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Table 1 Characteristics of surveys showing departure from a normal distribution (Shapiro–Wilk test, p < 0.05) and effect of transformation and smoothing on specific characteristics (N = 533)
| Surveys failing Shapiro–Wilk test (p < 0.05) N = 533 (62.6 %) | N (%) | N (%) with “normal” distribution after transformation or smoothing | ||
|---|---|---|---|---|
| Box-Cox | Spline | Loess | ||
| All surveysa | 533 (100) | 301 (56.5) | 318 (59.7) | 304 (57.0) |
| By key survey characteristics | ||||
| Skewedb | 183 (34.3) | 113 (61.7) | 81 (49.4) | 89 (48.6) |
| Non-normal kurtosisc | 196 (36.8) | 62 (31.6) | 137 (69.9) | 139 (70.9) |
| Skewed and non-normal kurtosisb, c | 70 (13.1) | 23(32.9) | 41 (58.6) | 43 (61.4) |
| Large design effect (>3) | 164 (30.8) | 86 (52.4) | 81 (49.4) | 92 (56.1) |
| High digit preference (score < 0.75) | 294 (55.2) | 143 (48.6) | 170 (57.8) | 178 (60.6) |
| Large sample size (n > 900) | 204 (38.3) | 122 (59.8) | 95 (46.6) | 101 (49.5) |
