Are Cleveland Police correct to claim they have no gender pay gap?<\/strong><\/span><\/h4>\n![\"\"](\"https:\/\/marriott-stats.com\/nigels-blog\/wp-content\/uploads\/2020\/08\/Error-Spotting-Cleveland-Police-300x283.png\")
Here are the vital statistics for the Cleveland Police force in 2018<\/a> created from my free downloadable tool which has data for over 11,700 employers<\/a>.\u00a0 They state that for every \u00a31 earned by the median man, the median woman also earns \u00a31.\u00a0 They also state that just over 20% of the two highest paying income quarters and just under a half of the two lowest paying income quarters are women.\u00a0 Is it mathematically possible to have data like this?<\/p>\n5 Percentiles in brief<\/strong><\/span><\/h4>\nLet’s remind ourselves of the definition of the median, quartiles and quarters.\u00a0 In the graphic below, I have an employer with 7 men and 5 women who are standing in a line in order of their hourly earnings.\u00a0 The line has been split into four equal sized groups of employees with 3 employees in each group which are called Income Quarters.<\/strong><\/span><\/p>\n![\"\"](\"https:\/\/marriott-stats.com\/nigels-blog\/wp-content\/uploads\/2020\/08\/Error-Spotting-Quarters-2-300x76.png\")
<\/p>\n
Median, Quartiles and Quarters are all subsets of a wider group of statistics known as Percentiles<\/strong><\/span>.\u00a0 From left to right in the graphic above a number of percentiles are given their own name and the following 5 percentiles are the boundaries that surround and define the 4 Income Quarters<\/strong><\/span>.<\/p>\n\n- 0th percentile is the Minimum<\/strong><\/span> = \u00a310 per hour<\/li>\n
- 25th percentile is the Lower Quartile<\/strong><\/span> = \u00a310 per hour<\/li>\n
- 50th percentile is the Middle Quartile<\/strong><\/span> better known as the Median<\/strong><\/span> = \u00a317.50 per hour = average of the two men in the middle earning \u00a315 & \u00a320 per hour.<\/li>\n
- 75th percentile is the Upper Quartile<\/span><\/strong> = \u00a330 per hour = average of the two men earning \u00a325 & \u00a335 hour.<\/li>\n
- 100th percentile is the Maximum<\/span><\/strong> = \u00a350 per hour<\/li>\n<\/ul>\n
Every employee can therefore be compared to these 5 boundaries to decide which income quarter they are in.\u00a0 So a man earning \u00a325 an hour lies between the median and the upper quartile and is in the upper middle income quarter.<\/p>\n
How the laws of Mathematics work<\/span><\/strong><\/h4>\nIn the bottom two quarters (the 6 employees earning less than the median), there are 3 men and 3 women i.e. the gender ratio is 50:50 men:women.\u00a0 The alternative method getting to this ratio is to observe that 1\/3 of staff in the lower income quarter are women and 2\/3 of staff in the lower middle income quarter are women.\u00a0 The average of these two numbers (1\/3 & 2\/3) is 1\/2 hence 50% of staff in the lower half of the hourly earnings line are women.\u00a0 We can take such an average since there are equal number of staff in each quarter.<\/p>\n
In the top two quarters (the employees earning more than the median), there are 4 men and 2 women i.e. the gender ratio is 67:33 men:women.\u00a0 The alternative method of getting to this ratio is to observe that 1\/3 of staff in the upper income quarter are women and 1\/3 of staff in the upper middle income quarter are women.\u00a0 The average of these two numbers (1\/3 & 1\/3) is 1\/3 hence 33% of staff in the upper half of the hourly earnings line are women.\u00a0 We can take such an average since there are equal number of staff in each quarter.<\/p>\n
I define the Gender Ratio Differential<\/strong><\/span> (GRaD<\/strong><\/span>) to be the difference between these two ratios i.e.<\/p>\nGRaD = Gender Ratio of Top Half – Gender Ratio of Bottom Half = 67:33 – 50:50 = +17 : -17<\/strong><\/span><\/p>\nCan you see why if the GRaD for women is negative (-17 in this instance) then the median woman must be earning less than the median man?\u00a0 Conversely if the GRaD for women had been positive instead, the median woman would be earning more than the median man?<\/p>\n
The median woman is the woman standing in the middle of the female only line (5 in all) when sorted by hourly earnings.\u00a0 She is highlighted in the graphic above and is earning \u00a315 per hour.\u00a0 A negative GRaD for women tells us that a majority of women are in the bottom half of the overall income line.\u00a0 That majority must include the median woman since by definition of the median, there are equal numbers of women on either side of her in the line.\u00a0 To make up a majority, the median woman has to be part of that majority and consequently she ends up in the bottom half of the overall hourly earnings line.<\/p>\n
