Long Distance Commuting in Scotland

Listen

Technical annex 3 SHS Analysis

Tukey HSD and mean distance

1. Each table shows how the average commuting distance varies for one particular factor, considered in isolation. Tukey ( HSD) test is a procedure for testing all possible pairs of means from a dataset where there are a relatively large number of groups, with low number groups, considered rather conservative.

2. Taking age and mean distance as an example, Table 1 shows how the average distance varies with age group:

  • the first column lists the different age groups
  • the second column gives the sample numbers for each age group
  • the remaining columns show the mean distance for each age group. Each 'sub-set' contains age-groups whose values do not differ significantly. For example, the difference between the mean distances of 8.1km for those aged 60+ and 9.0 for those aged less than 20 is not significantly significant. Similarly, the difference between the mean distances of 9.0km for those aged less than 20 and 10.4km for those aged 50 to 60 is not statistically significant
  • When a 'sub-set' contains the value for only one category, it means that it differs significantly from the values for all other categories. For example, Table C2 (in which the categories are the number of cars available to the household) shows that the mean distances for 'none' (6.6km), one (10.6km) and 'two' (14.5km) all differ significantly
  • The Tukey ( HSD) significance measure is given at the bottom row of each table (a value of 1 indicates a strongly significant result)

Table 1: Age and average distance

age group

sample number

1

2

3

60+

2,141

8.1

less than 20

701

9.0

9.0

50 to 59

7,440

10.4

10.4

20 to 29

5,588

11.6

40 to 49

9,276

11.8

30 to 39

10,580

11.8

sig.

0.654

0.0955

0.0817

Table 2: Car ownership and average distance

number of cars household has access to

sample number

1

2

3

none

5,903

6.6

one

18,539

10.6

two

11,284

14.5

sig.

1

1

1

Table 3: Mode and average distance

mode

sample number

1

2

3

4

5

walk/cycle

6,552

1.3

bus

3,786

10.0

car

21,750

14.8

other

585

19.4

train

771

26.4

sig.

1

1

1

1

1

Table 4: Employment status and average distance

employment status

sample number

1

2

3

self employed

3,687

4.4

employed part time

7,687

7.4

employed full time

24,352

13.4

sig.

1

1

1

Table 5: Social class and average distance

social class

sample number

1

2

unskilled occupations

807

7.4

partly skilled occupations

2,649

9.2

9.2

skilled non-manual occupations

3,344

9.6

9.6

skilled manual occupations

5,646

10.8

10.8

managerial and technical occupations

7,319

13.1

13.1

professional etc occupations

1,600

13.5

13.5

inadequately described not stated

23

15.3

sig.

0.0881

0.0798

Table 6: 6-Fold urban/rural classification and average distance

6-fold urban/rural classification

sample number

1

2

3

4

small remote towns, pop 3-10k, drive>30

1,672

8.2

urban settlements of over 125,000 pop.

11,423

8.4

other urban

10,749

11.5

remote rural, pop<3k, drive>30

3,372

12.7

small accessible towns, pop 3-10k, drive<30

3,803

14.0

accessible rural, pop<3k, drive<30

4,684

14.9

sig.

1.0

1.0

1.0

0.2

Table 7: Household income and average distance

household income

sample number

1

2

3

4

5

up to £10,000

3,934

7.4956

over £10,000, up to £20,000

13,316

9.5795

over £20,000 up to £30,000

11,030

11.711

over £30,000, up to £40,000,

4,818

14.129

over £40,000

2,628

17.214

sig.

1

1

1

1

1

Table 8: Household type and average distance

household type

sample number

1

2

3

single pensioner

465

6.7

single parent

2,127

7.7

7.7

older smaller

1,461

8.9

single adult

7,101

10.8

large adult

4,151

11.2

small adult

9,122

11.8

large family

3,220

11.9

small family

8,079

12.1

sig.

0.7429

0.5757

0.3585

First ANOVA

3. Table 9 lists all variables included in the initial 'full' ANOVA and the sample number within each value label. This first ANOVA includes the following variables: Employment status, mode, car ownership, gender, urban/rural area, household income, age, council area and household type. Table 10 details the findings from the first ANOVA.

Table 9. Variables and sample numbers within the first ANOVA

variable label

value label

N

employment status

self employed

2,317

employed full time

23,709

employed part time

7,400

main mode

car

21,738

walk/cycle

6,549

bus

3,784

train

771

other

584

number of cars household has access to

none

5,636

one

17,357

two

10,433

sex

male

15,628

female

17,798

6 fold urban / rural

urban settlements of over 125,000 pop.

