Background
Randomised response models
Non-randomised methods
Practical issues
Aims
Methods
Measures
Forced Response model
-
2 - 4 = ignore the question and tick the 'Yes'
-
11, 12 = ignore the question and tick 'No'
-
5-10 = answer the question truthfully by ticking either 'Yes' or 'No'
Additional questions
-
In your opinion, should Mephedrone be a controlled substance? (Yes/No)
-
What percentage of students in the UK do you think use Mephedrone (0% = nobody, 100% = everybody)? (Yes/No)
-
On a scale of 1 (not harmful at all) to 10 (very harmful), how harmful do you think Mephedrone is for your health?
Analyses
Statistical analyses
Hair analysis
Hair digestion
Liquid Liquid Extraction (LLE)
Qualitative analysis
LC run time (min) | Acetonitrile in presence of (0.1% Formic acid) | Water (%) | ||
---|---|---|---|---|
0 | 60 | 40 | ||
3 | 100 | 0 | ||
4 | 100 | 0 | ||
5 | 60 | 40 | ||
10 | 60 | 40 | ||
Retention time (min)
|
Lower Limit of Detection (ng)
|
Flow rate (μL/min)
|
Injection volume (μL)
|
Column Temperature (°C)
|
1.92 | 0.5 | 200 | 3.0 | 45 |
Sampling
Results
Results from the survey
Area | ||||
---|---|---|---|---|
Rural
|
Metropolitan
|
ALL
| ||
Social projection | Male | 28.00 ± 23.690 | 35.51 ± 23.231 | 31.45 ± 23.717 |
Female | 26.56 ± 20.780 | 40.68 ± 22.898 | 33.79 ± 22.926 | |
ALL | 27.45 ± 22.572 | 37.74 ± 23.155 | ||
Health risk | Male | 5.87 ± 2.415 | 6.71 ± 1.912 | 6.26 ± 2.139 |
Female | 6.73 ± 1.968 | 7.01 ± 2.303 | 6.87 ± 2.139 | |
ALL | 6.20 ± 2.286 | 6.84 ± 2.083 |
Estimation using the Forced Response model
Hair analysis
The simplified SSC algorithm
-
My birthday is in the first 6 months (January - June) of the year.
-
My house number is an even number.
-
The last digit of my phone number is even
-
My mother's birthday falls between July and December
-
I have taken Mephedrone at least once in the previous three months
X | Observed P(X) |
---|---|
0 | 0.063 |
1 | 0.270 |
2 | 0.376 |
3 | 0.215 |
4 | 0.068 |
5 | 0.008 |
SSC algorithm taking the divergence from the 50/50 distribution into consideration
Frequency count | Probability | Frequency count | Probability | |
---|---|---|---|---|
Birthday on/ina | ||||
odd/even days | 245,269 | 0.509872 | 235,771 | 0.490128 |
first half (up to and including the 15th)/second half of the month | 239,157 | 0.497167 | 241,883 | 0.502833 |
first half/second half of the year | 232,666 | 0.483673 | 248,374 | 0.516327 |
odd/even numbered months | 242,683 | 0.504497 | 238,357 | 0.495503 |
Birthday on/inb | ||||
odd/even days | 253,438 | 0.511098 | 242,432 | 0.488902 |
first half (up to and including the 15th)/second half of the month | 247,927 | 0.499984 | 247,943 | 0.500016 |
first half/second half of the year | 247,447 | 0.499016 | 248,423 | 0.500984 |
Odd/even numbered months | 251,226 | 0.506637 | 244,644 | 0.493363 |
Birthday on/inc | ||||