The median man is the man standing in the middle of the male only line (7 in all) when sorted by hourly earnings.\u00a0 He is highlighted in the graphic above and is earning \u00a320 per hour.\u00a0 A positive GRaD for men tells us that a majority of men are in the top half of the overall hourly earnings line.\u00a0 That majority must include the median man since by definition of the median there are equal numbers of men on either side of him in the line.\u00a0 To make up a majority, the median man has to be part of that majority and consequently he ends up in the top half of the overall hourly earnings line.<\/p>\n
Thus the median woman earns less than the median man because the GRaD for women is negative.\u00a0 If the GRaD for women had been positive, the median woman would earn more than the median man.<\/p>\n
Cleveland Police’s GRaD is negative for women<\/span><\/strong><\/h4>\nCleveland Police’s GRaD can be calculated as follows –<\/p>\n
Cleveland Police GRaD = 78.5 : 21.5\u00a0 –\u00a0 52 : 48 = +26.5 : -26.5<\/span><\/strong><\/p>\nYou should be able to work out that the average % of women in the top two quarters is 21.5% (= average of 21% & 22%) and in the bottom two quarters is 48% (= average of 41% & 55%).<\/p>\n
Since the GRaD for women is negative, the median woman at Cleveland Police must be earning less than the median man and hence their reported gender pay gap is incorrect.<\/p>\n
There is another logic that can be used to explain why this is so.\u00a0 The median woman is the woman standing in the middle of a female only line when the women are standing in order of their hourly earnings.\u00a0 If we assume that the %s in the Cleveland Police chart represent actual numbers of employees of each gender in each quarter, then they would have 261 men (=79+78+59+45) and 139 women (=21+22+41+55).\u00a0 The man in the middle of the male line is the 131st man and the woman in the middle of the female line is the 70th woman.\u00a0 Counting from the lower income quarter, the 131st man must be in the upper middle income quarter since there are 104 (=59+45) in the bottom two quarters.\u00a0 Likewise, the 70th woman must be in the lower middle income quarter since there are 55 women in the lower income quarter.<\/p>\n
The advantage of the alternative logic is that it tells you which quarter the median man and woman are in where as the GRaD calculation simply tells you which half they are in.<\/p>\n
The exception to the rule<\/strong><\/span><\/h4>\nThe GRaD calculation is a very easy one to do in your head whenever you are reading a gender pay gap report for an employer.\u00a0 \u00a0However, there is an exception to the rule that you have to be aware of and if you’ve understood the concept of the Gender Ratio Differential, you may have spotted it already.<\/p>\n
Compare these two graphics below.\u00a0 The first is the same 12 employee example I used earlier, the second also has 12 employees who line up in the same order but have different hourly earnings.<\/p>\n
<\/p>\n
![\"\"](\"https:\/\/marriott-stats.com\/nigels-blog\/wp-content\/uploads\/2020\/08\/Error-Spotting-Quarters-Exception-300x76.png\")
<\/p>\n
For the new graphic, laws of maths tell you that the median woman is again in the lower middle income quarter and the median man is in the upper middle income quarter.\u00a0 This time though both the median man and median woman are earning the same \u00a310 per hour i.e. there is no gender pay gap.<\/p>\n
The reason is obvious.\u00a0 9 out of the 12 employees earn exactly the same i.e. \u00a310 per hour.\u00a0 This includes 4 of the 5 women and 5 of the 7 men.\u00a0 Basically when a majority of staff are earning exactly the same and the effect is seen in both men and women, then by definition of the median, the median man must be earning the same as the median woman hence the gender pay gap is the same even though the GRad is not zero for both genders.<\/p>\n
![\"\"](\"https:\/\/marriott-stats.com\/nigels-blog\/wp-content\/uploads\/2020\/08\/Error-Spotting-Lees-Cleaning-300x283.png\")
What kind of industries see lots of staff earning the same pay rate?\u00a0 Lees Cleaning with a GRaD of +13.5 : -13.5 shown here are an example and that shouldn’t surprise us since the cleaners are very likely to be earning the minimum wage.\u00a0 Hospitality and Care sectors also pay a lot of their staff a basic wage and it so happens that these are the 3 industries where you are most likely to find employers with no median gender pay gap.\u00a0 They can still have a mean gender pay gap which will be driven by the salaries of the managers and directors but the median is often zero.<\/p>\n
This exception means I need to modify my GRaD rule<\/p>\n
