4.1 Calculating standardized mean differences

To calculate standardized mean differences (SMD), we need means, SDs, and sample sizes per group. In this example, we’ll be looking at the dat.normand1999 dataset included with metafor:

source	n1i	m1i	sd1i	n2i	m2i	sd2i
Edinburgh	155	55	47	156	75	64
Orpington-Mild	31	27	7	32	29	4
Orpington-Moderate	75	64	17	71	119	29
Orpington-Severe	18	66	20	18	137	48
Montreal-Home	8	14	8	13	18	11
Montreal-Transfer	57	19	7	52	18	4
Newcastle	34	52	45	33	41	34
Umea	110	21	16	183	31	27
Uppsala	60	30	27	52	23	20

To calculate effect sizes, we use the function metafor::escalc, which incorporates formulas to compute many different effect sizes. A detailed explanation, with references to the formulas used, can be found by selecting the function, and pressing F1.

df_smd <- escalc(measure = "SMD",
                 m1i = m1i,
                 m2i = m2i,
                 sd1i = sd1i,
                 sd2i = sd2i,
                 n1i = n1i,
                 n2i = n2i,
                 data = dat.normand1999)
df_smd

source	n1i	m1i	sd1i	n2i	m2i	sd2i	yi	vi
Edinburgh	155	55	47	156	75	64	-0.3551696	0.0130647
Orpington-Mild	31	27	7	32	29	4	-0.3479400	0.0644689
Orpington-Moderate	75	64	17	71	119	29	-2.3175692	0.0458121
Orpington-Severe	18	66	20	18	137	48	-1.8879823	0.1606177
Montreal-Home	8	14	8	13	18	11	-0.3839641	0.2054333
Montreal-Transfer	57	19	7	52	18	4	0.1721487	0.0369106
Newcastle	34	52	45	33	41	34	0.2720521	0.0602671
Umea	110	21	16	183	31	27	-0.4245963	0.0148630
Uppsala	60	30	27	52	23	20	0.2895562	0.0362717

Note that the function returns the original data, with two added columns: yi and vi. These are the SMD effect size and its variance.