Sampling variance in the Trade Union Membership Statistics 

## Contents

| Sampling variance in the Trade Union Membership Statistics                                |    3 |
|-------------------------------------------------------------------------------------------|------|
|                                                                                           |      |
| Introduction on sampling variation 3                                                      |      |
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| Method used to calculate confidence intervals for the Trade Union Membership Statistics 3 |      |
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| Table 1                                                                                   |      |
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| 95% Confidence intervals for trade union membership by gender and sector 5                |      |
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| Table 2                                                                                   |      |
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| 95% confidence intervals for trade union membership by nation and region, 2011            |      |
|                                                                                           |    6 |
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| Table 3                                                                                   |      |
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| 95% confidence intervals for average (mean) employee wages, 2011, by gender               |      |
| and sector 7                                                                              |      |
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| Table 4                                                                                   |      |
|                                                                                           |      |
| 95% confidence intervals for trade union membership density by industry and               |      |
| workplace size, 2011                                                                      |    8 |
|                                                                                           |      |
| Table 5                                                                                   |      |
|                                                                                           |      |
| 95% confidence intervals for trade union membership density by occupation and             |      |
| age, 2011 9                                                                               |      |
|                                                                                           |      |
| Table 6                                                                                   |      |
|                                                                                           |      |
| 95% confidence intervals for employees with trade union presence in the                   |      |
| workplace by sector and industry, 2011                                                    |   10 |
|                                                                                           |      |
| Table 7                                                                                   |      |
|                                                                                           |      |
| 95% confidence intervals for employees with trade union presence in the                   |      |
| workplace by workplace size, nation and region, 2011                                      |   11 |
|                                                                                           |      |
| Table 8                                                                                   |      |
|                                                                                           |      |
| 95% confidence intervals for employees whose pay and conditions are affected              |      |
| by a collective agreement, by sector and industry, 2011 12                                |      |
|                                                                                           |      |
| Table 9                                                                                   |      |
|                                                                                           |      |
| 95% confidence intervals for employees whose pay and conditions are affected              |      |
| by a collective agreement, by workplace size, nation and region, 2011 13                  |      |
|                                                                                           |      |

## Sampling Variance In The Trade Union Membership Statistics Introduction On Sampling Variation

The labour force survey (LFS) is a sample survey, which provides estimates of various measures of the population that reflect the particular sample selected. As any valid sample from the population is likely to produce different estimates for the population than other valid samples, there is uncertainty around the population estimates resulting from the selection of a particular sample (as opposed to any other valid sample). This is known as the sampling error. As the LFS uses random sampling of households it is possible to provide estimates of the sampling error (measured as the standard error), which forms the basis of the confidence interval placed around estimate. Normally a 95% confidence interval would be used, which means that in 19 out of 20 different samples  we would expect the true (population) level or rate considered to be within the 95% confidence interval for the sample estimate. Where a simple random sample is used, the 95% confidence interval for an estimate is set at ±1.96 standard errors around the sample estimate. 

Any estimate of the range of sampling variability should take into account the sampling approach, as this will affect the probability of selection of individuals within the population, and therefore the extent of the variability around the survey estimate relative to that obtained from a simple random sample. The design factor measures the ratio of the standard error produced by a complex sample design relative to the standard error that would result from simple random sampling.To take account of the sampling design, the 95% confidence interval can be calculated as: 

$$\pm\ 1.96\ \mathrm{x\design\factor\x\SE\ (standard\error)}$$

## Method Used To Calculate Confidence Intervals For The Trade Union Membership Statistics

The LFS  sample design has two additional elements: implicit stratification by geography 
(from the use of a systematic sample of addresses based on postcode area), and clustering, based on collecting results for individuals based on a sample of addresses (as individuals within a household are more likely to share some characteristics). Some calculated design factors for headline measures are presented in ONS's LFS User Guide, Volume 1 - LFS Background and Methodology 20111. However, these do not directly relate to the estimates of trade union membership. In the methodology user guide, ONS advise that users can calculate their own confidence intervals by estimating their own design factors by applying a 'complex samples' analysis in a statistical package. These will be '*conservative*' because while such an approach will take account of the LFS's design, it won't take account of the calibration weighting that ONS undertakes to ensure estimates are consistent across those groups calibrated on, thus reducing the standard errors. We have estimated standard errors and confidence intervals for the 2011 estimates of trade union membership using a complex samples approach in SPSS. The address variable, ADD, has been used as the cluster variable, in line with ONS's suggestion, and UALA, representing unitary and local authorities,  has been used as a stratum variable. The calculated 95% confidence intervals for the key trade union membership levels and density estimates for 2011 presented in the latest trade union membership publication (for 2011). The tables present the estimate, and the upper and lower bounds of the estimate at 95% confidence. If the confidence intervals of two estimated values do not overlap then they are considered statistically significantly different at the 5% significance level. Confidence intervals will be provided for all the 2012 figures provided in this year's bulletin when it is published in  April. If you have any comments or would like further information, please contact us at: Labourmarket.analysis@bis.gsi.gov.uk 

