# CochranHorganData: Populations Analyzed in Gunning and Horgan (2004) and Cochran... In stratification: Univariate Stratification of Survey Populations

## Description

The first population Debtors is an accounting population of debtors in an Irish firm, detailed in Horgan (2003). The other populations are three of the skewed populations in Cochran (1961). These are:
UScities: the population in thousands of US cities in 1940;
UScolleges: the number of students in four-year US colleges in 1952-1953;
USbanks: the resources in millions of dollars of large commercial US banks.

## Usage

 1 2 3 4 Debtors UScities UScolleges USbanks

## Format

The formats of these data sets are, respectively:
num [1:3369] 40 40 40 40 40 40 40 40 40 40 ...
num [1:1038] 10 10 10 10 10 10 10 10 10 10 ...
num [1:677] 200 201 202 202 207 210 211 213 215 217 ...
num [1:357] 70 71 72 72 72 73 73 73 73 73 ...

Jane M. Horgan

## References

Cochran, W.G. (1961). Comparison of methods for determining stratum boundaries. Bulletin of the International Statistical Institute, 32(2), 345-358.

Gunning, P. and Horgan, J.M. (2004). A new algorithm for the construction of stratum boundaries in skewed populations. Survey Methodology, 30(2), 159-166.

Horgan, J.M. (2003). A list sequential sampling scheme with applications in financial auditing. IMA Journal of Management Mathematics, 14, 1-18.

## Examples

 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 ### Reproduction of the results in Table 4 and Table 7 part 3 (case L=5) of ### Gunning and Horgan (2004). The differences in the nh come from different ### rounding. The more important differences observed for the cumulative ### root frequency method are due to the use of different numbers of classes. strata.geo(x=Debtors, n=100, Ls=5, alloc=c(0.5,0,0.5)) strata.cumrootf(x=Debtors, n=100, Ls=5, alloc=c(0.5,0,0.5), nclass=40) strata.LH(x=Debtors, CV=0.0360, Ls=5, alloc=c(0.5,0,0.5), takeall=1, algo="Sethi") strata.geo(x=UScities, n=100, Ls=5, alloc=c(0.5,0,0.5)) strata.cumrootf(x=UScities, n=100, Ls=5, alloc=c(0.5,0,0.5), nclass=40) strata.LH(x=UScities, CV=0.0144, Ls=5, alloc=c(0.5,0,0.5), takeall=1, algo="Sethi") strata.geo(x=UScolleges, n=100, Ls=5, alloc=c(0.5,0,0.5)) strata.cumrootf(x=UScolleges, n=100, Ls=5, alloc=c(0.5,0,0.5), nclass=40) strata.LH(x=UScolleges, CV=0.0184, Ls=5, alloc=c(0.5,0,0.5), takeall=1, algo="Sethi") strata.geo(x=USbanks, n=100, Ls=5, alloc=c(0.5,0,0.5)) strata.cumrootf(x=USbanks, n=100, Ls=5, alloc=c(0.5,0,0.5), nclass=40) strata.LH(x=USbanks, CV=0.0110, Ls=5, alloc=c(0.5,0,0.5), takeall=1, algo="Sethi")

### Example output

Given arguments:
x = Debtors
n = 100, Ls = 5
allocation: q1 = 0.5, q2 = 0, q3 = 0.5
model = none

Strata information:
|      type rh |       bh     E(Y)      Var(Y)   Nh  nh   fh
stratum 1 | take-some  1 |   148.28    83.60      997.12 1054   3 0.00
stratum 2 | take-some  1 |   549.67   307.76    14063.78 1267  14 0.01
stratum 3 | take-some  1 |  2037.60  1008.41   163709.80  732  27 0.04
stratum 4 | take-some  1 |  7553.33  3702.59  1917482.45  265  33 0.12
stratum 5 | take-some  1 | 28001.00 12313.39 25748882.16   51  23 0.45
Total                                                    3369 100 0.03

Total sample size: 100
Anticipated population mean: 838.6388
Anticipated CV: 0.03585596
Given arguments:
x = Debtors
nclass = 40, n = 100, Ls = 5
allocation: q1 = 0.5, q2 = 0, q3 = 0.5
model = none

Strata information:
|      type rh |    bh     E(Y)     Var(Y)   Nh  nh   fh
stratum 1 | take-some  1 |   739   247.69    35243.4 2568  45 0.02
stratum 2 | take-some  1 |  1438   998.87    37091.7  352   6 0.02
stratum 3 | take-some  1 |  3535  2233.27   340565.4  284  15 0.05
stratum 4 | take-some  1 |  8428  5277.78  1581440.3  124  15 0.12
stratum 5 | take-some  1 | 28001 13390.66 26097549.6   41  19 0.46
Total                                                3369 100 0.03

