Local Authority Typology: Methodology and Cluster Profiles

School Attainment Tool — Technical Report

Published

March 19, 2026

1 Overview

This report describes the construction of a Local Authority (LA) typology for secondary schools in England, developed as part of the School Attainment Tool. The typology groups England’s 152 local authorities into a small number of empirically derived clusters based on a wide range of educational, demographic, workforce, and structural indicators. The aim is to help contextualise school-level performance data — recognising that schools operate in very different local environments — and to support comparisons between similar LAs rather than the national average alone.

The analysis covers four academic years (2021–22 to 2024–25) and is built from school-level panel data linked to DfE KS4 performance tables, school workforce census data, Ofsted inspection outcomes, and pupil absence statistics.

2 Data Sources

The typology draws on four administrative datasets published by the Department for Education (DfE):

Dataset	Source	Years covered
KS4 Performance Tables	DfE (via Explore Education Statistics)	2021–22 to 2024–25
School Workforce Census	DfE (via Explore Education Statistics)	2021–22 to 2024–25
Pupil Absence Statistics	DfE (via Explore Education Statistics API)	2021–22 to 2024–25
Ofsted School Inspections	Ofsted (Official Statistics, Aug 2024 snapshot)	Most recent inspection
EduBase (school register)	DfE Get Information About Schools	Oct 2024 snapshot

All data are at school level and are aggregated to local authority level for the purpose of clustering.

3 Indicator Construction

Over 200 LA-level indicators are constructed from the school-level panel. These are grouped into thematic domains.

3.1 Attainment Indicators

The primary attainment measure is the Attainment 8 (ATT8) score, which measures average performance across eight GCSE subjects (English, mathematics, three further EBacc subjects, and three open slots). Indicators include:

Indicator	Description
`att8_mean`	Mean ATT8 score across all schools in the LA (averaged across years)
`att8_median`	Median ATT8 score
`att8_sd`	Standard deviation of ATT8 — measures within-LA spread of school performance
`att8_cv`	Coefficient of variation (SD/mean) — relative spread
`att8_iqr`	Inter-quartile range of ATT8
`att8_p25`, `att8_p75`	25th and 75th percentile ATT8
`att8_fsm_mean`	Mean ATT8 for disadvantaged pupils (FSM6 classification)
`att8_nfsm_mean`	Mean ATT8 for non-disadvantaged pupils
`att8_gap_mean`	Disadvantage gap — mean difference between non-FSM and FSM ATT8 scores
`att8_gap_sd`	Within-LA variation in the disadvantage gap
`gap_driver_index`	Gap driver index — z(FSM ATT8) minus z(non-FSM ATT8). Negative values indicate the gap is driven by low disadvantaged attainment; positive values indicate it is driven by high non-disadvantaged attainment (see Section 7.7)
`att8_girls_mean`, `att8_boys_mean`	Mean ATT8 by gender
`att8_gender_gap`	Gender gap in ATT8 (girls minus boys)
`att8_eng_mean`, `att8_mat_mean`	Mean ATT8 in the English and Maths elements respectively
`att8_eng_mat_diff`	Relative performance on English vs Maths within the LA
`p8_mean`	Mean Progress 8 score — measures value-added relative to prior attainment
`p8_fsm_mean`, `p8_nfsm_mean`	Progress 8 by disadvantage group
`p8_gap_mean`	Gap in Progress 8 between non-FSM and FSM pupils

Attainment 8 is scored on a scale of approximately 0–90. The national average is around 46–48 points. Progress 8 is a value-added measure centred on zero; positive scores indicate above-average progress given prior attainment.

3.2 Attainment Trends

Temporal trends are estimated by fitting a simple linear regression of the attainment measure on a year index (0 = 2021–22, 1 = 2022–23, 2 = 2023–24, 3 = 2024–25) separately for each LA.

