learn-people-analytics-with-phoebe / Deep-dive session 10 of 10
Learn People Analytics with Phoebe · Deep-dive session 10 of 10

The pay gap bench, and defending a number

Nine sessions have built one habit: before a people number is believed, ask what it is a count of, what it is divided by, and who is missing from the table. Tonight the habit meets 3,000 real employers. Every one of them filed a gender pay gap in 2024, and every one of them filed the shape of its pay pyramid alongside it. The bench fits, live, the band pay ladder that best explains the reported gaps from the pyramid alone, and shows how much of what a company reports is who sits where rather than who is paid what at the same level. Then it pulls the lever every well-meaning plan reaches for, hire more women, and shows that at the bottom of the pyramid it widens the reported gap it was pulled to close. Then the break button, because a number you cannot make disappear is a number you do not understand. And then the sentence.

🔴 Bench night HR analysts, people data teams, and the leaders they report to Browser only, no code needed 45 min
0-3 · Welcome 3-14 · Reading the pyramid 14-40 · The bench, then the sentence 40-45 · Q&A
Part 0

Where we start

A bench is not a dashboard. A dashboard shows a number; a bench lets you break it. Everything on this page is recomputed from the same 3,000 filings, sampled from the 11,301 usable ones the UK service published for 2024, the moment you touch a control. The employers are real and named in the data; no page names one as good or bad, because the point is the mechanism every one of them shares, not any one of them.

🎫 Clear all three quiz questions to stamp your passport Live = presented in the 45 minutes Self-study = the full depth, after class ★ Bench = every number computed in your browser

★ What you walk out with tonight. A pyramid you can read in one glance, the difference between a gap made of composition and a gap made of pay, the anti-lever you can name when somebody proposes it, and one sentence for a leader that carries the number, what it is made of, and what the filing cannot show.

Part 1 · covers the pyramid and the ladder

Reading the pyramid

8 min live

A UK filing carries four pairs of numbers: the share of men and women in each of four equal-sized pay bands. At the median employer, women are 56 percent of the bottom band and 40 percent of the top, and 81 percent of employers have more women at the bottom than at the top. Give each band a relative pay level, a ladder, and the pyramid alone produces a gap, before anybody in it is paid differently from a colleague at the same level.

THE PYRAMID, THE LADDER, AND THE GAP THEY MAKE TOGETHER median employer of 11,301 filings, 2024 · women's share hatched, men's white · ladder fitted on all filings bottom band 56% women lower middle 53% women upper middle 47% women top band 40% women equal-sized bands by hourly pay 1.00 1.20 1.45 2.80 the fitted ladder relative band pay composition-only 9.8% median, modelled reported 11.0% median, as filed Most of the median filing is the pyramid. The rest, about 2 points, is pay inside the bands, the ladder being steeper than fitted, or hours the filing cannot see.
🔍 Click to zoom - the ladder is fitted, not published; it is the one that best explains 11,301 reported gaps from their pyramids alone
LiveComposition and pay: the two things a gap is made of5 min▶

A reported gap compares the average (or median) hourly pay of all women with that of all men. Two mechanisms feed it. Composition: if women sit lower in the pyramid, their average is lower even when every band pays everyone the same. Within-band pay: if a woman and a man in the same band are paid differently, the gap moves without the pyramid moving. The filing publishes the pyramid and the gap, and nothing about within-band pay, so the second can only be read as what is left after the first.

The ladder is what turns a pyramid into a number. Nobody publishes band pay, so the bench fits the relative pay of the four bands that best explains the reported mean gaps across all 11,301 filings: 1 / 1.20 / 1.45 / 2.80. Under it, composition alone explains R2 0.353 of the variance in reported gaps and produces a median composition-only gap of 9.8 percent against a reported median of 11.0. A third of employers report less than their pyramid alone would, which says within-band pay at those employers runs the other way, or their ladder is flatter than the fitted one.

What the ladder is not: a pay scale. It is a statement about UK filings as a whole, and the bench lets you refit it on any subset so that you can see how much it moves. On the 3,000-row sample it comes out 1 / 1.3 / 1.5 / 3.0, close and not identical, which is the honest amount of uncertainty to carry.

Self-studyWhy "explained by composition" is not "justified"3 min▶

Decomposing a gap into composition and within-band pay is the filing-level cousin of the Oaxaca-Blinder decomposition taught in session 6, and it carries the same trap: the "explained" part is explained by where women are, which is itself the thing most pay-equity work is about. A company whose gap is entirely composition has no within-band pay problem and a very large question about why its top band is 40 percent women. The decomposition tells you which question to ask. It does not answer it, and it does not say the gap is fine.

