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EVALUATION OF STATISTICAL TECHNIQUES IN THE SCOTTISH INDEX OF MULTIPLE DEPRIVATION

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Appendix B.

This Appendix contains tables of the probability-weighted number and percentage of data zones classified as highly deprived (within most deprived 15% according to the SIMD rank) for each local authority under the original SIMD algorithm in comparison with groups of alternative methods, with probabilities of each data zone being severely deprived estimated from application of each method to 1,000 simulated indicator datasets.

Local Authority

Total

Shrinkage Method

Original

None

National

IG

Rural Group

N

N (%)

N (%)

N (%)

N (%)

N (%)

Glasgow City

694

369.8 (53.3)

362.4 (52.2)

362.2 (52.2)

362.4 (52.2)

365.0 (52.6)

Inverclyde

110

36.0 (32.7)

35.3 (32.1)

35.3 (32.1)

36.3 (33.0)

35.0 (31.8)

Dundee City

179

52.8 (29.5)

52.2 (29.2)

51.9 (29.0)

53.9 (30.1)

53.2 (29.7)

West Dunbartonshire

118

32.0 (27.2)

31.3 (26.5)

31.4 (26.6)

31.9 (27.0)

31.7 (26.9)

North Lanarkshire

418

102.8 (24.6)

98.4 (23.5)

100.6 (24.1)

95.7 (22.9)

101.4 (24.3)

Renfrewshire

214

41.8 (19.5)

42.4 (19.8)

42.2 (19.7)

42.5 (19.8)

43.2 (20.2)

North Ayrshire

179

33.5 (18.7)

33.5 (18.7)

33.5 (18.7)

33.5 (18.7)

33.1 (18.5)

East Ayrshire

154

26.8 (17.4)

27.3 (17.7)

26.7 (17.3)

27.5 (17.9)

25.5 (16.5)

South Lanarkshire

398

65.7 (16.5)

65.2 (16.4)

66.4 (16.7)

63.2 (15.9)

66.0 (16.6)

Clackmannanshire

64

10.3 (16.0)

10.1 (15.7)

10.3 (16.0)

9.4 (14.6)

10.0 (15.6)

Edinburgh, City of

549

60.3 (11.0)

61.7 (11.2)

61.0 (11.1)

62.4 (11.4)

61.8 (11.3)

South Ayrshire

147

13.2 (9.0)

14.5 (9.8)

13.8 (9.4)

15.3 (10.4)

13.2 (9.0)

Fife

453

32.1 (7.1)

33.2 (7.3)

33.6 (7.4)

33.7 (7.4)

32.8 (7.2)

Argyll & Bute

122

8.6 (7.0)

9.2 (7.5)

9.0 (7.4)

9.2 (7.5)

8.8 (7.2)

Falkirk

197

14.0 (7.1)

14.2 (7.2)

14.1 (7.1)

13.4 (6.8)

14.0 (7.1)

Aberdeen City

267

17.4 (6.5)

19.8 (7.4)

18.4 (6.9)

20.7 (7.8)

19.3 (7.2)

Stirling

110

6.5 (5.9)

6.9 (6.2)

6.9 (6.3)

6.7 (6.1)

6.4 (5.8)

Dumfries & Galloway

193

9.8 (5.1)

11.4 (5.9)

11.1 (5.8)

10.6 (5.5)

9.7 (5.0)

West Lothian

211

9.7 (4.6)

9.2 (4.3)

10.1 (4.8)

9.2 (4.4)

9.6 (4.6)

East Renfrewshire

120

5.5 (4.6)

6.2 (5.2)

6.3 (5.3)

6.1 (5.1)

6.4 (5.3)

East Dunbartonshire

127

3.4 (2.7)

3.8 (3.0)

3.8 (3.0)

3.7 (2.9)

3.7 (2.9)

Highland

292

9.7 (3.3)

10.7 (3.7)

10.6 (3.6)

11.4 (3.9)

10.0 (3.4)

Angus

142

3.4 (2.4)

4.4 (3.1)

4.1 (2.9)

4.4 (3.1)

4.0 (2.8)

Perth & Kinross

175

3.6 (2.0)

4.1 (2.3)

4.0 (2.3)