Indicator	Description
`att8_trend_slope`	Annual change in mean ATT8 (points per year) — positive = improving
`att8_fsm_trend_slope`	Annual ATT8 trend for disadvantaged pupils
`att8_nfsm_trend_slope`	Annual ATT8 trend for non-disadvantaged pupils
`p8_trend_slope`	Annual trend in Progress 8

3.3 Pupil Composition

Indicator	Description
`pct_fsm_mean`	Mean % of pupils eligible for Free School Meals in last 6 years (FSM6) — principal disadvantage proxy
`pct_fsm_sd`, `pct_fsm_cv`	Within-LA spread of FSM rates
`pct_eal_mean`	Mean % of pupils with English as an Additional Language (EAL)
`pct_eal_sd`, `pct_eal_cv`	Within-LA spread of EAL rates
`pct_prior_lo_mean`	Mean % of KS4 pupils with low prior attainment (KS2)
`pct_prior_hi_mean`	Mean % of KS4 pupils with high prior attainment (KS2)
`prior_lo_hi_ratio`	Ratio of low to high prior attainment — measure of prior attainment composition
`pct_sen_ehcp_mean`	Mean % of pupils with an Education, Health and Care Plan (EHCP)
`pct_sen_support_mean`	Mean % of pupils receiving SEN support (without EHCP)
`pct_fsm_ever_mean`	Mean % of pupils ever eligible for FSM (broader deprivation measure)
`totpups_mean`	Mean total pupils on roll — a proxy for school size
`totpups_sd`, `totpups_cv`	Within-LA spread of school sizes

FSM6 (Free School Meals in the last six years) is the DfE’s standard measure of disadvantage for performance accountability purposes. It is a cumulative measure — a pupil is counted if they were ever eligible for FSM in any of the previous six years.

3.4 Absence

Indicator	Description
`abs_overall_mean`	Mean overall absence rate (% of sessions missed)
`abs_overall_sd`, `abs_overall_cv`	Within-LA spread of absence rates
`abs_persist_mean`	Mean persistent absence rate (% of pupils missing 10%+ of sessions)
`abs_persist_sd`, `abs_persist_cv`	Within-LA spread of persistent absence
`abs_persist_to_overall_ratio`	Ratio of persistent to overall absence — indicates severity
`abs_trend_slope`	Annual trend in overall absence rate
`abs_persist_trend`	Annual trend in persistent absence rate

Persistent absence (PA) is defined as missing 10% or more of possible sessions in a school year. It is a key indicator of educational engagement and is used by DfE for school accountability.

3.5 Ofsted Inspection Outcomes

Indicator	Description
`ofsted_good_plus_pct`	% of schools rated Good or Outstanding
`ofsted_outstanding_pct`	% of schools rated Outstanding
`ofsted_good_pct`	% of schools rated Good
`ofsted_ri_pct`	% of schools rated Requires Improvement
`ofsted_inadequate_pct`	% of schools rated Inadequate
`ofsted_below_good_pct`	% of schools below Good (RI + Inadequate)
`ofsted_numeric_mean`	Mean numeric Ofsted grade (1=Outstanding to 4=Inadequate)
`ofsted_numeric_sd`	SD of Ofsted grades — within-LA variation in inspection outcomes

Ofsted ratings are based on the most recent inspection outcome for each school as at the August 2024 snapshot.

3.6 Socioeconomic Segregation

A Gorard segregation index is computed at school level for each LA and year. This measures the degree to which FSM pupils are unevenly distributed across schools within the LA, relative to a hypothetical even distribution.

Indicator	Description
`gorard_mean`	Mean Gorard segregation index (0 = perfectly even, 1 = complete segregation)
`gorard_sd`	Within-LA variation in segregation
`gorard_trend`	Trend in segregation over time

The Gorard index for LA \(l\) in year \(t\) is computed as: \[G_{lt} = \frac{1}{2} \sum_{s \in l} \left| \frac{n_{s,\text{FSM}}}{N_{l,\text{FSM}}} - \frac{n_{s,\text{total}}}{N_{l,\text{total}}} \right|\] where \(n_{s,\text{FSM}}\) is the number of FSM pupils in school \(s\), \(N_{l,\text{FSM}}\) is the total number of FSM pupils in the LA, and equivalent total-pupil quantities. Higher values indicate greater concentration of disadvantaged pupils in particular schools.

