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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)

From: Is Middle-Upper Arm Circumference “normally” distributed? Secondary data analysis of 852 nutrition surveys

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)

  1. aShapiro–Wilk test (p < 0.05); b D’Agostino test (p < 0.05); c Anscombe–Glynn test (p < 0.05)