I call upon Parliament to abolish the **Gender Pay Gap** by requiring employers to report their **Gender Swap Number** instead. When presented alongside an employer’s **Gender Pay Fingerprint**, the **Gender Swap Number** tells everyone how much work the employer needs to do to eliminate their gender pay gap and allows for a fairer comparison between employers.

**This article assumes you are familiar with these terms**

If not, I recommend you read these articles of mine which explain them in more depth.

**Median & the median gender pay gap**– the linked article explains what a median pay gap is and how to spot incorrect pay gaps. The method of spotting incorrect pay gaps is recast in a different role in this article and will become the**Gender Swap Number.****Eliminating a pay gap**– the linked article discusses a fictional employer with a pay gap today, what it would look like in the future when their pay gap is eliminated and how long it will take an employer to get there. The same concepts will appear again in this article.**Pay Fingerprints**(**Gender & Ethnicity**) – two linked articles (one for gender, one for ethnicity) explain why pay fingerprints are a simple but powerful graphic for understanding why an employer has a pay gap today. It’s not strictly necessary to read these for this article but I will show that**Pay Fingerprints**are a natural complement to the concept of a**Gender Swap Number**.

**How can a 65% pay gap be eliminated?**

Take a look at this fictional employer with 16 employees (8 men & 8 women) where the median woman earns 35p for every £1 earned by the median man.

It should be obvious that the reason for the large gap between the median man and median woman is because there are more women than men in the lower pay half (75% female) and more men than women in the upper pay half (75% men).

For the median man and median woman to be paid the same, they have to be standing in the same place as the median employee when employees are standing in a line based on their pay as above. The definition of the median means that when the median man stands in the line above, he must see the same number of men to his left and to his right. Likewise when the median woman stands in the line above, she must see the same number of women to her left and to her right.

This can be achieved if two women from the lower pay half swap places with two men from the upper pay half as shown below.

With that swap, there are now 4 men & 4 women in the lower pay half and 4 men & 4 women in the upper half. Since we have an even number of men and women overall, the median man is the average of the two men standing in the middle of the male line (£25 & £40) and the median woman is the average of the two women standing in the middle of the female line (£30 & £35). In this instance those averages turn out to be the same and the median gender pay gap has been eliminated.

**The Gender Swap Number**

The numbers of women and men that need to swap pay halves is the **Gender Swap Numbe**r.

In the above example, I am defining it to be +2 to denote the fact that 2 women from the LOWER pay half needed to swap places with 2 men from the UPPER pay half to eliminate the median pay gap.

If the gender pay gap had favoured women in the first example (imagine every employees flips gender) then the Gender Swap Number would be -2 to denote that 2 women from the UPPER pay half need to swap places with 2 men from the LOWER pay half to eliminate the median pay gap

**Important! ** Ethnicity Swap Numbers or indeed Swap Numbers for any protected characteristic can be calculated in exactly the same way. The +2 calculated here could have easily been the number of purple employees that need to swap places with green employees. What I have written here can be added to my 7 Recommendations for Ethnicity Pay Gap Reporting.

There are many names I could have used for this concept (and I am open to suggestions) but for now, I’ve deliberately chosen the word **Swap** to focus on the key point that men and women have to swap places by pay halves to close a pay gap. 99% of the time, this does not involve real human beings swapping jobs e.g. male managers becoming male secretaries, female secretaries becoming female managers, it will happen by the respective men and women leaving the company or being promoted (or demoted) and the respective vacancies being filled by a person of the opposite gender.

**The Gender Swap Number Calculation in Full**

A swap number of +2 for an employer of 16 employees is clearly a very different proposition for a swap number of +2 for an employer of 16,000 so the swap number needs to be expressed as a percentage or a rate. But percentage/rate of what? Here I lay out the step by step calculation in full for anyone who wants to do the calculations. Feel free to use the example above to follow the calculations here.

**Count the number of men and women in each of the 4 pay quarters.**- You will have already done this calculation if you are legally obliged to submit gender pay gap data to the government.

**Count the number of men and women in each of the 2 pay halves**. This is simply combining the relevant pay quarters i.e.**LHM**= Lower Half Men = Number of men in lower pay quarter + number of men in lower middle pay quarter.**LHF**= Lower Half Women = Number of women in lower pay quarter + number of women in lower upper pay quarter.**UHM**= Upper Half Men = Number of men in upper pay quarter + number of men in upper middle pay quarter.**UHF**= Upper Half Women = Number of women in upper pay quarter + number of women in upper upper pay quarter.

**Calculate the Swap Numbers separately for each gender**:-**MSN**= Male Swap Number = (LHM – UHM)/2 = ( number of men in lower pay half – number of men in upper pay half )/2**FSN**= Female Swap Number = (LHF – UHF)/2 = ( number of women in lower pay half – number of women in upper pay half )/2- By definition MSN & FSN must have opposite signs unless one or both are equal to zero e.g. if FSN is +10 then MSN should be -10 but can be -9 or -11 if one gender has an even number of employees and the other gender has an odd number of employees.