10,843

other urban

10,248

small accessible towns, pop 3-10k, drive<30

3,603

small remote towns, pop 3-10k, drive>30

1,585

accessible rural, pop<3k, drive<30

4,247

remote rural, pop<3k, drive>30

2,900

household income

up to £10,000

3,558

over £10,000, up to £20,000

12,463

over £20,000 up to £30,000

10,345

over £30,000, up to £40,000,

4,586

over £40,000

2,474

random adult age

up to and including 19

687

20-24

2,019

25-29

3,413

30-34

4,658

35-39

5,300

40-44

4,621

45-49

4,068

50-54

3,736

55-59

3,079

60-64

1,387

65-69

300

70-74

108

75-79

37

80+

13

household type

single adult

6,680

small adult

8,567

single parent

2,050

small family

7,574

large family

2,981

large adult

3,886

older smaller

1,286

single pensioner

402

Table 10: Full ANOVA

source

type III sum of squares

df

mean square

F

sig.

corrected Model

2469227

436

5,663

19

0

intercept

157,810

1

157,810

519

0.0000

employment status

8,332

2

4,166

14

0.0000

main mode

214,628

4

53,657

176

0.0000

cars

106

2

53

0

0.8407

age

6,100

5

1,220

4

0.0012

sex

26,790

1

26,790

88

0.0000

rural

103,435

5

20,687

68

0.0000

income

12,690

4

3,173

10

0.0000

council

121,057

31

3,905

13

0.0000

household type

4,261

7

609

2

0.0512

employment status * mode

15,764

8

1,971

6

0.0000

employment status * cars

2,105

4

526

2

0.1404

employment status * age

2,939

10

294

1

0.4712

employment status * sex

1,870

2

935

3

0.0463

employment status * rural

3,370

10

337

1

0.3521

employment status * income

2,552

8

319

1

0.3968

employment status * household type

6,099

14

436

1

0.1290

mode * cars

12,041

8

1,505

5

0.0000

mode * age

23,557

20

1,178

4

0.0000

mode * sex

36,126

4

9,032

30

0.0000

mode * rural

186,171

20

9,309

31

0.0000

mode * income

61,349

16

3,834

13

0.0000

mode * household type

18,667

28

667

2

0.0003

cars * age

5,487

10

549

2

0.0546

cars * sex

2,803

2

1,402

5

0.0100

cars * rural

3,179

10

318

1

0.4023

cars * income

2,779

8

347

1

0.3316

cars * household type

3,580

14

256

1

0.6255

age * sex

5,951

5

1,190

4

0.0015

age * rural

8,497

25

340

1

0.3117

age * income

11,141

20

557

2

0.0131

age * household type

7,797

30

260

1

0.6944

sex * rural

5,316

5

1,063

3

0.0037

sex * income

4,897

4

1,224

4

0.0029

sex * household type

5,702

7

815

3

0.0091

rural * income2

9,364

20

468

2

0.0584

rural * household type

21,767

35

622

2

0.0003

income * household type

24,387

28

871

3

0.0000

error

10,040,443

32,989

304

total

17,273,644

33,426

corrected total

12,509,671

33,425

R Squared = .197 (Adjusted R Squared = .187)

Second ANOVA

4. The second ANOVA samples only responses where the usual mode of travel to work was car (as driver or passenger). As a consequence, main mode and car ownership were excluded. Employment status was also excluded to shift the focus to those who are commuting by car every day rather than those who may only commute once or twice a week.

5. The second ANOVA includes the following variables: age, gender, urban/rural area, household income and household type. Table 11 lists all variables included in the second ANOVA and the sample number within each value label. Table 12 details the findings from the second ANOVA.

Table 11: Variables and sample numbers within the second ANOVA

Variable

Value label

N

Sex

Male

10,870

Female

11,411

Age

less than 20'

479

20 to 30

3,437

30 to 40

6,899

40 to 50

5,994

50to 60

4,413

60+

1,059

6 fold Urban / rural classification

Urban settlements of over 125,000 pop.

6,299

Other urban

7,138

Small accessible towns, pop 3-10k, drive<30

2,620

Small remote towns, pop 3-10k, drive>30

932

Accessible rural, pop<3k, drive<30

3,294

Remote rural, pop<3k, drive>30

1,998

Household Income

0 to 10k

1,706

10 to 20k

7,667

20 to 30k

7,338

30 to 40k

3,582

40k+

1,988

Household type

Single adult

3,963

Small adult

5,751

Single parent

1,205

Small family

5,479

Large family

2,173

Large adult

2,769

Older smaller

748

Single pensioner

193

Table 12: Second ANOVA

Source

Type III Sum of Squares

df

Mean Square

F

Sig.

Corrected Model

641,901

201

3,194

9

0.0000

Intercept

243,598

1

243,598

649

0.0000

Sex

12,223

1

12,223

33

0.0000

AGE2

5,348

5

1,070

3

0.0141

Rural

53,636

5

10,727

29

0.0000

income2

13,404

4

3,351

9

0.0000

HHTYPE

4,162

7

595

2

0.1347

Sex * AGE2

10,380

5

2,076

6

0.0000

Sex * Rural

3,792

5

758

2

0.0723

Sex * income2

6,725

4

1,681

4

0.0013

Sex * HHTYPE

12,303

7

1,758

5

0.0000

AGE2 * Rural

7,563

25

303

1

0.7387

AGE2 * income2

10,491

20

525

1

0.1106

AGE2 * HHTYPE

12,610

30

420

1

0.2972

Rural * income2

15,834

20

792

2

0.0026

Rural * HHTYPE

22,319

35

638

2

0.0061

income2 * HHTYPE

23,302

28

832

2

0.0002

Error

8,285,447

22,079

375

Total

13,853,312

22,281

Corrected Total

8,927,347

22,280

R Squared = .072 (Adjusted R Squared = .063)

Page updated: Monday, July 31, 2006