In the previous article, we introduced the Q test based on 1-way analysis of variance —an approach of subgroup analysis to compare more than 2 subgroups of studies as defined on the basis of a categorical characteristic of the trials, and the R ² index that quantifies the proportion of heterogeneity explained by the covariate of interest. In the present article, we use a real example to illustrate the Q test and the R ² index. The interested reader can use the Excel file (See Supplementary Appendix , available at www.ajodo.org ) as an exercise to understand the calculations.

Application to real data

We will use the data from 6 studies that examine the efficiency on the initial orthodontic alignment of a conventional vs a self-ligating system. Half of the studies are randomized controlled studies (subgroup A), and the rest are controlled clinical studies (subgroup B). Our goal is to determine whether the effect sizes differ in these 2 study types (subgroups). To answer this question, we will apply a subgroup analysis. Table I illustrates the dataset. The effect size of interest is the mean difference.

Table I

Initial orthodontic alignment using Damon and conventional appliances

Study	Damon	Conventional			Mean difference
	Mean	SD	n	Mean	SD	n	Y i	v i	<SPAN role=presentation tabIndex=0 id=MathJax-Element-1-Frame class=MathJax style="POSITION: relative" data-mathml='Tp2′>T2pTp2 T p 2	w i	<SPAN role=presentation tabIndex=0 id=MathJax-Element-2-Frame class=MathJax style="POSITION: relative" data-mathml='wi2′>w2iwi2 w i 2	w i Y i	<SPAN role=presentation tabIndex=0 id=MathJax-Element-3-Frame class=MathJax style="POSITION: relative" data-mathml='wiYi2′>wiY2iwiYi2 w i Y i 2
Randomized controlled studies (A)
Scott	1.41	1.41	32	1.68	0.66	28	−0.27	0.08	0.048	8.00	64.00	−2.16	0.58
Pandis	1.98	0.90	25	2.22	0.96	25	−0.24	0.07	0.048	8.70	75.69	−2.09	0.50
Wahab	2.16	1.08	14	3.15	1.17	15	−0.99	0.17	0.048	4.65	21.62	−4.60	4.56
Total A							–	–		21.35	161.31	−8.85	5.64
Controlled clinical studies (B)
Ong	1.46	0.65	44	1.57	0.59	40	−0.11	0.02	0.048	15.38	236.54	−1.69	0.19
Miles	0.51	0.66	29	0.60	0.75	29	−0.09	0.03	0.048	13.33	177.69	−1.20	0.11
Pandis	1.81	0.71	27	1.41	0.63	27	0.40	0.03	0.048	13.33	177.69	5.33	2.13
Total B							–	–		42.04	591.92	2.44	2.43
Total							–	–		63.39	753.49	−6.41	8.07

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