Build-along · the bench

Four rungs, computed in front of you

★ 20 min · the main event

Work the rungs in order. Read the pyramid, then fit the ladder and read how much it explains, then set composition against reported. Filter to one employer size and watch which numbers move. Then press the anti-lever and read where the women were added. Then press the break button. Say out loud what changed each time.

Read it in this order. The pyramid's bottom and top shares, then the ladder and its R2, then the composition-only median against the reported one. The first five tiles are computed from the filings and carry "computed". The last tile is the anti-lever's projection and carries "modelled", because it assumes the fitted ladder and equal pay inside every band, and no employer has actually done it.

THE ANTI-LEVER: THE SAME WOMEN, TWO PLACES median employer · women equal to 10 percent of headcount added · modelled under the fitted ladder 9.6% as filed 14.9% added at the bottom band -3.2% added at the top band 0 THE LEVER EVERYONE PULLS "We hired more women this year, so the gap should close." It widened, because they were hired at the bottom. Where, not how many. On the bench's 3,000-row sample the three bars read 9.8, 15.1 and -2.9. The mechanism is identical; the profile is the sample's median employer.
🔍 Click to zoom - the red bar is the reported gap after a hiring drive that put its new women in the lowest band, and the drive was real progress by headcount
LiveWhat the break button proves, and what it cannot4 min▶

Press it. Inside every employer the four band shares are shuffled, so each employer keeps exactly its shares of women and men and loses only the order they sit in. The R2 of composition against reported gaps collapses from 0.41 on the sample to about -1.8, which is worse than predicting every employer's gap with the overall mean. Composition explains the gap only when the pyramid is the right way up, which is the whole claim. Press again and the real order comes back with the real R2.

What it cannot prove is that any employer's gap is composition rather than pay. The bench models equal pay within bands because the filing shows nothing within bands; the residual is everything the model cannot see, and at a given employer that residual might be pay, hours, part-time patterns or a steeper ladder. The decomposition names the question. The pay equity regression in session 6, on data the filing does not contain, is what answers it.

Part 2 · covers the sentence for the meeting

Defending the number

6 min live

A people number is defended by saying what it is made of. For a gap: the reported figure, the share of it the pyramid produces, the residual the filing cannot explain, and the two things a leader can actually change, where people are hired and promoted, and what they are paid at the same level. For attrition: the flow, the base, the period, the assumption. The sentence is short, and every clause in it has a number behind it that the bench or the bridge can reproduce.

WHERE THE REAL R2 SITS AGAINST 100 SHUFFLES placebo: bands shuffled inside every employer, refit under the ladder, 100 times · mean -1.84, sd 0.07 -2.0 -1.84 0 real order: R2 0.41 +0.41 the pyramid, the right way up shuffled: worse than the mean "Our reported gap is 11 percent; about 9 of it is the pyramid, women being 56 percent of the bottom band and 40 of the top; the rest the filing cannot explain. Hiring women at the bottom widens it. The levers are promotion and same-level pay, and the audit is next."
🔍 Click to zoom - the hump is what chance produces when the bands are in the wrong order; the moss dot is what the real filings produce
LiveThe sentence, and the three questions it survives4 min▶

"So is the gap composition or pay?" Mostly composition at the median employer, about 9 points of 11 under the fitted ladder, and the filing cannot see the rest; it could be pay, hours or a steeper ladder. The same-level question needs the salary table, which is session 6's regression, not the filing.

"So we should hire more women?" Where. Added to the bottom band the modelled gap goes from 9.6 to 14.9; added to the top it goes to -3.2. The pyramid is a promotion and hiring-level question before it is a headcount question.

"How do you know the pyramid explains anything?" Shuffle the bands inside every employer and composition explains nothing, R2 below zero, every time. The real order explains 0.35 of the variance across 11,301 employers and 0.41 on the sample; the two numbers are quoted together because the difference is the honest width.

Self-studyWhat the bench does not show, so you do not claim it2 min▶

It does not show any employer's within-band pay, hours or part-time share; the filing does not contain them. It does not show the national gap: the ONS figures of 7.0 percent full-time and 13.1 percent all employees for April 2024 are economy-wide hourly-earnings medians, not per-employer medians, and are not comparable to the filing numbers. It does not rank employers. And it does not say a gap made of composition is acceptable; it says which lever the gap responds to.