4.1 (2.3)

3.9 (2.3)

Scottish Borders

130

2.0 (1.6)

2.4 (1.8)

2.3 (1.8)

2.6 (2.0)

2.2 (1.7)

Midlothian

112

1.1 (1.0)

1.1 (1.0)

1.1 (1.0)

1.2 (1.0)

1.1 (1.0)

Aberdeenshire

301

2.6 (0.9)

3.7 (1.2)

3.5 (1.2)

3.6 (1.2)

3.4 (1.1)

East Lothian

120

0.6 (0.5)

0.7 (0.5)

0.7 (0.6)

0.5 (0.4)

0.6 (0.5)

Eilean Siar

36

0.0 (0.0)

0.0 (0.0)

0.0 (0.0)

0.0 (0.0)

0.0 (0.0)

Moray

116

0.0 (0.0)

0.0 (0.0)

0.0 (0.0)

0.0 (0.0)

0.0 (0.0)

Orkney Islands

27

0.0 (0.0)

0.0 (0.0)

0.0 (0.0)

0.0 (0.0)

0.0 (0.0)

Shetland Islands

30

0.0 (0.0)

0.0 (0.0)

0.0 (0.0)

0.0 (0.0)

0.0 (0.0)

Table B.1.Number of data zones in each LA, and probability-weighted number (%) of data zones amongst the 15% most deprived data zones nationally, according to the SIMD calculated using the original method and alternative univariate shrinkage options

Local Authority

Total

Transformation used prior to Factor Analysis

None

Rank +Normal

Rank

Rank +Exponential

N

N (%)

N (%)

N (%)

N (%)

Glasgow City

694

369.8 (53.3)

367.0 (52.9)

368.2 (53.0)

371.5 (53.5)

Inverclyde

110

36.0 (32.7)

35.7 (32.4)

36.3 (33.0)

35.6 (32.3)

Dundee City

179

52.8 (29.5)

52.8 (29.5)

52.8 (29.5)

52.4 (29.3)

West Dunbartonshire

118

32.0 (27.2)

31.3 (26.5)

32.6 (27.6)

31.3 (26.6)

North Lanarkshire

418

102.8 (24.6)

103.5 (24.8)

103.4 (24.7)

101.3 (24.2)

Renfrewshire

214

41.8 (19.5)

41.9 (19.6)

42.5 (19.9)

41.1 (19.2)

North Ayrshire

179

33.5 (18.7)

33.4 (18.6)

33.7 (18.8)

33.0 (18.4)

East Ayrshire

154

26.8 (17.4)

27.0 (17.6)

27.1 (17.6)

26.9 (17.5)

South Lanarkshire

398

65.7 (16.5)

65.5 (16.4)

66.8 (16.8)

64.7 (16.3)

Clackmannanshire

64

10.3 (16.0)

10.1 (15.8)

10.2 (16.0)

9.9 (15.5)

Edinburgh, City of

549

60.3 (11.0)

60.4 (11.0)

59.9 (10.9)

61.4 (11.2)

South Ayrshire

147

13.2 (9.0)

14.1 (9.6)

12.7 (8.6)

13.9 (9.4)

Fife

453

32.1 (7.1)

31.4 (6.9)

32.7 (7.2)

31.4 (6.9)

Argyll & Bute

122

8.6 (7.0)

8.8 (7.2)

8.5 (6.9)

8.8 (7.2)

Falkirk

197

14.0 (7.1)

13.6 (6.9)

14.0 (7.1)

13.9 (7.1)

Aberdeen City

267

17.4 (6.5)

18.1 (6.8)

16.3 (6.1)

18.9 (7.1)

Stirling

110

6.5 (5.9)

6.7 (6.1)

6.5 (5.9)

6.7 (6.0)

Dumfries & Galloway

193

9.8 (5.1)

10.4 (5.4)

9.3 (4.8)

10.1 (5.3)

West Lothian

211

9.7 (4.6)

9.3 (4.4)

9.9 (4.7)

9.2 (4.3)

East Renfrewshire

120

5.5 (4.6)

5.6 (4.7)

5.6 (4.6)

5.6 (4.6)

East Dunbartonshire

127

3.4 (2.7)