odd/even days | 5,739 | 0.514386 | 5,418 | 0.4856144 |
first half (up to and including the 15th)/second half of the month | 5,562 | 0.498521 | 5,595 | 0.501479 |
first half/second half of the year | 5,606 | 0.502465 | 5,551 | 0.497535 |
Odd/even numbered months | 5,731 | 0.513669 | 5,426 | 0.486331 |
Triangulating the SSC with the FR and hair analysis
Implementation
Potential exposure
Design | Innocuous | Sensitivea | ||||||
---|---|---|---|---|---|---|---|---|
5%
|
10%
|
15%
|
20%
|
30%
|
40%
|
50%
| ||
1 + 1 | 50.00 | 2.50 | 5.00 | 7.50 | 10.00 | 15.00 | 20.00 | 25.00 |
2 + 1 | 25.00 | 1.25 | 2.50 | 3.75 | 5.00 | 7.50 | 10.00 | 12.50 |
3 + 1 | 12.50 | 0.62 | 1.25 | 1.87 | 2.50 | 3.75 | 5.00 | 6.25 |
4 + 1 | 6.25 | 0.31 | 0.62 | 0.94 | 1.25 | 1.87 | 2.50 | 3.12 |
5 + 1 | 3.12 | 0.16 | 0.31 | 0.48 | 0.62 | 0.94 | 1.25 | 1.56 |
6 + 1 | 1.56 | 0.08 | 0.16 | 0.23 | 0.31 | 0.47 | 0.62 | 0.78 |
7 + 1 | 0.78 | 0.04 | 0.08 | 0.12 | 0.16 | 0.23 | 0.31 | 0.39 |
8 + 1 | 0.39 | 0.02 | 0.04 | 0.06 | 0.08 | 0.12 | 0.16 | 0.19 |
Questions are honestly answered | 0 and 5 answers are combined | Any other response options are selected | |
---|---|---|---|
0 | 1/16 - d/16 | 1/16 | 1/16 - d/20 |
1 | 1/4 - 3d/16 | 1/4 - 3d/16 | 1/4 - 7d/40 |
2 | 3/8 - d/8 | 3/8 - d/8 | 3/8 - 9d/80 |
3 | 1/4 + d/8 | 1/4 + d/8 | 1/4 - 11d/80 |
4 | 1/16 + 3d/16 | 1/16 + 3/16d | 1/16 + d/5 |
5 | d/16 |
Required minimum sample size
Sample size | 4 baseline questions B(4*k, 05) | 5 baseline questions B(5*k, 05) | 6 baseline questions B(6*k, 05) | |||
---|---|---|---|---|---|---|
Lower
|
Upper
|
Lower
|
Upper
|
Lower
|
Upper
| |
100 | 1.800 | 2.200 | 2.280 | 2.720 | 2.760 | 3.240 |
200 | 1.860 | 2.140 | 2.345 | 2.655 | 2.830 | 3.170 |
300 | 1.887 | 2.113 | 2.373 | 2.627 | 2.860 | 3.140 |
400 | 1.903 | 2.098 | 2.390 | 2.610 | 2.880 | 3.120 |
500 | 1.912 | 2.088 | 2.402 | 2.598 | 2.892 | 3.108 |
750 | 1.928 | 2.072 | 2.420 | 2.580 | 2.912 | 3.088 |
1000 | 1.938 | 2.062 | 2.431 | 2.569 | 2.924 | 3.076 |
1500 | 1.949 | 2.051 | 2.443 | 2.557 | 2.938 | 3.062 |
2000 | 1.956 | 2.044 | 2.451 | 2.549 | 2.947 | 3.054 |
Power analysis
Prevalence Rate | ||||||||||
---|---|---|---|---|---|---|---|---|---|---|
0.05 | 0.1 | 0.15 | 0.2 | 0.25 | 0.3 | 0.35 | 0.4 | 0.45 | 0.5 | |
Standard Deviation (s)
| ||||||||||
1.022 | 1.043 | 1.063 | 1.080 | 1.092 | 1.104 | 1.112 | 1.118 | 1.118 | 1.121 | |
Effect Size (Δ) |
Minimum Sample Size (n)
| |||||||||
0.01 | 28247 | 29421 | 30566 | 31563 | 32251 | 32975 | 33479 | 33799 | 33823 | 33993 |
0.02 | 7062 | 7355 | 7641 | 7891 | 8063 | 8244 | 8370 | 8450 | 8456 | 8498 |
0.03 | 3139 | 3269 | 3396 | 3507 | 3583 | 3664 | 3720 | 3755 | 3758 | 3777 |
0.04 | 1765 | 1839 | 1910 | 1973 | 2016 | 2061 | 2092 | 2112 | 2114 | 2125 |
0.05 | 1130 | 1177 | 1223 | 1263 | 1290 | 1319 | 1339 | 1352 | 1353 | 1360 |
