of plausible median pay gaps.\u00a0 Again, I repeat that my simulation model does not include bonuses, which can expand the range of plausible range of median gender pay gaps, and these two companies use the same pay system so it is much more plausible to conclude there is no evidence of gender discrimination on Mars.\u00a0 Otherwise, we would have to conclude that the lovely smell of chocolate causes women to discriminate against men and the horrible smell of (wet) petfood causes men to discriminate against women!<\/p>\n

    Gender Splits Determine Plausible Range of Median Gender Pay Gaps<\/strong><\/span><\/h5>\n

    Now that I have set up my simulation model, I can change the rules for determining gender, pay band and increment to anything I wish.\u00a0 Of particular interest to me is how does the range of plausible median gender pay gaps change if I change the\"\"\u00a0gender split in the organisation?\u00a0 I carried this out using the same pay bands and increments but for three other gender splits, 50%<\/strong> women, 20%<\/strong> women and 10%<\/strong> women.\u00a0 The results for the 95%<\/strong> confidence interval (the plausible range where you would expect the pay gap to end up 95%<\/strong> of the time) are shown in the table.<\/p>\n

    Two things should strike you about this table.\u00a0 For larger companies, any company reporting a median gender pay gap of 5% or less<\/strong> cannot be accused of gender discrimination in the absence of any other evidence.\u00a0 For smaller companies, it is difficult to prove discrimination solely on gender pay gap data, especially when women make up a small proportion of the workforce.\u00a0 This does raise the question of whether the threshold of 250<\/strong> employees is in fact too low and perhaps the threshold should be 1,000<\/strong> employees before a company has to report its gender pay gap.\u00a0 More importantly, it also shows that if you substitute women for a minority (say disabled people) in the scenario where 1 in 10<\/strong> employees are in the minority category, then you will again be unable to draw any meaningful conclusions.\u00a0 This explains why I am opposed to mandatory pay gap reporting for ethnicity, sexuality, disability, etc.<\/p>\n

    Update October 2021<\/em><\/strong><\/span><\/h5>\n

    My opinions on whether mandatory ethnicity and disability pay gap reporting should be introduced in the UK have evolved since I wrote this article.\u00a0 See these articles.<\/em><\/p>\n

      \n
    1. June 2019<\/strong> – My evidence to the Treasury Select Committee on \u201cEffectiveness of Gender Pay Gap Reporting<\/em><\/strong><\/a>\u201d. The last question was about Ethnicity Pay Gaps.<\/li>\n
    2. July 2019<\/strong> – Should the UK introduce Ethnicity Pay Gap Reporting<\/strong><\/a>? I list the statistical, data and ethical challenges that have to be overcome before EPGR can be introduced<\/li>\n
    3. February 2020<\/strong> – How could the UK introduce Ethnicity Pay Gap Reporting?<\/strong><\/a> I explore 5 different ways EPGR could be introduced to overcome the barriers listed in the previous post and whilst I stated a preference for the 5th<\/sup> option, I knew that there were still barriers to overcome.<\/li>\n
    4. November 2020<\/strong> – Why Employers should report their Ethnicity Pay Fingerprints<\/strong><\/a>. My submission to the CRED commission demonstrating why breaking down the 4 pay quarters by ethnicity is the simplest and most insightful way of summarising an employer.\u00a0 This was the moment when I realised that the standard mean & median pay gap calculations needed to be abolished and by focusing on pay quarters, it would be possible for employers of sufficient size to report ethnicity data.\u00a0 However, I automatically assumed that the Big 5 ethnicities would be the categories used.<\/li>\n
    5. June 2021<\/strong> \u2013 My 7+5 recommendations for amending pay gap legislation<\/strong><\/a>. I list 7 recommendations for changing the way employers report their pay gaps (front end) and 5 recommendations for changing what data they have to use in their calculations (back end).\u00a0 Whilst the blog focuses on gender, I wrote the blog with the intention that the amended legislation could also be used for ethnicity provided some issues specific to ethnicity in recommendation 2 were addressed.<\/li>\n
    6. August 2021<\/strong> \u2013 How many ethnic categories should an employer report?<\/strong> <\/a>I address the issues relating to ethnic categories relevant to recommendation 2 of the above post.\u00a0 I look at what categories could be used, how an employer could decide which ones to use, what the minimum number of employees per category should be.\u00a0 Most importantly, I created 676 fictional employers based on the 2011 census to estimate what percentage of employers would be able to report multiple ethnic categories.<\/li>\n
    7. September 2021<\/strong> – My 9-point briefing note for Parliament<\/a><\/strong>.\u00a0 Ahead of two parliamentary debates about ethnicity pay gap reporting in the House of Commons<\/a> and House of Lords<\/a>, I wrote this 9 point briefing note for parliamentarians.\u00a0 Elliot Colburn, who opened the Commons debate, mentioned my name and referred to my note in his speech.<\/li>\n<\/ol>\n

      — Need help with understanding your gender pay gap? —<\/strong><\/span><\/h4>\n

      I offer the following services.<\/p>\n

        \n
      1. Analysis<\/strong><\/span> – I can dig deep into your data to identify the key drivers of your pay gaps.\u00a0 I can build a model using a large number of variables such as pay band, seniority, job function, location, etc and use this to identify the priority areas for closing your gaps.<\/li>\n
      2. Training<\/strong><\/span> – I run training courses in basic statistics which are designed for non-statisticians such as people working in HR.\u00a0 The courses will show you how to perform the relevant calculations in Microsoft Excel, how to interpret what they mean for you and how to incorporate these in an action plan to close your gaps.<\/li>\n
      3. Expert Witness<\/strong><\/span> – Has your gender pay gap data uncovered an issue resulting in legal action?\u00a0 Need an expert independent statistician who can testify whether the data supports or contradicts a claim of discrimination?\u00a0 I have experience of acting as an expert witness for either plaintiff or defendant and I know how to testify and explain complex data in simple language that can be easily understood by non-statisticians.<\/li>\n<\/ol>\n

        If you would like to have a no-obligation discussion about how I can help you, please do contact me<\/a>.<\/p>\n

        — Want to know more about the gender pay gap?\u00a0 —<\/strong><\/span><\/h4>\n

        I have written a number of articles about pay gaps.\u00a0 You can find the full list of my articles grouped by theme here<\/a>.<\/p>\n

        I also comment on pay gaps on my Twitter thread<\/a>.\u00a0 Some notable tweets are here.<\/p>\n

          \n
        1. My complaint about comments made by the head of the TUC on the 2018 pay gap.<\/a><\/li>\n
        2. Some observations on the government’s guidance to producing gender pay gap statistics and the numerous deficiencies in these<\/a>.<\/li>\n
        3. My comments on why incorrect gender pay gap data is being submitted<\/a>.<\/li>\n
        4. At last, the BBC publishes a good article on gender pay gaps!<\/a><\/li>\n<\/ol>\n","protected":false},"excerpt":{"rendered":"

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