\n- If the GRaD is 0:0 then the median gender pay gap must be zero.<\/span><\/li>\n
- If the median gender pay gap is zero then the GRaD does not have to be zero if the employer is likely to have a majority of staff on the same pay scale.<\/span><\/li>\n
- If the employer has a pay system with a lot of pay scales then for the median gender pay gap to be zero, the GRaD must be zero as wel<\/span>l.<\/li>\n<\/ol>\n
Do we know if Cleveland Police come under rule 2 as above.\u00a0 The answer is no they don’t since when we read their gender pay gap narrative<\/a>, I find this paragraph that explains how they did their calculation at the bottom of page 1.<\/p>\n“The calculation of the median average involves listing all the hourly rates in ascending order and picking the middle rate if the i.e.: 45 hourly rates in the list the 23 hourly rate in the median. If there are 46 in the list the median would be the mean of the hourly rates 23 and 24.”<\/em><\/span><\/p>\nThis clearly refers to 40 odd pay rates so rule 2 doesn’t apply.\u00a0 It also explains why they made a mistake.\u00a0 They were taking the median pay scale not the median woman.\u00a0 Before you say “how stupid<\/em>” I had already warned the EHRC (Equality & Human Rights Commission) in point 2 of this post “12 ways to improve gender pay gap reporting<\/a><\/em>” that the statutory guidance was very poorly written and easily misunderstood by those who do not have statistical skills.<\/p>\nGRaD can identify other errors.<\/span><\/strong><\/h4>\n![\"\"](\"https:\/\/marriott-stats.com\/nigels-blog\/wp-content\/uploads\/2020\/08\/Error-Spotting-Hair-Care-300x283.png\")
Take a look at HairCare Ltd here.\u00a0 Have they made an error?\u00a0 If so, what did they do wrong?<\/p>\n
Their GRaD is -17.5 : +17.5 i.e. positive for women.\u00a0 By the rules I’ve set out here, the median woman should be earning more than the median man.\u00a0 Yet they are claiming that the median woman earns 41 pence in the pound less than the median man.\u00a0 That can’t be right.<\/p>\n
In case you’re thinking, this might be a majority minimum wage payer, the exception is not relevant here because they are not claiming their median gender pay gap is zero.\u00a0 The exception is only relevant to employers claiming no gender pay gap.<\/p>\n
What could they have done wrong here?\u00a0 Unfortunately they do not provide a written narrative but two possibilities suggest themselves to me.<\/p>\n
\n- They inadvertently entered 98% for women in the upper income quarter when they submitted their data to the government’s gender pay gap portal when they intended to enter 98% for men and 2% for women.<\/li>\n
- They really do have a gender pay gap in favour of women i.e. the median woman earns more than the median man as indicated by their GRaD.\u00a0 But when entering such a pay gap on the government portal, you have to enter it as -41% if the pay gap favours women.\u00a0 If they entered +41% instead, it will be counted as a pay gap favouring men.<\/li>\n<\/ol>\n
I don’t which is correct but clearly they need to take a look at their submission again.<\/p>\n
<\/p>\n
– Want to know more about spotting errors?\u00a0 –<\/strong><\/span><\/h4>\nI have written a number of articles about errors made in gender pay gap calculations.<\/p>\n
\n- Why the gender pay gap is not the same as unequal pay<\/a><\/li>\n
- Three distinct errors that have been made by at least 10% of all organisations when submitting their gender pay gap data<\/a><\/li>\n
- How to distinguish between a true pay gap and a pay gap that arises naturally due to the laws of chance<\/a><\/li>\n
- Why Gender Pay Fingerprints are superior to Gender Pay Gaps<\/a><\/li>\n
- My 12 steps to improve public confidence in gender pay gap data<\/a><\/li>\n
- How to identify unusual year on year changes in gender pay gaps<\/a><\/li>\n<\/ol>\n
Finally visit my Twitter thread<\/a> to see my comments on gender pay gaps in the media.\u00a0 Some notable ones are here.<\/p>\n\n- Some observations on the government’s guidance to producing gender pay gap statistics and the numerous deficiencies in these<\/a>.<\/li>\n
- My comments on why incorrect gender pay gap data is being submitted.<\/a><\/li>\n<\/ol>\n
<\/p>\n
– Need help with interpreting your pay gaps? –<\/strong><\/span><\/h4>\nI offer the following services.<\/p>\n
\n- Analytics<\/span><\/strong><\/span><\/a>\u00a0– 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
- Training<\/span><\/strong><\/span><\/a> – 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
- Expert Witness<\/span><\/strong><\/span><\/a> – 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 as can be seen from my testimony to the Treasury Select Committee<\/a>.<\/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 <\/p>\n
