A random effects meta-analysis model with Box-Cox transformation

Table 3 Posterior median and 95 percent credible interval of: overall mean and square root of between-study variance from the normal random effects model, overall median and normalised IQR from the proposed model

NRE		BC		BC-SI
	Square root of
	between-study		Normalised		Normalised
Overall mean	variance	Overall median	IQR^a	Overall median	IQR^a
Post. (s.d.)	Post. (s.d.)	Post. (s.d.)	Post. (s.d.)	Post. (s.d.)	Post. (s.d.)
(95% CI)	(95% CI)	(95% CI)	(95% CI)	(95% CI)	(95% CI)
Example 1: Teacher expectancy on pupil IQ
0.083 (0.061)	0.146 (0.087)	0.030 (0.051)	0.084 (0.074)	n/a	n/a
(−0.021,0.222)	(0.011,0.344)	(−0.058,0.144)	(0.004,0.278)
Example 2: Antidepressants for reducing pain in fibromyalgia syndrome
−0.418 (0.067)	0.164 (0.097)	−0.369 (0.056)	0.094 (0.077)	−0.361 (0.057)	0.098 (0.081)
(−0.567,−0.298)	(0.013,0.384)	(−0.489,−0.267)	(0.005,0.291)	(−0.484,−0.259)	(0.005,0.306)

^aNormalised IQR =(ξ ₇₅−ξ ₂₅)/(z ₇₅−z ₂₅)
Post.: posterior median, s.d.: standard deviation, CI: credible interval
NRE: normal random effects model, BC: proposed model using Box-Cox transformation
BC-SI: proposed model using Box-Cox transformation with the sign inversion for negatively skewed data

ISSN: 1471-2288