 

Trade union membership, 2011 


95% confidence interval 
 
lower bound 
Upper bound 
 
population estimate  
in employment, UK 


whole economy 
numbers (000s) 


all 
6,665 
 
6,282 
7,048 
men 
3,089 
 
2,897 
3,281 
women 
3,577 
 
3,365 
3,789 
whole economy 
density % 


all 
23.2% 
 
22.7% 
23.7% 
men 
20.2% 
 
19.5% 
20.9% 
women 
26.8% 
 
26.1% 
27.5% 
employees, UK 


whole economy 
numbers (000s) 


all 
6,389 
 
6,022 
6,756 
men 
2,913 
 
2,731 
3,096 
women 
3,476 
 
3,270 
3,681 
public sector 


all 
3,882 
 
3,654 
4,110 
men 
1,299 
 
1,209 
1,389 
women 
2,583 
 
2,427 
2,739 
private sector 


all 
2,507 
 
2,343 
2,671 
men 
1,614 
 
1,499 
1,729 
women 
893 
 
824 
962 
whole economy 
density % 


all 
26.0% 
 
25.4% 
26.6% 
men 
23.4% 
 
22.6% 
24.2% 
women 
28.7% 
 
28.0% 
29.4% 
public sector 


all 
56.5% 
 
55.5% 
57.6% 
men 
55.4% 
 
53.6% 
57.2% 
women 
57.1% 
 
55.8% 
58.4% 
private sector 


all 
14.1% 
 
13.6% 
14.7% 
men 
15.9% 
 
15.2% 
16.7% 
women 
11.8% 
 
11.2% 
12.4% 

## Trade Union Membership, 2011



95% confidence interval 
population 
 
estimate  
 
lower bound 
upper bound 
numbers 
Employees 
(000s) 