Total sample size: 100
Anticipated population mean: 838.6388
Anticipated CV: 0.0357907
Given arguments:
x = Debtors
CV = 0.036, Ls = 5, takenone = 0, takeall = 1
allocation: q1 = 0.5, q2 = 0, q3 = 0.5
model = none
algo = Sethi: maxiter = 500

Strata information:
|      type rh  initbh |       bh     E(Y)      Var(Y)   Nh nh   fh
stratum 1 | take-some  1    99.0 |   349.33   146.49     7238.03 1856 13 0.01
stratum 2 | take-some  1   198.0 |  1190.18   626.26    46421.46  991 17 0.02
stratum 3 | take-some  1   410.0 |  3483.12  2013.98   377580.90  350 17 0.05
stratum 4 | take-some  1   888.8 | 10334.93  5589.95  2955057.91  146 20 0.14
stratum 5 |  take-all  1 28001.0 | 28001.00 15839.62 24644840.08   26 26 1.00
Total                                                            3369 93 0.03

Total sample size: 93
Anticipated population mean: 838.6388
Anticipated CV: 0.03512165
Note: CV=RRMSE (Relative Root Mean Squared Error) because takenone=0.
Given arguments:
x = UScities
n = 100, Ls = 5
allocation: q1 = 0.5, q2 = 0, q3 = 0.5
model = none

Strata information:
|      type rh |     bh   E(Y) Var(Y)   Nh  nh   fh
stratum 1 | take-some  1 |  18.17  14.18   7.21  364  18 0.05
stratum 2 | take-some  1 |  33.01  24.55  12.82  418  28 0.07
stratum 3 | take-some  1 |  59.98  43.55  46.77  130  17 0.13
stratum 4 | take-some  1 | 108.98  77.67 152.91   87  20 0.23
stratum 5 | take-some  1 | 199.00 153.05 569.07   39  17 0.44
Total                                           1038 100 0.10

Total sample size: 100
Anticipated population mean: 32.57418
Anticipated CV: 0.01445161
Given arguments:
x = UScities
nclass = 40, n = 100, Ls = 5
allocation: q1 = 0.5, q2 = 0, q3 = 0.5
model = none

Strata information:
|      type rh |    bh   E(Y) Var(Y)   Nh  nh   fh
stratum 1 | take-some  1 |  19.4  14.54   8.26  393  20 0.05
stratum 2 | take-some  1 |  28.8  24.02   6.30  336  15 0.04
stratum 3 | take-some  1 |  52.3  38.21  44.48  165  19 0.12
stratum 4 | take-some  1 |  94.6  70.90 137.07   94  19 0.20
stratum 5 | take-some  1 | 199.0 141.16 947.29   50  27 0.54
Total                                          1038 100 0.10

Total sample size: 100
Anticipated population mean: 32.57418
Anticipated CV: 0.01488882
Given arguments:
x = UScities
CV = 0.0144, Ls = 5, takenone = 0, takeall = 1
allocation: q1 = 0.5, q2 = 0, q3 = 0.5
model = none
algo = Sethi: maxiter = 500

Strata information:
|      type rh initbh |     bh   E(Y)  Var(Y)   Nh  nh   fh
stratum 1 | take-some  1     15 |  14.72  11.93    2.07  189   4 0.02
stratum 2 | take-some  1     20 |  21.62  17.80    3.58  270   8 0.03
stratum 3 | take-some  1     26 |  35.59  26.23   10.77  336  17 0.05
stratum 4 | take-some  1     40 |  80.29  51.27  151.69  164  30 0.18
stratum 5 |  take-all  1    199 | 199.00 120.66 1329.19   79  79 1.00
Total                                                   1038 138 0.13

Total sample size: 138
Anticipated population mean: 32.57418
Anticipated CV: 0.01414471
Note: CV=RRMSE (Relative Root Mean Squared Error) because takenone=0.
Given arguments:
x = UScolleges
n = 100, Ls = 5
allocation: q1 = 0.5, q2 = 0, q3 = 0.5
model = none

Strata information:
|      type rh |      bh    E(Y)     Var(Y)  Nh  nh   fh
stratum 1 | take-some  1 |  434.00  305.13    4501.30  94   3 0.03
stratum 2 | take-some  1 |  941.76  674.31   20621.59 255  15 0.06
stratum 3 | take-some  1 | 2043.61 1315.09  102487.82 198  27 0.14
stratum 4 | take-some  1 | 4434.60 2961.50  387698.22  74  20 0.27
stratum 5 | take-some  1 | 9624.00 6749.70 2138520.32  56  35 0.62
Total                                                 677 100 0.15