3.7 School Type and Structural Composition

Indicator	Description
`pct_selective`	% of schools with selective admissions policy (grammar schools)
`pct_comprehensive`	% of schools with comprehensive (non-selective) admissions
`pct_academy`	% of schools that are academies (any type)
`pct_converter_acad`	% converter academies (previously good schools that converted)
`pct_sponsored_acad`	% sponsored academies (typically underperforming schools taken over by sponsor)
`pct_free_school`	% free schools
`pct_va_school`	% Voluntary Aided schools
`pct_vc_school`	% Voluntary Controlled schools
`pct_community`	% community schools (LA-maintained)
`pct_religious`	% of schools with a religious character
`pct_ce`	% Church of England schools
`pct_rc`	% Roman Catholic schools

3.8 Workforce Indicators

Indicator	Description
`retention_mean`	Mean teacher retention (FTE remaining in the same school year-on-year)
`retention_sd`, `retention_cv`	Within-LA spread of retention
`retention_trend`	Annual trend in teacher retention
`sickness_mean`	Mean average teacher sickness absence days per year
`sickness_sd`, `sickness_cv`	Within-LA spread of sickness absence
`sickness_trend`	Annual trend in teacher sickness absence
`ptr_qual_mean`	Mean pupil-to-qualified-teacher ratio
`ptr_qual_sd`	Within-LA spread of PTR
`ptr_trend`	Annual trend in PTR
`ptr_adult_mean`	Mean pupil-to-adult ratio (including teaching assistants)
`pay_main_mean`	Mean % of teachers on main pay range
`pay_upper_mean`	Mean % of teachers on upper pay range
`leadership_pay_mean`	Mean % of teachers on leadership pay range
`fte_ta_to_teacher_ratio`	Ratio of teaching assistant FTE to teacher FTE
`fte_leadership_prop`	Leadership teachers as proportion of all teachers
`pct_taking_sickness_mean`	Mean % of teachers taking any sickness absence

Teacher retention is measured as the FTE count of teachers remaining in the same school in the next year’s census, expressed as a proportion of the current year’s teacher count. Higher values = more stable workforce. The pupil-to-qualified-teacher ratio (PTR) measures class sizes relative to qualified teacher supply — higher values indicate more pupils per qualified teacher, which can signal workforce pressure.

3.9 Derived / Composite Indicators

Indicator	Description
`att8_between_school_sd`	SD of ATT8 across schools — within-LA inequality in attainment
`fsm_att8_cor`	Within-LA correlation between FSM rate and ATT8 — how tightly linked are disadvantage and attainment
`eal_att8_cor`	Within-LA correlation between EAL rate and ATT8
`abs_att8_cor`	Within-LA correlation between absence rate and ATT8
`retention_att8_cor`	Within-LA correlation between teacher retention and ATT8
`avg_years_per_school`	Average number of data years available per school (churn indicator)

4 Clustering Methodology

4.1 Feature Selection and Pre-processing

All numeric LA-level indicators described in Section 3 are candidates for clustering. Three pre-processing filters are applied sequentially:

Missing data filter — Variables with more than 30% missing values across LAs are excluded. This removes indicators that are sparsely populated (e.g. workforce variables for small LAs).
Near-zero variance filter — Variables with a standard deviation below \(10^{-6}\) are excluded. These contribute no discriminating information.
High collinearity filter — From any pair of variables with \(|r| > 0.97\) (Pearson correlation, using pairwise complete observations), one variable is dropped. This prevents near-duplicate features from dominating the distance metric.

After these filters, the remaining variables are z-score standardised (centred at the mean, scaled to unit variance) using parameters estimated from the full set of 152 LAs. This ensures that each variable contributes equally to the Euclidean distances used by k-means, regardless of its original scale.

Missing values remaining after filtering are imputed with each variable’s column median prior to scaling.

Feature selection summary
Stage	Variable count
All numeric indicators	~210+
After >30% missing filter	~180+
After near-zero variance filter	~175+
After \|r\| > 0.97 collinearity filter	~123 (final)
Final variables used in clustering	123

4.2 Outlier LA Exclusion

A small number of LAs have an unusually low number of secondary schools and would otherwise form singleton clusters or distort the k-means solution. LAs with fewer than 5 unique schools in the panel are excluded from the initial clustering:

LAs excluded from initial k-means (assigned post-hoc)
Local Authority	Reason
City of London	Fewer than 5 schools in panel data
Isles Of Scilly	Fewer than 5 schools in panel data

These LAs are not discarded — after the main clustering is complete, each is assigned to the nearest centroid using Euclidean distance in the scaled feature space.

4.3 Optimal k Selection

K-means was run on the main LA set across k = 5 to 10 clusters, with nstart = 100 random initialisations and iter.max = 300 iterations per run to ensure stable solutions. Three complementary criteria were evaluated:

Silhouette width — measures how similar each LA is to its own cluster compared to the nearest other cluster. Higher = better-separated clusters.
Calinski-Harabasz (CH) index — ratio of between-cluster variance to within-cluster variance. Higher = more compact and well-separated clusters.
WSS elbow — the within-cluster sum of squares. The “elbow” (point of fastest rate of improvement) indicates diminishing returns from adding more clusters.