Nation 


England 
5,125 
 
4,784 
5,466 
Wales 
400 
 
302 
499 
Scotland 
638 
 
548 
728 
Northern Ireland 
226 
 
190 
262 
Regions 


North East 
341 
 
257 
425 
North West 
825 
 
668 
983 
Yorkshire & Humberside 
555 
 
463 
647 
East Midlands 
456 
 
342 
569 
West Midlands 
550 
 
443 
656 
East of England 
535 
 
404 
666 
London 
636 
 
568 
705 
South East 
719 
 
581 
856 
South West 
509 
 
407 
610 
 
density % 


Nation 


England 
24.8% 
 
24.2% 
25.4% 
Wales 
34.9% 
 
32.3% 
37.6% 
Scotland 
29.8% 
 
28.0% 
31.7% 
Northern Ireland 
33.6% 
 
31.4% 
35.9% 
Regions 


North East 
34.2% 
 
31.6% 
36.8% 
North West 
30.3% 
 
28.7% 
31.9% 
Yorkshire & Humberside 
27.0% 
 
25.3% 
28.7% 
East Midlands 
25.4% 
 
23.4% 
27.5% 
West Midlands 
26.6% 
 
24.9% 
28.4% 
East of England 
22.4% 
 
20.9% 
23.9% 
London 
20.6% 
 
19.1% 
22.1% 
South East 
20.7% 
 
19.4% 
22.2% 
South West 
24.7% 
 
22.9% 
26.6% 
Mean hourly earnings (£), 2011  


UK employees 
 
 
95% confidence interval 
lower 
 
Estimate 
 
bound  
higher bound 
whole economy 


all employees 
£12.60 
 
£12.39 
£12.81 
trade union members 
£14.18 
 
£13.92 
£14.44 
non-members 
£12.01 
 
£11.75 
£12.27 


by sector 


public sector 


all employees 
£14.11 
 
£13.83 
£14.38 
trade union members 
£15.06 
 
£14.74 
£15.39 
non-members 
£12.76 
 
£12.30 
£13.22 


private sector 


all employees 
£12.03 
 
£11.77 
£12.29 
trade union members 
£12.83 
 
£12.42 
£13.25 
non-members 
£11.88 
 
£11.58 
£12.18 


by gender 


male 


all employees 
£13.74 
 
£13.44 
£14.04 
trade union members 
£14.72 
 
£14.32 
£15.12 
non-members 
£13.40 
 
£13.03 
£13.77 


female 


all employees 
£11.43 
 
£11.23 
£11.64 
trade union members 
£13.73 
 
£13.43 
£14.03 
non-members 
£10.50 
 
£10.25 
£10.76 

## 

Trade union membership, 2011 


UK employees 
 
 
95% confidence interval 
lower 
population 
 
bound 
upper bound 
estimate  
 
by industry 
density, % 


Agriculture, forestry & fishing 
* 
 
* 
* 
Mining & quarrying 
23.5% 
 
16.8% 
31.9% 
Manufacturing 
18.7% 
 
17.2% 
20.2% 
Electricity, gas, steam & air conditioning supply 
43.2% 
 
37.1% 
49.6% 
Water supply, sewerage, waste & remediation activities 
28.7% 
 
23.7% 
34.3% 
Construction 
14.8% 
 
13.1% 
16.6% 
Wholesale, retail trade and motor repair 
11.9% 
 
10.9% 
12.9% 
Transport and storage 
38.9% 
 
36.3% 
41.5% 
Accommodation & food service 
3.6% 
 
2.8% 
4.6% 
Information & communication 
11.7% 
 
9.9% 
13.8% 
Financial & insurance activities 
16.7% 
 
14.8% 
18.9% 
Real estate activities 
12.8% 
 
9.0% 
18.0% 
Professional & adminstrative services 
10.4% 
 
9.3% 
11.5% 
Public administration and defence 
53.4% 
 
51.2% 
55.5% 
Education 
51.5% 
 
49.8% 
53.1% 
Human health & social work 
41.4% 
 
40.0% 
42.9% 
Other services 
13.6% 
 
11.9% 
15.6% 
by workplace size 


Less than 50 
16.3% 
 
15.7% 
17.0% 
50 or more 
34.9% 
 
34.1% 
35.8% 

 

Trade union membership, 2011 


UK employees 
 
 
95% confidence interval 
lower 
population 
 
bound 
upper bound 
estimate  
 
 
density, % 


by occupation 


Managers and senior officials 
13.8% 
 
12.6% 
15.1% 
Professional occupations 
45.4% 
 
44.0% 
46.7% 
Associate professional and technical occupations 
25.7% 
 
24.4% 
27.1% 
Administrative and secretarial occupations 
21.2% 
 
19.9% 
22.5% 
Skilled trade occupations 
20.1% 
 
18.5% 
21.7% 
Personal service occupations 
28.0% 
 
26.5% 
29.5% 
Sales and customer service occupations 
15.5% 
 
14.2% 
16.9% 
Process, plant and machine operatives 
28.6% 
 
26.5% 
30.7% 
Elementary occupations 
16.7% 
 
15.5% 
17.9% 
by age 


16-19 
3.1% 
 
2.2% 
4.3% 
20-24 
11.4% 
 
10.2% 
12.7% 
25-29 
18.2% 
 
16.9% 
19.6% 
30 to 34 
24.0% 
 
22.5% 
25.5% 
35 to 39 
26.7% 
 
25.3% 
28.2% 
40 to 44 
29.4% 
 
28.1% 
30.8% 
45 to 49 
33.6% 
 
32.1% 
35.2% 
50 to 54 
36.2% 
 
34.6% 
37.8% 
55 to 59 
35.3% 
 
33.6% 
37.0% 
60 to 64 
29.1% 
 
27.0% 
31.3% 
65-69 
14.1% 
 
11.7% 
17.0% 
Over 70 
13.5% 
 
8.4% 
21.0% 
 

 

Employees with trade union presence in the workplace, 2011 


UK employees, % 
 
 
95% confidence interval 
 
Estimate 
 
lower bound  
higher bound 
all 
44.8% 
 
44.1% 
45.5% 
public sector 
87.1% 
 
86.3% 
87.8% 
private sector 
28.5% 
 
27.8% 
29.2% 


by industry 


Agriculture, forestry and fishing 
* 
 
* 
* 
Mining and quarrying 
39.3% 
 
31.8% 
47.4% 
Manufacturing 
38.1% 
 
36.2% 
40.0% 
Electricity, gas and steam & air conditioning supply 
65.6% 
 
59.3% 
71.5% 
Water supply, sewerage, waste & remediation activities 
56.4% 
 
50.7% 
62.0% 
Construction 
27.3% 
 
25.2% 
29.5% 
Wholesale, retail and motor trade 
26.9% 
 
25.5% 
28.3% 
Transport, storage 
58.7% 
 
56.0% 
61.4% 
accommodation and food services 
7.6% 
 
6.4% 
8.9% 
information and communications 
23.8% 
 
21.2% 
26.5% 
Financial and insurance activities 
39.7% 
 
36.9% 
42.6% 
Real estate services 
35.6% 
 
29.9% 
41.7% 
Professional & administrative services 
21.0% 
 
19.6% 
22.5% 
Public admin and defence 
84.0% 
 
82.3% 
85.6% 
Education 
82.1% 
 
80.8% 
83.3% 
Health and social work 
63.3% 
 
61.9% 
64.8% 
Other services 
27.2% 
 
24.8% 
29.7% 

 
Note: this table provides estimates for industry based on SIC 2007, and so is slightly different for some industries than in table 3.8 in the 2011 publication. 