Here are the vital statistics for the Cleveland Police force in 2018<\/a> created from my free downloadable tool which has data for over 11,700 employers<\/a>.\u00a0 They state that for every \u00a31 earned by the median man, the median woman also earns \u00a31.\u00a0 They also state that just over 20% of the two highest paying income quarters and just under a half of the two lowest paying income quarters are women.\u00a0 Is it mathematically possible to have data like this?<\/p>\n5 Percentiles in brief<\/strong><\/span><\/h4>\nLet’s remind ourselves of the definition of the median, quartiles and quarters.\u00a0 In the graphic below, I have an employer with 7 men and 5 women who are standing in a line in order of their hourly earnings.\u00a0 The line has been split into four equal sized groups of employees with 3 employees in each group which are called Income Quarters.<\/strong><\/span><\/p>\n<\/p>\n
Median, Quartiles and Quarters are all subsets of a wider group of statistics known as Percentiles<\/strong><\/span>.\u00a0 From left to right in the graphic above a number of percentiles are given their own name and the following 5 percentiles are the boundaries that surround and define the 4 Income Quarters<\/strong><\/span>.<\/p>\n\n- 0th percentile is the Minimum<\/strong><\/span> = \u00a310 per hour<\/li>\n
- 25th percentile is the Lower Quartile<\/strong><\/span> = \u00a310 per hour<\/li>\n
- 50th percentile is the Middle Quartile<\/strong><\/span> better known as the Median<\/strong><\/span> = \u00a317.50 per hour = average of the two men in the middle earning \u00a315 & \u00a320 per hour.<\/li>\n
- 75th percentile is the Upper Quartile<\/span><\/strong> = \u00a330 per hour = average of the two men earning \u00a325 & \u00a335 hour.<\/li>\n
- 100th percentile is the Maximum<\/span><\/strong> = \u00a350 per hour<\/li>\n<\/ul>\n
Every employee can therefore be compared to these 5 boundaries to decide which income quarter they are in.\u00a0 So a man earning \u00a325 an hour lies between the median and the upper quartile and is in the upper middle income quarter.<\/p>\n
How the laws of Mathematics work<\/span><\/strong><\/h4>\nIn the bottom two quarters (the 6 employees earning less than the median), there are 3 men and 3 women i.e. the gender ratio is 50:50 men:women.\u00a0 The alternative method getting to this ratio is to observe that 1\/3 of staff in the lower income quarter are women and 2\/3 of staff in the lower middle income quarter are women.\u00a0 The average of these two numbers (1\/3 & 2\/3) is 1\/2 hence 50% of staff in the lower half of the hourly earnings line are women.\u00a0 We can take such an average since there are equal number of staff in each quarter.<\/p>\n
In the top two quarters (the employees earning more than the median), there are 4 men and 2 women i.e. the gender ratio is 67:33 men:women.\u00a0 The alternative method of getting to this ratio is to observe that 1\/3 of staff in the upper income quarter are women and 1\/3 of staff in the upper middle income quarter are women.\u00a0 The average of these two numbers (1\/3 & 1\/3) is 1\/3 hence 33% of staff in the upper half of the hourly earnings line are women.\u00a0 We can take such an average since there are equal number of staff in each quarter.<\/p>\n
I define the Gender Ratio Differential<\/strong><\/span> (GRaD<\/strong><\/span>) to be the difference between these two ratios i.e.<\/p>\nGRaD = Gender Ratio of Top Half – Gender Ratio of Bottom Half = 67:33 – 50:50 = +17 : -17<\/strong><\/span><\/p>\nCan you see why if the GRaD for women is negative (-17 in this instance) then the median woman must be earning less than the median man?\u00a0 Conversely if the GRaD for women had been positive instead, the median woman would be earning more than the median man?<\/p>\n
The median woman is the woman standing in the middle of the female only line (5 in all) when sorted by hourly earnings.\u00a0 She is highlighted in the graphic above and is earning \u00a315 per hour.\u00a0 A negative GRaD for women tells us that a majority of women are in the bottom half of the overall income line.\u00a0 That majority must include the median woman since by definition of the median, there are equal numbers of women on either side of her in the line.\u00a0 To make up a majority, the median woman has to be part of that majority and consequently she ends up in the bottom half of the overall hourly earnings line.<\/p>\n