Total sample size: 100
Anticipated population mean: 1563
Anticipated CV: 0.018296
Given arguments:
x = UScolleges
nclass = 40, n = 100, Ls = 5
allocation: q1 = 0.5, q2 = 0, q3 = 0.5
model = none

Strata information:
|      type rh |      bh    E(Y)     Var(Y)  Nh  nh   fh
stratum 1 | take-some  1 |  671.15  448.41   19168.34 224  15 0.07
stratum 2 | take-some  1 | 1377.88  955.24   31216.18 254  21 0.08
stratum 3 | take-some  1 | 2791.33 1951.69  159263.61 103  19 0.18
stratum 4 | take-some  1 | 5618.22 3931.69  824511.35  58  25 0.43
stratum 5 | take-some  1 | 9624.00 7526.66 1235296.65  38  20 0.53
Total                                                 677 100 0.15

Total sample size: 100
Anticipated population mean: 1563
Anticipated CV: 0.01705522
Given arguments:
x = UScolleges
CV = 0.0184, Ls = 5, takenone = 0, takeall = 1
allocation: q1 = 0.5, q2 = 0, q3 = 0.5
model = none
algo = Sethi: maxiter = 500

Strata information:
|      type rh initbh |      bh    E(Y)     Var(Y)  Nh  nh   fh
stratum 1 | take-some  1  524.4 |  512.32  354.18    9111.04 133   4 0.03
stratum 2 | take-some  1  763.4 |  869.76  673.31   10190.63 180   6 0.03
stratum 3 | take-some  1 1080.6 | 1577.36 1103.98   30823.03 185  10 0.05
stratum 4 | take-some  1 1977.0 | 3675.52 2314.81  293595.46 110  18 0.16
stratum 5 |  take-all  1 9624.0 | 9624.00 6246.14 2835174.47  69  69 1.00
Total                                                        677 107 0.16

Total sample size: 107
Anticipated population mean: 1563
Anticipated CV: 0.01785935
Note: CV=RRMSE (Relative Root Mean Squared Error) because takenone=0.
Given arguments:
x = USbanks
n = 100, Ls = 5
allocation: q1 = 0.5, q2 = 0, q3 = 0.5
model = none

Strata information:
|      type rh |     bh   E(Y)   Var(Y)  Nh  nh   fh
stratum 1 | take-some  1 | 118.59  93.92   192.23 114  13 0.11
stratum 2 | take-some  1 | 200.92 147.58   429.18 116  20 0.17
stratum 3 | take-some  1 | 340.39 258.03  2027.22  64  25 0.39
stratum 4 | take-some  1 | 576.68 442.90  2929.73  39  18 0.46
stratum 5 |  take-all  1 | 978.00 788.96 16224.79  24  24 1.00
Total                                             357 100 0.28

Total sample size: 100
Anticipated population mean: 225.6246
Anticipated CV: 0.01071521
Given arguments:
x = USbanks
nclass = 40, n = 100, Ls = 5
allocation: q1 = 0.5, q2 = 0, q3 = 0.5
model = none

Strata information:
|      type rh |     bh   E(Y)   Var(Y)  Nh  nh   fh
stratum 1 | take-some  1 | 115.35  93.05   177.82 110  12 0.11
stratum 2 | take-some  1 | 183.38 142.05   260.83 109  15 0.14
stratum 3 | take-some  1 | 319.43 240.01  1787.25  68  24 0.35
stratum 4 | take-some  1 | 523.50 415.26  3361.67  42  21 0.50
stratum 5 |  take-all  1 | 978.00 752.39 21938.24  28  28 1.00
Total                                             357 100 0.28

Total sample size: 100
Anticipated population mean: 225.6246
Anticipated CV: 0.01040122
Given arguments:
x = USbanks
CV = 0.011, Ls = 5, takenone = 0, takeall = 1
allocation: q1 = 0.5, q2 = 0, q3 = 0.5
model = none
algo = Sethi: maxiter = 500

Strata information:
|      type rh initbh |     bh   E(Y)   Var(Y)  Nh  nh   fh
stratum 1 | take-some  1  100.0 |  99.54  84.84    81.79  70   4 0.06
stratum 2 | take-some  1  131.4 | 130.83 114.40    87.71  68   4 0.06
stratum 3 | take-some  1  176.0 | 189.70 149.91   252.96  85   9 0.11
stratum 4 | take-some  1  318.0 | 339.31 251.83  2179.66  71  21 0.30
stratum 5 |  take-all  1  978.0 | 978.00 574.73 36236.80  63  63 1.00
Total                                                    357 101 0.28

Total sample size: 101
Anticipated population mean: 225.6246
Anticipated CV: 0.01067923
Note: CV=RRMSE (Relative Root Mean Squared Error) because takenone=0.

stratification documentation built on May 1, 2019, 9:13 p.m.