 

 
| UK employees, %          |       |     |
|--------------------------|-------|-----|
| 95% confidence interval  |       |     |
| by workplace size        |       |     |
|                          |       |     |
| Less than 50             | 26.7% |     |
| 50 or more               | 61.6% |     |
|                          |       |     |
| Nation                   |       |     |
|                          |       |     |
| England                  | 44.0% |     |
| Wales                    | 55.8% |     |
| Scotland                 | 48.1% |     |
| Northern Ireland         | 41.8% |     |
| Region                   |       |     |
|                          |       |     |
| North East               | 53.5% |     |
| North West               | 48.9% |     |
| Yorkshire and the Humber | 47.5% |     |
| East Midlands            | 44.7% |     |
| West Midlands            | 45.4% |     |
| East of England          | 41.0% |     |
| London                   | 38.0% |     |
| South East               | 40.4% |     |
| South West               | 45.7% |     |

 

Employees whose pay and conditions are affected by a collective agreement, 2011 
 
UK employees, % 
 
 
95% confidence interval 
 
Estimate 
 
lower bound  
higher bound 
all 
31.2% 
 
30.6% 
31.8% 
public sector 
67.8% 
 
66.7% 
68.8% 
private sector 
16.9% 
 
16.4% 
17.5% 


by industry 


Agriculture, forestry and fishing 
* 
 
* 
* 
Mining and quarrying 
22.0% 
 
15.5% 
30.3% 
Manufacturing 
23.2% 
 
21.6% 
25.0% 
Electricity, gas and steam & air conditioning supply 
50.9% 
 
43.8% 
58.1% 
Water supply, sewerage, waste & remediation activities 
39.6% 
 
34.0% 
45.4% 
Construction 
18.0% 
 
16.0% 
20.2% 
Wholesale, retail and motor trade 
16.0% 
 
14.9% 
17.3% 
Transport, storage 
47.3% 
 
44.5% 
50.2% 
accommodation and food services 
4.6% 
 
3.7% 
5.9% 
information and communications 
13.9% 
 
11.9% 
16.2% 
Financial and insurance activities 
25.0% 
 
22.4% 
27.8% 
Real estate services 
19.0% 
 
14.1% 
25.2% 
Professional & administrative services 
11.6% 
 
10.5% 
12.9% 
Public admin and defence 
71.1% 
 
68.9% 
73.1% 
Education 
59.0% 
 
57.2% 
60.8% 
Health and social work 
43.8% 
 
42.2% 
45.4% 
Other services 
17.5% 
 
15.4% 
19.7% 
 

Note: this table provides estimates for industry based on SIC 2007, and so is slightly different for some industries than in tables 3.8 and 3.9 in the 2011 publication. 

Employees whose pay and conditions are affected by a collective agreement, 2011 
 
UK employees, % 
 
 
95% confidence interval 
 
Estimate 
 
lower bound  
higher bound 
by workplace size 


Less than 50 
17.3% 
 
16.6% 
18.0% 
50 or more 
44.1% 
 
43.2% 
45.0% 


Nation 


England 
30.0% 
 
29.3% 
30.7% 
Wales 
39.2% 
 
35.6% 
43.0% 
Scotland 
34.7% 
 
32.8% 
36.5% 
Northern Ireland 
40.6% 
 
37.4% 
43.9% 
Region 


North East 
35.8% 
 
32.8% 
38.8% 
North West 
34.6% 
 
33.0% 
36.2% 
Yorkshire and the Humber 
31.8% 
 
29.9% 
33.8% 
East Midlands 
31.1% 
 
29.2% 
33.0% 
West Midlands 
33.3% 
 
31.3% 
35.5% 
East of England 
28.1% 
 
26.1% 
30.2% 
London 
24.2% 
 
22.6% 
26.0% 
South East 
26.6% 
 
24.8% 
28.5% 
South West 
31.3% 
 
29.7% 
32.9% 


by gender 


Male 
28.4% 
 
27.6% 
29.3% 
Female 
34.0% 
 
33.2% 
34.8% 


by union membership 


Member 
73.2% 
 
72.2% 
74.2% 
Non-member 
15.5% 
 
15.0% 
16.1% 
 

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