The median man is the man standing in the middle of the male only line (7 in all) when sorted by hourly earnings.\u00a0 He is highlighted in the graphic above and is earning \u00a320 per hour.\u00a0 A positive GRaD for men tells us that a majority of men are in the top half of the overall hourly earnings line.\u00a0 That majority must include the median man since by definition of the median there are equal numbers of men on either side of him in the line.\u00a0 To make up a majority, the median man has to be part of that majority and consequently he ends up in the top half of the overall hourly earnings line.<\/p>\n
Thus the median woman earns less than the median man because the GRaD for women is negative.\u00a0 If the GRaD for women had been positive, the median woman would earn more than the median man.<\/p>\n
Cleveland Police’s GRaD is negative for women<\/span><\/strong><\/h4>\nCleveland Police’s GRaD can be calculated as follows –<\/p>\n
Cleveland Police GRaD = 78.5 : 21.5\u00a0 –\u00a0 52 : 48 = +26.5 : -26.5<\/span><\/strong><\/p>\nYou should be able to work out that the average % of women in the top two quarters is 21.5% (= average of 21% & 22%) and in the bottom two quarters is 48% (= average of 41% & 55%).<\/p>\n
Since the GRaD for women is negative, the median woman at Cleveland Police must be earning less than the median man and hence their reported gender pay gap is incorrect.<\/p>\n
There is another logic that can be used to explain why this is so.\u00a0 The median woman is the woman standing in the middle of a female only line when the women are standing in order of their hourly earnings.\u00a0 If we assume that the %s in the Cleveland Police chart represent actual numbers of employees of each gender in each quarter, then they would have 261 men (=79+78+59+45) and 139 women (=21+22+41+55).\u00a0 The man in the middle of the male line is the 131st man and the woman in the middle of the female line is the 70th woman.\u00a0 Counting from the lower income quarter, the 131st man must be in the upper middle income quarter since there are 104 (=59+45) in the bottom two quarters.\u00a0 Likewise, the 70th woman must be in the lower middle income quarter since there are 55 women in the lower income quarter.<\/p>\n
The advantage of the alternative logic is that it tells you which quarter the median man and woman are in where as the GRaD calculation simply tells you which half they are in.<\/p>\n
The exception to the rule<\/strong><\/span><\/h4>\nThe GRaD calculation is a very easy one to do in your head whenever you are reading a gender pay gap report for an employer.\u00a0 \u00a0However, there is an exception to the rule that you have to be aware of and if you’ve understood the concept of the Gender Ratio Differential, you may have spotted it already.<\/p>\n
Compare these two graphics below.\u00a0 The first is the same 12 employee example I used earlier, the second also has 12 employees who line up in the same order but have different hourly earnings.<\/p>\n
<\/p>\n
<\/p>\n
For the new graphic, laws of maths tell you that the median woman is again in the lower middle income quarter and the median man is in the upper middle income quarter.\u00a0 This time though both the median man and median woman are earning the same \u00a310 per hour i.e. there is no gender pay gap.<\/p>\n
The reason is obvious.\u00a0 9 out of the 12 employees earn exactly the same i.e. \u00a310 per hour.\u00a0 This includes 4 of the 5 women and 5 of the 7 men.\u00a0 Basically when a majority of staff are earning exactly the same and the effect is seen in both men and women, then by definition of the median, the median man must be earning the same as the median woman hence the gender pay gap is the same even though the GRad is not zero for both genders.<\/p>\n
What kind of industries see lots of staff earning the same pay rate?\u00a0 Lees Cleaning with a GRaD of +13.5 : -13.5 shown here are an example and that shouldn’t surprise us since the cleaners are very likely to be earning the minimum wage.\u00a0 Hospitality and Care sectors also pay a lot of their staff a basic wage and it so happens that these are the 3 industries where you are most likely to find employers with no median gender pay gap.\u00a0 They can still have a mean gender pay gap which will be driven by the salaries of the managers and directors but the median is often zero.<\/p>\n
This exception means I need to modify my GRaD rule<\/p>\n
\n- If the GRaD is 0:0 then the median gender pay gap must be zero.<\/span><\/li>\n
- If the median gender pay gap is zero then the GRaD does not have to be zero if the employer is likely to have a majority of staff on the same pay scale.<\/span><\/li>\n
- If the employer has a pay system with a lot of pay scales then for the median gender pay gap to be zero, the GRaD must be zero as wel<\/span>l.<\/li>\n<\/ol>\n