0.1 | 282 | 294 | 306 | 316 | 323 | 330 | 335 | 338 | 338 | 340 |
0.15 | 126 | 131 | 136 | 140 | 143 | 147 | 149 | 150 | 150 | 151 |
0.2 | 71 | 74 | 76 | 79 | 81 | 82 | 84 | 84 | 85 | 85 |
0.25 | 45 | 47 | 49 | 51 | 52 | 53 | 54 | 54 | 54 | 54 |
0.3 | 31 | 33 | 34 | 35 | 36 | 37 | 37 | 38 | 38 | 38 |
0.35 | 23 | 24 | 25 | 26 | 26 | 27 | 27 | 28 | 28 | 28 |
0.4 | 18 | 18 | 19 | 20 | 20 | 21 | 21 | 21 | 21 | 21 |
0.45 | 14 | 15 | 15 | 16 | 16 | 16 | 17 | 17 | 17 | 17 |
0.5 | 11 | 12 | 12 | 13 | 13 | 13 | 13 | 14 | 14 | 14 |
Prevalence Rate | ||||||||||
---|---|---|---|---|---|---|---|---|---|---|
0.05 | 0.1 | 0.15 | 0.2 | 0.25 | 0.3 | 0.35 | 0.4 | 0.45 | 0.5 | |
Standard Deviation (s)
| ||||||||||
1.138 | 1.157 | 1.172 | 1.190 | 1.202 | 1.203 | 1.214 | 1.219 | 1.224 | 1.227 | |
Effect Size (Δ)
|
Minimum Sample Size(n)
| |||||||||
0.01 | 35063 | 36243 | 37157 | 38294 | 39129 | 39155 | 39914 | 40224 | 40548 | 40713 |
0.02 | 8766 | 9061 | 9289 | 9574 | 9782 | 9789 | 9979 | 10056 | 10137 | 10178 |
0.03 | 3896 | 4027 | 4129 | 4255 | 4348 | 4351 | 4435 | 4469 | 4505 | 4524 |
0.04 | 2191 | 2265 | 2322 | 2393 | 2446 | 2447 | 2495 | 2514 | 2534 | 2545 |
0.05 | 1403 | 1450 | 1486 | 1532 | 1565 | 1566 | 1597 | 1609 | 1622 | 1629 |
0.1 | 351 | 362 | 372 | 383 | 391 | 392 | 399 | 402 | 405 | 407 |
0.15 | 156 | 161 | 165 | 170 | 174 | 174 | 177 | 179 | 180 | 181 |
0.2 | 88 | 91 | 93 | 96 | 98 | 98 | 100 | 101 | 101 | 102 |
0.25 | 56 | 58 | 59 | 61 | 63 | 63 | 64 | 64 | 65 | 65 |
0.3 | 39 | 40 | 41 | 43 | 43 | 44 | 44 | 45 | 45 | 45 |
0.35 | 29 | 30 | 30 | 31 | 32 | 32 | 33 | 33 | 33 | 33 |
0.4 | 22 | 23 | 23 | 24 | 24 | 24 | 25 | 25 | 25 | 25 |
0.45 | 17 | 18 | 18 | 19 | 19 | 19 | 20 | 20 | 20 | 20 |
0.5 | 14 | 14 | 15 | 15 | 16 | 16 | 16 | 16 | 16 | 16 |
Standard error (SE) | Percentage points (1.96SE) | Minimum n |
---|---|---|
(0.05) | ±0.0980 | 178 |
(0.04) | ±0.0784 | 278 |
(0.03) | ±0.0588 | 494 |
(0.02) | ±0.0392 | 1112 |
(0.01) | ±0.0196 | 4445 |
Efficiency
Non-compliance
Potential innocuous questions
Discussion
-
The model is simple to administer, offering a self-administration option without any sense of deception.
-
The SSC model reduces the complexity in instructions and places low cognitive demands upon respondents.
-
Unlike the FR model, SSC asks each respondent to answer, in a fuzzy way, the (sensitive) research question and hence improves the face validity of the research tool.
-
Unlike other RRT/NR models, the SSC avoids a forced 'yes' response, which can be off-putting for people whose honest answer would normally be 'no' to the sensitive question. Also, respondents are not required to answer the sensitive question directly.
-
In the SSC model, no obvious self protective strategy is present (e.g. self-protective 'no' saying), thus this approach can overcome the 'self protective no' bias.