3.3 (2.6)

3.5 (2.8)

3.3 (2.6)

Highland

292

9.7 (3.3)

10.9 (3.7)

9.3 (3.2)

10.3 (3.5)

Angus

142

3.4 (2.4)

3.8 (2.7)

3.5 (2.4)

3.7 (2.6)

Perth & Kinross

175

3.6 (2.0)

3.8 (2.1)

3.4 (2.0)

3.7 (2.1)

Scottish Borders

130

2.0 (1.6)

2.1 (1.6)

2.0 (1.5)

2.1 (1.6)

Midlothian

112

1.1 (1.0)

1.1 (1.0)

1.1 (1.0)

1.1 (1.0)

Aberdeenshire

301

2.6 (0.9)

3.0 (1.0)

2.6 (0.9)

2.8 (0.9)

East Lothian

120

0.6 (0.5)

0.4 (0.3)

0.6 (0.5)

0.4 (0.4)

Eilean Siar

36

0.0 (0.0)

0.0 (0.0)

0.0 (0.0)

0.0 (0.0)

Moray

116

0.0 (0.0)

0.0 (0.0)

0.0 (0.0)

0.0 (0.0)

Orkney Islands

27

0.0 (0.0)

0.0 (0.0)

0.0 (0.0)

0.0 (0.0)

Shetland Islands

30

0.0 (0.0)

0.0 (0.0)

0.0 (0.0)

0.0 (0.0)

Table B.2.Number of data zones in each LA, and probability-weighted number (%) of data zones amongst the 15% most deprived data zones nationally, according to the SIMD calculated using the original method (Rank + Normal transformation) and methods using factor analysis applied to alternative transformations of component indicator variables

Local Authority

Total

Original

Transformation used prior to PCA

Rank + Normal

None

Rank

Rank + Exponential

N

N (%)

N (%)

N (%)

N (%)

N (%)

Glasgow City

694

369.8 (53.3)

374.4 (54.0)

374.2 (53.9)

372.0 (53.6)

376.7 (54.3)

Inverclyde

110

36.0 (32.7)

35.3 (32.1)

31.2 (28.4)

35.7 (32.5)

34.9 (31.7)

Dundee City

179

52.8 (29.5)

55.2 (30.9)

55.7 (31.1)

55.2 (30.9)

54.3 (30.3)

West Dunbartonshire

118

32.0 (27.2)

32.0 (27.2)

30.0 (25.4)

32.6 (27.7)

31.4 (26.6)

North Lanarkshire

418

102.8 (24.6)

101.8 (24.3)

111.7 (26.7)

102.8 (24.6)

100.7 (24.1)

Renfrewshire

214

41.8 (19.5)

41.4 (19.3)

40.4 (18.9)

41.9 (19.6)

40.6 (19.0)

North Ayrshire

179

33.5 (18.7)

32.2 (18.0)

31.1 (17.3)

32.6 (18.2)

31.7 (17.7)

East Ayrshire

154

26.8 (17.4)

25.4 (16.5)

24.5 (15.9)

25.6 (16.6)

25.6 (16.6)

South Lanarkshire

398

65.7 (16.5)

65.6 (16.5)

66.9 (16.8)

66.8 (16.8)

64.7 (16.3)

Clackmannanshire

64

10.3 (16.0)

9.9 (15.4)

8.6 (13.5)

9.9 (15.4)

9.9 (15.4)

Edinburgh, City of

549

60.3 (11.0)

62.1 (11.3)

59.7 (10.9)

61.9 (11.3)

62.3 (11.3)

South Ayrshire

147

13.2 (9.0)

12.9 (8.8)

9.6 (6.6)

12.5 (8.5)

13.4 (9.1)

Fife

453

32.1 (7.1)

31.7 (7.0)

31.9 (7.0)

32.1 (7.1)

31.2 (6.9)

Argyll & Bute

122

8.6 (7.0)

8.2 (6.8)

7.5 (6.2)

8.0 (6.6)

8.6 (7.0)

Falkirk

197

14.0 (7.1)

14.6 (7.4)

21.2 (10.8)

14.3 (7.3)

14.8 (7.5)

Aberdeen City

267

17.4 (6.5)