**Calculate the Gender Swap Number (Rate per 1000 employees)****GSN = Gender Swap Number**= (FSN – MSN)/2 = we subtract one from the other because MSN & FSN have opposite signs as explained above.**GSN1****K**=**Gender Swap Number Rate per 1000 Employees**=**GSN*** 1000 / Total Number of Employees (LHF + UHF + LHM + UHM)

**OPTIONAL – Calculate the Gender Swap Percentages.**- Female Swap Percentage = FSN / Total number of women (LHF + UHF)
- Male Swap Percentage = MSN / Total number of men (LHM + UHM)

So if you’ve followed the calculations correctly and used the data from the example seen earlier, you should get a **Gender Swap Number (GSN**) of +2 which equates to a **Gender Swap Number Rate per 1000 Employees (GSN1K)** of +125 i.e. for every 1000 employees, 125 women from the lower pay half will have to swap places with 125 men from the upper pay half.

An alternative is to use the **Gender Swap Percentages** instead where you should end with a **Female Swap Percentage** of +25% and a **Male Swap Percentage **of -25%. This means that 25% of the women (from the lower pay half) need to swap places with 25% of the men (from the upper pay half).

Note that in our example we had equal numbers of men and women. If there is an imbalance of men and women in the employer then the gender swap percentages will be different. For example, if an employer has 100 men and 20 women and the gender swap number is +4 then the Female Swap Percentage is +20% and the Male Swap Percentage is -4%.

**Does a Gender Swap Number of 0 mean there is no gender pay gap?**

Most of the time the answer is yes but occasionally there can still be a median gender pay gap. However, such pay gaps would be purely statistical ones due to random chance and are not indications of a genuine median pay gap. The following example shows a man and women swapping places in the lower pay half leading to an artificial median pay gap which is not meaningful.

Of course there can still be a difference between the average man and the average woman even if the median gender pay gap is zero. In all the examples shown here, the average man is earning more than the average woman.

**Does a Gender Pay Gap of 0 mean the Gender Swap Number is also 0?**

Most of the time the answer is yes but there is one situation when it is not the case which is common among minimum wage employers. The following example shows an employer with 7 women & 9 men who pays 12 out of 16 employees the same rate of £10 per hour. The median man is paid the same as the median woman but the Gender Swap Number is not zero but +1.

In such employers, the median gender pay gap is misleading since when we look at the upper pay quarter, we see 1 woman and 3 men with the two highest paid employees being men. This is a situation where the mean gender pay gap is more meaningful than the median but you have to be able to recognise such situations as exceptions which is not always obvious to someone who is not a statistical thinker. The Gender Swap Number overcomes this issue and gives a fairer picture than either the median or mean gender pay gap.

**Gender Swap Numbers are fairer than Gender Pay Gaps**

In the previous two sections I showed examples of how the Gender Swap Number gives a better measure of an employer than a gender pay gap statistic. There is a 3rd & more compelling reason why swap numbers give a fairer picture of an employer than pay gaps.

Let’s look back at my original example below where the median woman earns 35p for every £1 earned by the median man.

Now take a look at this example where the median woman earns 65p for every £1 earned by the median man.

What is the gender swap numbers for these two examples? It’s +2 for both of them even though the median gender pay gaps are very different. In other words, both employers have to do the same amount of work to eliminate their pay gaps but the effect of these interventions will be very different on the median pay gap. The reason for the discrepancy is obvious, the pay scale is narrower for the second example compared to the first example.

I believe the purpose of gender pay gap reporting is to encourage employers to look at their own data and see why they have pay gaps. They then need to identify how to close their pay gaps. If two employers need to do the same amount of work to close a gap then I think it is unfair to compare their median pay gaps if these are also affected by the payscales used by the employers. This is why I say Gender Swap Numbers are fairer to employers from the point of comparison.

**How long will it take an employer to reduce their GSN to zero?**

In other words, how long will it take an employer to genuinely, not artificially, eliminate their gender pay gap?

I answered this question in my article “** Eliminate your pay gap by playing Blackjack**” where I demonstrated that closing pay gaps takes longer than you think even if employers have 50:50 male:female candidate pools for vacancies & promotions and there is no discrimination at any point. If you have not read this article, I strongly recommend you do so since the outcome as illustrated in these charts (explained in the article) is quite sobering and requires a distinct strategy in order to shorten the time to equality.

**Should a gender swap number of zero be the goal?**

So should employers be setting themselves the goal of reducing their gender swap number to zero? The answer is that this is a necessary step to eliminate a pay gap but it may not be sufficient on its own. Conversely, there is no way at all a pay gap can genuinely be eliminated without reducing the gender swap number to zero.

This is where I recommend the gender swap number is married with the gender pay fingerprint. Fingerprint is my term for the 4 pay quarters that an employer has to report on. The point to look out for is that even if the gender ratio of each pay half is the same (which is the outcome if the gender swap number is zero), the gender ratios of the pay quarters need not be the same. Take a look at the next two examples to see this. The first example is what we saw earlier when the employer changed their gender swap number from +2 to zero, the second example still has a gender swap number of zero but two more pairs of employees have swapped places.

In the first example, the proportion of women in each pay quarter reading from left to right is 75%, 25%, 50%, 50%.

In the second example, the proportion of women in each pay quarter reading from left to right is 75%, 25%, 75%, 25%.

In other words, women are less likely to found in the higher paid roles in the second example. It is the pay fingerprint that highlights this.

So there you have it. I hope you agree with me that Gender Swap Numbers are easy to calculate, easy to interpret, fairer to employers when making comparisons and also give a metric which can be used to track progress.

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