The final k is chosen as the median of the k values preferred by each of the three criteria, clamped to the range [5, 10].

Cluster selection metrics across candidate k values
k	WSS	Silhouette	Calinski-Harabasz	WSS improvement
5	12840.2	0.0738	13.16	—
6	12292.0	0.0736	12.22	4.3%
7	11892.1	0.0737	11.26	3.3%
8	11513.6	0.0786	10.57	3.2%
9	11207.5	0.0652	9.92	2.7%
10	10936.7	0.0661	9.36	2.4%

k selection criteria
Criterion	Preferred k
Best silhouette	8
Best Calinski-Harabasz	5
WSS elbow	—
Chosen k (median)	7

4.4 Final Clustering

The final k-means solution used:

k = 7 clusters
nstart = 200, iter.max = 500 (for the final run, to maximise stability)
set.seed(42) for reproducibility
151 LAs in the main clustering set; 2 outlier LA(s) assigned post-hoc

The solution explains 31.9% of total variance in the scaled feature matrix (between-cluster SS / total SS).

Final cluster sizes
Cluster	Label	Number of LAs
1	High EAL / Low Absence	29
2	High Attainment / Segregated	9
3	Segregated / Non-FSM Driven Gap	18
4	High Turnover / Low EAL	37
5	Stable Workforce / Academy-Heavy	27
6	Weak Ofsted / Persistent Absence	11
7	FSM-Driven Gap / Wide Gap	22

5 Radar Chart Variables

The Shiny application displays radar (spider) charts for each cluster and for individual LAs. Ten variables are shown on the radar, chosen to represent the key policy-relevant dimensions:

Radar chart variables
Variable	Label	Direction	Description
att8_mean	ATT8	↑ Higher = better	Mean Attainment 8 score
pct_fsm_mean	% FSM	↓ Lower = better (inverted)	% pupils eligible for Free School Meals (6-year)
abs_overall_mean	Absence	↓ Lower = better (inverted)	Overall absence rate (%)
ofsted_good_plus_pct	Good+ Ofsted	↑ Higher = better	% schools rated Good or Outstanding
retention_mean	Retention	↑ Higher = better	Teacher retention (FTE remaining in same school)
pct_eal_mean	% EAL	↑ Higher = better	% pupils with English as an Additional Language
att8_fsm_mean	FSM ATT8	↑ Higher = better	Mean ATT8 for disadvantaged (FSM) pupils — higher = better outcomes for FSM pupils
gorard_mean	Segregation	↓ Lower = better (inverted)	Gorard FSM segregation index
sickness_mean	Sickness	↓ Lower = better (inverted)	Mean teacher sickness days per year
ptr_qual_mean	PTR	↓ Lower = better (inverted)	Pupil-to-qualified-teacher ratio

Radar values are expressed as z-scores relative to the England average (z = 0 = England mean). For variables where a lower value is better (absence, % FSM, segregation, sickness, PTR), the z-score is negated so that the outward direction on every axis consistently means “better than average.” Values are clipped to the range [−2.5, +2.5] and shifted to [0, 5] for display. The dotted ring at the midpoint represents the England average.

Why FSM ATT8 replaced the Disadvantage Gap on the radar

In an earlier version of the radar chart, the “Disadvantage Gap” axis was displayed (inverted, so that a narrower gap pointed outward). However, the raw gap conflates two very different situations: an LA might have a wide gap because its FSM pupils do poorly (a policy concern), or because its non-FSM pupils do exceptionally well (less concerning). By showing FSM ATT8 directly, the radar now reveals the actual attainment level of disadvantaged pupils — higher = outward = better. The raw gap, its decomposition (gap_driver_index), and both group-level means remain available in the data table and bar chart.

Reading inverted variables on the radar

Five of the ten radar axes are inverted (marked ↓ in the table above): % FSM, Absence, Segregation, Sickness, and PTR. For these variables, a value that is worse than the England average will appear inside the dotted ring (closer to the centre), even though the underlying z-score is positive (above average).

The same logic applies to all inverted axes: higher absence, higher FSM rates, greater segregation, more sickness days, and larger pupil-to-teacher ratios all plot inward because they represent worse outcomes.

6 Cluster Profiles

6.1 Summary Comparison Table

The table below shows the mean value of each key indicator for each cluster, alongside the England-wide mean.