Every rate on the page has its base written under it, and the base is a headcount computed as a function of a date, not a column. Deep-dive session 1. Apex: 210 over 1,022, 941.5 or 861 is 20.5, 22.3 or 24.4 percent.
The bridge reconciles: start plus joiners minus leavers equals end, asserted in code. Deep-dive session 1. 1,022 + 49 - 210 = 861.
I can say who is not in the table, and every tenure or survival number carries that caveat. Deep-dive session 2. A snapshot holds only the people who survived to be photographed; the Apex curve is biased upward for that reason.
Any annualised or benchmarked figure states its arithmetic and its assumption. Deep-dive session 3. 44.6 is 22.3 doubled and assumes H2 repeats H1; a monthly quits rate times 12 is a rough scale, not an annual rate.
"Regretted", "engaged" and every other classification is shown as a choice with the categories visible. Deep-dive sessions 3 and 7. 137 of 210 is regretted under one list of five categories; a different list gives a different share.
For a pay gap I can say how much the pyramid produces and how much the filing cannot explain, and I have the placebo behind the first number. The bench. About 9 of 11 points; R2 0.35 on all filings, 0.41 on the sample, below zero when the bands are shuffled.
I can name the anti-lever when somebody proposes it, with the two modelled figures side by side. The bench. Women added at the bottom band: 9.6 to 14.9; at the top: -3.2.
Nothing on the page computes a protected characteristic the law forbids, and any automated decision on people has its audit named. Deep-dive session 9. GDPR Articles 9 and 22, the EU AI Act's Annex III, New York's Local Law 144; the AI + HR course for the simulator.
Homework

After the bench

30 min
  1. Filter the bench to each employer size in turn and write the fitted ladder and R2 for each. Say in one sentence whether the ladder is steeper or flatter for large employers, and by how much.
  2. Find your own employer's filing on the gov.uk service (any UK employer with 250 or more staff has one). Write its four female band shares and its two gaps, then compute its composition-only gap under the fitted ladder by hand.
  3. Run the anti-lever on your own pyramid with women added at the bottom and at the top. Write both figures beside the filed gap.
  4. Write the sentence for your own organisation, in the shape from Part 2, with blanks where you do not yet have the number. The blanks are the work plan.
Check yourself

Three questions

Clear all three and deep-dive session 10 gets stamped in your passport.

1 · A leader says "we hired 10 percent more women this year, so the gap should have closed". The bench says what?

The pyramid produces most of the median filing. Women added at the bottom make the pyramid steeper and the gap wider, and the hiring drive was real progress by headcount. The lever is level, not count.

2 · What does the break button demonstrate, and what does it not?

A detector that cannot be made to fail has not been tested; the shuffle is the failing state. Removing the pyramid's order removes composition's explanatory power and nothing else.

3 · Which is the sentence that defends the number?

The number, what it is made of, what the filing cannot show, the anti-lever, the levers, and the next step. Option B compares a per-employer median with an economy-wide one, which the page says is not a comparison.

Sources covered

What this session teaches, and where it came from

✓Every share, median, ladder, R2 and placebo figure on the benchComputed in the browser from 3,000 employers' 2024 filings sampled from the gov.uk gender pay gap service (Open Government Licence v3.0); the same code agrees with the offline build exactly on every deterministic number and on the placebo to within 0.01
✓The fitted ladder 1 / 1.20 / 1.45 / 2.80 and the full-set figures: R2 0.353, composition-only median 9.8, 33.8 percent below, anti-lever 9.57 / 14.88 / -3.18Computed from all 11,301 usable 2024 filings offline; the ladder and the anti-lever are modelled under equal pay within a band and the page says so
✓The six UK figures and the four bandsEquality Act 2010 (Gender Pay Gap Information) Regulations 2017, read at source
◐ONS 7.0 and 13.1 percent, April 2024Named as economy-wide medians that are not comparable with filing medians
◐Oaxaca-Blinder, and the law on automated people decisionsNamed; sessions 6 and 9 own them

Every fact on this page, and its verification tier, is recorded in the course's source map.

Deep-dive session 10 cheat sheet · pin this

A gap is composition plus payThe filing shows the pyramid and the gap, and nothing inside a band.
The fitted ladder1 / 1.20 / 1.45 / 2.80 on 11,301 filings; 1 / 1.3 / 1.5 / 3.0 on the sample. Quote both.
Composition explains R2 0.35Median composition-only gap 9.8 against 11.0 reported; a third report less than their pyramid.
The anti-leverSame women: bottom band 9.6 to 14.9; top band to -3.2. Where, not how many.
The placeboShuffle the bands: R2 -1.84. The order is the whole claim.
The sentenceNumber, what it is made of, what the filing cannot show, the anti-lever, the levers, the next step.