Do we know if Cleveland Police come under rule 2 as above.\u00a0 The answer is no they don’t since when we read their gender pay gap narrative<\/a>, I find this paragraph that explains how they did their calculation at the bottom of page 1.<\/p>\n“The calculation of the median average involves listing all the hourly rates in ascending order and picking the middle rate if the i.e.: 45 hourly rates in the list the 23 hourly rate in the median. If there are 46 in the list the median would be the mean of the hourly rates 23 and 24.”<\/em><\/span><\/p>\nThis clearly refers to 40 odd pay rates so rule 2 doesn’t apply.\u00a0 It also explains why they made a mistake.\u00a0 They were taking the median pay scale not the median woman.\u00a0 Before you say “how stupid<\/em>” I had already warned the EHRC (Equality & Human Rights Commission) in point 2 of this post “12 ways to improve gender pay gap reporting<\/a><\/em>” that the statutory guidance was very poorly written and easily misunderstood by those who do not have statistical skills.<\/p>\nGRaD can identify other errors.<\/span><\/strong><\/h4>\nTake a look at HairCare Ltd here.\u00a0 Have they made an error?\u00a0 If so, what did they do wrong?<\/p>\n
Their GRaD is -17.5 : +17.5 i.e. positive for women.\u00a0 By the rules I’ve set out here, the median woman should be earning more than the median man.\u00a0 Yet they are claiming that the median woman earns 41 pence in the pound less than the median man.\u00a0 That can’t be right.<\/p>\n
In case you’re thinking, this might be a majority minimum wage payer, the exception is not relevant here because they are not claiming their median gender pay gap is zero.\u00a0 The exception is only relevant to employers claiming no gender pay gap.<\/p>\n
What could they have done wrong here?\u00a0 Unfortunately they do not provide a written narrative but two possibilities suggest themselves to me.<\/p>\n
\n- They inadvertently entered 98% for women in the upper income quarter when they submitted their data to the government’s gender pay gap portal when they intended to enter 98% for men and 2% for women.<\/li>\n
- They really do have a gender pay gap in favour of women i.e. the median woman earns more than the median man as indicated by their GRaD.\u00a0 But when entering such a pay gap on the government portal, you have to enter it as -41% if the pay gap favours women.\u00a0 If they entered +41% instead, it will be counted as a pay gap favouring men.<\/li>\n<\/ol>\n
I don’t which is correct but clearly they need to take a look at their submission again.<\/p>\n
<\/p>\n
– Want to know more about spotting errors?\u00a0 –<\/strong><\/span><\/h4>\nI have written a number of articles about errors made in gender pay gap calculations.<\/p>\n
\n- Why the gender pay gap is not the same as unequal pay<\/a><\/li>\n
- Three distinct errors that have been made by at least 10% of all organisations when submitting their gender pay gap data<\/a><\/li>\n
- How to distinguish between a true pay gap and a pay gap that arises naturally due to the laws of chance<\/a><\/li>\n
- Why Gender Pay Fingerprints are superior to Gender Pay Gaps<\/a><\/li>\n
- My 12 steps to improve public confidence in gender pay gap data<\/a><\/li>\n
- How to identify unusual year on year changes in gender pay gaps<\/a><\/li>\n<\/ol>\n
Finally visit my Twitter thread<\/a> to see my comments on gender pay gaps in the media.\u00a0 Some notable ones are here.<\/p>\n\n- Some observations on the government’s guidance to producing gender pay gap statistics and the numerous deficiencies in these<\/a>.<\/li>\n
- My comments on why incorrect gender pay gap data is being submitted.<\/a><\/li>\n<\/ol>\n
<\/p>\n
– Need help with interpreting your pay gaps? –<\/strong><\/span><\/h4>\nI offer the following services.<\/p>\n
\n- Analytics<\/span><\/strong><\/span><\/a>\u00a0– 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
- Training<\/span><\/strong><\/span><\/a> – 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
- Expert Witness<\/span><\/strong><\/span><\/a> – 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 as can be seen from my testimony to the Treasury Select Committee<\/a>.<\/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 <\/p>\n
<\/p>\n