Cluster profile means on key indicators (England mean shown for reference)
Indicator	C1	C2	C3	C4	C5	C6	C7	England
ATT8 mean	47.09	53.85	45.74	43.56	44.18	39.89	43.02	44.86
FSM ATT8	44.83	46.80	39.52	35.57	36.76	33.86	36.10	38.65
Non-FSM ATT8	54.29	56.65	49.97	48.21	48.73	46.16	51.11	50.44
Disadv. gap (pts)	9.46	9.85	10.45	12.64	11.97	12.30	15.01	11.79
Gap driver	0.24	0.01	0.31	-0.04	0.07	0.17	-0.73	0.00
Progress 8	0.29	0.21	-0.06	-0.15	-0.12	-0.45	0.05	-0.02
% FSM	35.50	18.90	27.60	25.60	30.90	38.70	19.70	28.40
% EAL	39.40	20.60	15.40	8.20	20.50	10.10	9.00	18.10
Absence (%)	7.60	7.70	9.10	9.30	9.30	10.30	9.10	8.90
Pers. absence (%)	22.50	21.60	26.70	27.20	27.00	30.60	25.70	25.90
Good+ Ofsted (%)	92.00	87.00	81.00	81.00	78.00	66.00	90.00	83.00
Gorard seg.	0.13	0.25	0.20	0.15	0.15	0.12	0.16	0.16
Retention (FTE)	57.25	57.92	52.75	46.16	60.16	56.14	56.79	54.43
Sickness (days)	7.47	7.46	8.50	8.61	8.56	9.20	7.73	8.23
PTR	16.69	18.06	17.39	17.36	17.59	17.04	17.36	17.30
% Selective	0.00	0.00	0.00	0.00	0.00	0.00	0.00	0.00
% Academy	0.50	0.80	0.70	0.70	0.80	0.70	0.50	0.70
ATT8 trend (pts/yr)	-0.54	-0.49	-0.74	-0.90	-0.82	-0.92	-0.72	-0.75

6.2 All-Cluster Radar Comparison

The radar chart below overlays all 7 cluster profiles on a single plot. Each axis represents a z-score relative to the England average (dotted ring). Axes are oriented so that outward = better — for variables where lower is better (e.g. absence, % FSM, segregation, sickness, PTR), the z-score is inverted so that worse-than-average values appear inside the ring. The “FSM ATT8” axis shows disadvantaged pupil attainment directly (higher = outward = better).

Radar profiles for all clusters (outward = better on every axis)

6.3 Cluster Map

The map below shows the geographic distribution of each cluster across English local authorities. Each LA is coloured by its cluster assignment. Click on an LA for a summary popup.

6.4 Individual Cluster Pen Portraits

Each cluster was assigned a descriptive label and pen portrait automatically from the z-score profile. Labels are formed by combining the top two distinguishing features (those with |z| > 0.5 on the priority-ordered indicator list), so that each name captures the most policy-relevant characteristics of that group. Each portrait is accompanied by a radar chart showing that cluster’s profile against the England average.

Radar chart polarity reminder

On every radar axis, outward = better. For inverted variables (% FSM, Absence, Segregation, Sickness, PTR), values that are worse than the England average appear inside the dotted ring — closer to the centre. The “FSM ATT8” axis directly shows disadvantaged pupil attainment (not inverted: higher = outward = better). See Section 5 for full details.

Cluster 1: High EAL / Low Absence

29 local authorities | Cluster 1 (29 local authorities)

ATT8: 47.1 | Gap: 9.5 (FSM: N/A / non-FSM: N/A) | FSM: 35.5% | Absence: 7.6% | Good+ Ofsted: 92% Attainment is above average (ATT8 = 47.1), with a narrower than average disadvantage gap (9.5 points). The narrower gap reflects non-disadvantaged pupils attaining closer to the national average (FSM ATT8: N/A, non-FSM ATT8: N/A). Schools serve higher levels of disadvantage than average (35.5% FSM), with substantially EAL pupils (39.4%). Overall absence is below the national average (7.6%), with persistent absence at 22.5%. Ofsted ratings are strong: 92% of schools are rated Good or Outstanding. There is lower than average FSM-based school segregation within LAs in this group (Gorard index: 0.135). Academy schools make up 50% of schools — lower than the national average. Workforce characteristics include lower teacher sickness absence (7.5 days).