17.9 (6.7)

15.5 (5.8)

17.1 (6.4)

18.7 (7.0)

Stirling

110

6.5 (5.9)

5.8 (5.3)

5.9 (5.4)

5.8 (5.3)

6.1 (5.6)

Dumfries & Galloway

193

9.8 (5.1)

8.9 (4.6)

7.2 (3.7)

8.5 (4.4)

9.0 (4.7)

West Lothian

211

9.7 (4.6)

8.9 (4.2)

10.4 (4.9)

8.9 (4.2)

8.6 (4.1)

East Renfrewshire

120

5.5 (4.6)

4.9 (4.1)

5.7 (4.7)

4.9 (4.1)

5.3 (4.4)

East Dunbartonshire

127

3.4 (2.7)

3.2 (2.5)

3.3 (2.6)

3.3 (2.6)

3.1 (2.4)

Highland

292

9.7 (3.3)

9.7 (3.3)

10.1 (3.4)

9.4 (3.2)

9.9 (3.4)

Angus

142

3.4 (2.4)

3.3 (2.3)

3.9 (2.7)

3.4 (2.4)

3.5 (2.4)

Perth & Kinross

175

3.6 (2.0)

3.4 (1.9)

3.2 (1.9)

3.3 (1.9)

3.4 (1.9)

Scottish Borders

130

2.0 (1.6)

1.9 (1.5)

1.3 (1.0)

1.8 (1.4)

2.0 (1.6)

Midlothian

112

1.1 (1.0)

1.1 (1.0)

1.0 (0.9)

1.1 (1.0)

1.1 (1.0)

Aberdeenshire

301

2.6 (0.9)

2.8 (0.9)

2.4 (0.8)

2.7 (0.9)

2.9 (1.0)

East Lothian

120

0.6 (0.5)

0.7 (0.6)

0.9 (0.8)

0.6 (0.5)

0.6 (0.5)

Eilean Siar

36

0.0 (0.0)

0.0 (0.0)

0.0 (0.0)

0.0 (0.0)

0.0 (0.0)

Moray

116

0.0 (0.0)

0.0 (0.0)

0.0 (0.0)

0.0 (0.0)

0.0 (0.0)

Orkney Islands

27

0.0 (0.0)

0.0 (0.0)

0.0 (0.0)

0.0 (0.0)

0.0 (0.0)

Shetland Islands

30

0.0 (0.0)

0.0 (0.0)

0.0 (0.0)

0.0 (0.0)

0.0 (0.0)

Table B.3.Number of data zones in each LA, and probability-weighted number (%) of data zones amongst the 15% most deprived data zones nationally, according to the SIMD calculated using the original method and methods using alternative transformations of indicator variables prior to principal components analysis ( PCA)

Local Authority

Total

Original

Simple Standardisation

N

N (%)

N (%)

Glasgow City

694

369.8 (53.3)

366.8 (52.9)

Inverclyde

110

36.0 (32.7)

35.2 (32.0)

Dundee City

179

52.8 (29.5)

53.3 (29.8)

West Dunbartonshire

118

32.0 (27.2)

33.1 (28.1)

North Lanarkshire

418

102.8 (24.6)

103.2 (24.7)

Renfrewshire

214

41.8 (19.5)

41.3 (19.3)

North Ayrshire

179

33.5 (18.7)

34.3 (19.2)

East Ayrshire

154

26.8 (17.4)

27.2 (17.7)

South Lanarkshire

398

65.7 (16.5)

67.1 (16.9)

Clackmannanshire

64

10.3 (16.0)

10.1 (15.8)

Edinburgh, City of

549

60.3 (11.0)

58.5 (10.6)

South Ayrshire

147

13.2 (9.0)

12.9 (8.8)

Fife

453

32.1 (7.1)

34.0 (7.5)

Argyll & Bute

122

8.6 (7.0)

8.4 (6.9)

Falkirk

197

14.0 (7.1)

14.3 (7.3)

Aberdeen City

267

17.4 (6.5)

16.1 (6.0)

Stirling

110

6.5 (5.9)

6.7 (6.1)

Dumfries & Galloway

193

9.8 (5.1)

8.7 (4.5)