Median, Quartiles and Quarters are all subsets of a wider group of statistics known as Percentiles<\/strong><\/span>.\u00a0 From left to right in the graphic above a number of percentiles are given their own name and the following 5 percentiles are the boundaries that surround and define the 4 Income Quarters<\/strong><\/span>.<\/p>\n Every employee can therefore be compared to these 5 boundaries to decide which income quarter they are in.\u00a0 So a man earning \u00a325 an hour lies between the median and the upper quartile and is in the upper middle income quarter.<\/p>\n In the bottom two quarters (the 6 employees earning less than the median), there are 3 men and 3 women i.e. the gender ratio is 50:50 men:women.\u00a0 The alternative method getting to this ratio is to observe that 1\/3 of staff in the lower income quarter are women and 2\/3 of staff in the lower middle income quarter are women.\u00a0 The average of these two numbers (1\/3 & 2\/3) is 1\/2 hence 50% of staff in the lower half of the hourly earnings line are women.\u00a0 We can take such an average since there are equal number of staff in each quarter.<\/p>\n In the top two quarters (the employees earning more than the median), there are 4 men and 2 women i.e. the gender ratio is 67:33 men:women.\u00a0 The alternative method of getting to this ratio is to observe that 1\/3 of staff in the upper income quarter are women and 1\/3 of staff in the upper middle income quarter are women.\u00a0 The average of these two numbers (1\/3 & 1\/3) is 1\/3 hence 33% of staff in the upper half of the hourly earnings line are women.\u00a0 We can take such an average since there are equal number of staff in each quarter.<\/p>\n I define the Gender Ratio Differential<\/strong><\/span> (GRaD<\/strong><\/span>) to be the difference between these two ratios i.e.<\/p>\n GRaD = Gender Ratio of Top Half – Gender Ratio of Bottom Half = 67:33 – 50:50 = +17 : -17<\/strong><\/span><\/p>\n Can you see why if the GRaD for women is negative (-17 in this instance) then the median woman must be earning less than the median man?\u00a0 Conversely if the GRaD for women had been positive instead, the median woman would be earning more than the median man?<\/p>\n The median woman is the woman standing in the middle of the female only line (5 in all) when sorted by hourly earnings.\u00a0 She is highlighted in the graphic above and is earning \u00a315 per hour.\u00a0 A negative GRaD for women tells us that a majority of women are in the bottom half of the overall income line.\u00a0 That majority must include the median woman since by definition of the median, there are equal numbers of women on either side of her in the line.\u00a0 To make up a majority, the median woman has to be part of that majority and consequently she ends up in the bottom half of the overall hourly earnings line.<\/p>\n The median man is the man standing in the middle of the male only line (7 in all) when sorted by hourly earnings.\u00a0 He is highlighted in the graphic above and is earning \u00a320 per hour.\u00a0 A positive GRaD for men tells us that a majority of men are in the top half of the overall hourly earnings line.\u00a0 That majority must include the median man since by definition of the median there are equal numbers of men on either side of him in the line.\u00a0 To make up a majority, the median man has to be part of that majority and consequently he ends up in the top half of the overall hourly earnings line.<\/p>\n Thus the median woman earns less than the median man because the GRaD for women is negative.\u00a0 If the GRaD for women had been positive, the median woman would earn more than the median man.<\/p>\n Cleveland Police’s GRaD can be calculated as follows – Cleveland Police GRaD = 78.5 : 21.5\u00a0 –\u00a0 52 : 48 = +26.5 : -26.5<\/span><\/strong><\/p>\n You should be able to work out that the average % of women in the top two quarters is 21.5% (= average of 21% & 22%) and in the bottom two quarters is 48% (= average of 41% & 55%).<\/p>\n Since the GRaD for women is negative, the median woman at Cleveland Police must be earning less than the median man and hence their reported gender pay gap is incorrect.<\/p>\n There is another logic that can be used to explain why this is so.\u00a0 The median woman is the woman standing in the middle of a female only line when the women are standing in order of their hourly earnings.\u00a0 If we assume that the %s in the Cleveland Police chart represent actual numbers of employees of each gender in each quarter, then they would have 261 men (=79+78+59+45) and 139 women (=21+22+41+55).\u00a0 The man in the middle of the male line is the 131st man and the woman in the middle of the female line is the 70th woman.\u00a0 Counting from the lower income quarter, the 131st man must be in the upper middle income quarter since there are 104 (=59+45) in the bottom two quarters.\u00a0 Likewise, the 70th woman must be in the lower middle income quarter since there are 55 women in the lower income quarter.<\/p>\n The advantage of the alternative logic is that it tells you which quarter the median man and woman are in where as the GRaD calculation simply tells you which half they are in.<\/p>\n The GRaD calculation is a very easy one to do in your head whenever you are reading a gender pay gap report for an employer.