West Lothian

211

9.7 (4.6)

10.2 (4.8)

East Renfrewshire

120

5.5 (4.6)

5.9 (5.0)

East Dunbartonshire

127

3.4 (2.7)

3.6 (2.8)

Highland

292

9.7 (3.3)

10.5 (3.6)

Angus

142

3.4 (2.4)

3.5 (2.5)

Perth & Kinross

175

3.6 (2.0)

3.8 (2.2)

Scottish Borders

130

2.0 (1.6)

2.1 (1.6)

Midlothian

112

1.1 (1.0)

1.0 (0.9)

Aberdeenshire

301

2.6 (0.9)

2.7 (0.9)

East Lothian

120

0.6 (0.5)

0.5 (0.4)

Eilean Siar

36

0.0 (0.0)

0.0 (0.0)

Moray

116

0.0 (0.0)

0.0 (0.0)

Orkney Islands

27

0.0 (0.0)

0.0 (0.0)

Shetland Islands

30

0.0 (0.0)

0.0 (0.0)

Table B.4.Number of data zones in each LA, and probability-weighted number (%) of data zones amongst the 15% most deprived data zones nationally, according to the SIMD calculated using the original method and an alternative using simple standardisation of domain scores (subtracting mean and dividing by standard deviation) prior to combination to form the SIMD score

Local Authority

Total

Original

Transformation of Health, Education & Access
domains followed by simple standardisation

N

N (%)

N (%)

Glasgow City

694

369.8 (53.3)

372.1 (53.6)

Inverclyde

110

36.0 (32.7)

35.6 (32.4)

Dundee City

179

52.8 (29.5)

53.9 (30.1)

West Dunbartonshire

118

32.0 (27.2)

31.5 (26.7)

North Lanarkshire

418

102.8 (24.6)

101.3 (24.2)

Renfrewshire

214

41.8 (19.5)

41.9 (19.6)

North Ayrshire

179

33.5 (18.7)

33.5 (18.7)

East Ayrshire

154

26.8 (17.4)

26.7 (17.3)

South Lanarkshire

398

65.7 (16.5)

64.9 (16.3)

Clackmannanshire

64

10.3 (16.0)

10.3 (16.0)

Edinburgh, City of

549

60.3 (11.0)

60.8 (11.1)

South Ayrshire

147

13.2 (9.0)

13.3 (9.1)

Fife

453

32.1 (7.1)

31.5 (7.0)

Argyll & Bute

122

8.6 (7.0)

8.7 (7.1)

Falkirk

197

14.0 (7.1)

13.8 (7.0)

Aberdeen City

267

17.4 (6.5)

18.0 (6.7)

Stirling

110

6.5 (5.9)

6.5 (5.9)

Dumfries & Galloway

193

9.8 (5.1)

9.9 (5.1)

West Lothian

211

9.7 (4.6)

9.4 (4.5)

East Renfrewshire

120

5.5 (4.6)

5.4 (4.5)

East Dunbartonshire

127

3.4 (2.7)

3.4 (2.7)

Highland

292

9.7 (3.3)

9.4 (3.2)

Angus

142

3.4 (2.4)

3.4 (2.4)

Perth & Kinross

175

3.6 (2.0)

3.6 (2.0)

Scottish Borders

130

2.0 (1.6)

2.0 (1.5)

Midlothian

112

1.1 (1.0)

1.1 (0.9)

Aberdeenshire

301

2.6 (0.9)

2.6 (0.9)

East Lothian

120

0.6 (0.5)

0.6 (0.5)

Eilean Siar

36

0.0 (0.0)

0.0 (0.0)

Moray

116

0.0 (0.0)

0.0 (0.0)

Orkney Islands

27

0.0 (0.0)

0.0 (0.0)

Shetland Islands

30

0.0 (0.0)

0.0 (0.0)

Table B.5. Number of data zones in each LA, and probability-weighted number (%) of data zones amongst the 15% most deprived data zones nationally, according to the SIMD calculated using the original method and an alternative where the health, education and access domains scores were transformed by scientific formulaand then all domains were standardised by subtracting the mean and dividing by the standard deviation prior to weighted combination

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Page updated: Tuesday, October 18, 2005