\u00a0 \u00a0However, there is an exception to the rule that you have to be aware of and if you’ve understood the concept of the Gender Ratio Differential, you may have spotted it already.<\/p>\n Compare these two graphics below.\u00a0 The first is the same 12 employee example I used earlier, the second also has 12 employees who line up in the same order but have different hourly earnings.<\/p>\n For the new graphic, laws of maths tell you that the median woman is again in the lower middle income quarter and the median man is in the upper middle income quarter.\u00a0 This time though both the median man and median woman are earning the same \u00a310 per hour i.e. there is no gender pay gap.<\/p>\n The reason is obvious.\u00a0 9 out of the 12 employees earn exactly the same i.e. \u00a310 per hour.\u00a0 This includes 4 of the 5 women and 5 of the 7 men.\u00a0 Basically when a majority of staff are earning exactly the same and the effect is seen in both men and women, then by definition of the median, the median man must be earning the same as the median woman hence the gender pay gap is the same even though the GRad is not zero for both genders.<\/p>\n This exception means I need to modify my GRaD rule<\/p>\n Do we know if Cleveland Police come under rule 2 as above.\u00a0 The answer is no they don’t since when we read their gender pay gap narrative<\/a>, I find this paragraph that explains how they did their calculation at the bottom of page 1.<\/p>\n “The calculation of the median average involves listing all the hourly rates in ascending order and picking the middle rate if the i.e.: 45 hourly rates in the list the 23 hourly rate in the median. If there are 46 in the list the median would be the mean of the hourly rates 23 and 24.”<\/em><\/span><\/p>\n This clearly refers to 40 odd pay rates so rule 2 doesn’t apply.\u00a0 It also explains why they made a mistake.\u00a0 They were taking the median pay scale not the median woman.\u00a0 Before you say “how stupid<\/em>” I had already warned the EHRC (Equality & Human Rights Commission) in point 2 of this post “12 ways to improve gender pay gap reporting<\/a><\/em>” that the statutory guidance was very poorly written and easily misunderstood by those who do not have statistical skills.<\/p>\n Their GRaD is -17.5 : +17.5 i.e. positive for women.\u00a0 By the rules I’ve set out here, the median woman should be earning more than the median man.\u00a0 Yet they are claiming that the median woman earns 41 pence in the pound less than the median man.\u00a0 That can’t be right.<\/p>\n In case you’re thinking, this might be a majority minimum wage payer, the exception is not relevant here because they are not claiming their median gender pay gap is zero.\u00a0 The exception is only relevant to employers claiming no gender pay gap.<\/p>\n What could they have done wrong here?\u00a0 Unfortunately they do not provide a written narrative but two possibilities suggest themselves to me.<\/p>\n I don’t which is correct but clearly they need to take a look at their submission again.<\/p>\n <\/p>\n I have written a number of articles about errors made in gender pay gap calculations.<\/p>\n Finally visit my Twitter thread<\/a> to see my comments on gender pay gaps in the media.\u00a0 Some notable ones are here.<\/p>\n <\/p>\n I offer the following services.<\/p>\n If you would like to have a no-obligation discussion about how I can help you, please do contact me<\/a>.<\/p>\n <\/p>\n\n
How the laws of Mathematics work<\/span><\/strong><\/h4>\n
Cleveland Police’s GRaD is negative for women<\/span><\/strong><\/h4>\n
<\/p>\nThe exception to the rule<\/strong><\/span><\/h4>\n
<\/p>\n<\/p>\nWhat kind of industries see lots of staff earning the same pay rate?\u00a0 Lees Cleaning with a GRaD of +13.5 : -13.5 shown here are an example and that shouldn’t surprise us since the cleaners are very likely to be earning the minimum wage.\u00a0 Hospitality and Care sectors also pay a lot of their staff a basic wage and it so happens that these are the 3 industries where you are most likely to find employers with no median gender pay gap.\u00a0 They can still have a mean gender pay gap which will be driven by the salaries of the managers and directors but the median is often zero.<\/p>\n\n
GRaD can identify other errors.<\/span><\/strong><\/h4>\n
Take a look at HairCare Ltd here.\u00a0 Have they made an error?\u00a0 If so, what did they do wrong?<\/p>\n\n
– Want to know more about spotting errors?\u00a0 –<\/strong><\/span><\/h4>\n
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– Need help with interpreting your pay gaps? –<\/strong><\/span><\/h4>\n
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