Table 3 

Simulation Results (Normal Distribution, Equal Experimental and Control Groups, Standard Deviation 40% of Control Mean Value). 

% Bias 
% Coverage 
% Statistical Power 
I^{2}(%) 






τ = 0s 
τ = 0.5s 
τ = 0s 
τ = 0.5s 
τ = 0s 
τ 0.5s 
τ 0.5s 









Δ 
n (exp/contr) 
k 
MD 
SMD 
RoM 
MD 
SMD 
RoM 
MD 
SMD 
RoM 
MD 
SMD 
RoM 
MD 
SMD 
RoM 
MD 
SMD 
RoM 
MD 
SMD 
RoM 


SMD = 0.2 
10/10 
5 
0 
4 
0 
0 
5 
1 
95 
97 
95 
90 
92 
90 
15 
11 
14 
15 
13 
14 
59 
48 
55 
10 
0 
5 
0 
1 
5 
0 
95 
97 
95 
92 
93 
92 
27 
22 
26 
19 
18 
19 
60 
48 
56 

30 
0 
5 
0 
1 
6 
0 
94 
96 
95 
94 
94 
94 
66 
61 
64 
39 
38 
38 
60 
48 
56 



MD = 8 
100/100 
5 
0 
0 
0 
0 
0 
1 
96 
97 
96 
88 
88 
87 
82 
82 
82 
21 
21 
21 
93 
92 
92 
RoM = 1.08 
10 
0 
0 
0 
0 
0 
0 
96 
96 
96 
92 
92 
91 
99 
99 
99 
27 
27 
28 
93 
92 
92 

30 
0 
0 
0 
0 
0 
0 
96 
96 
96 
94 
94 
94 
100 
100 
100 
56 
58 
59 
93 
92 
92 





SMD = 0.5 
10/10 
5 
0 
4 
0 
0 
5 
0 
95 
97 
95 
90 
92 
90 
64 
57 
62 
43 
40 
42 
59 
48 
56 
10 
0 
5 
0 
0 
5 
0 
95 
97 
95 
92 
93 
92 
91 
89 
90 
66 
64 
65 
60 
48 
56 

30 
0 
5 
0 
0 
6 
0 
94 
96 
94 
94 
93 
93 
100 
100 
100 
98 
97 
97 
60 
47 
57 



MD = 20 
100/100 
5 
0 
0 
0 
0 
0 
1 
96 
97 
96 
88 
88 
88 
100 
100 
100 
61 
61 
61 
93 
92 
92 
RoM = 1.2 
10 
0 
0 
0 
0 
0 
0 
96 
96 
96 
92 
92 
91 
100 
100 
100 
85 
86 
86 
93 
92 
92 

30 
0 
0 
0 
0 
1 
0 
96 
96 
96 
94 
94 
93 
100 
100 
100 
100 
100 
100 
93 
92 
92 





SMD = 0.8 
10/10 
5 
0 
4 
0 
0 
5 
0 
95 
97 
95 
90 
92 
90 
95 
94 
95 
75 
72 
73 
59 
47 
56 
10 
0 
5 
0 
0 
5 
0 
95 
96 
95 
92 
92 
92 
100 
100 
100 
95 
95 
95 
60 
47 
57 

30 
0 
5 
1 
0 
6 
0 
94 
94 
94 
94 
92 
93 
100 
100 
100 
100 
100 
100 
60 
46 
57 



MD = 32 
100/100 
5 
0 
0 
0 
0 
0 
1 
96 
96 
96 
88 
88 
87 
100 
100 
100 
91 
91 
91 
93 
92 
92 
RoM = 1.32 
10 
0 
0 
0 
0 
0 
1 
96 
96 
96 
92 
92 
91 
100 
100 
100 
100 
100 
100 
93 
91 
92 

30 
0 
0 
0 
0 
1 
0 
96 
96 
96 
94 
94 
93 
100 
100 
100 
100 
100 
100 
93 
91 
92 



Results of 10,000 simulations per scenario with a standard deviation equal to 40% of the control mean, for each combination of effect size (0.2, 0.5, and 0.8 standard deviation units), number of patients (10/10 and 100/100 experimental/control patients per trial), and number of trials (5, 10, and 30). The "% Bias" columns show the bias of each effect measure (MD, SMD, RoM) expressed as percentages of the expected values (negative sign denotes less than expected value), with and without heterogeneity. The "% coverage" columns show the percentage of cases that the true value falls within the 95% confidence interval of the simulated result, with and without heterogeneity. The "% statistical power" columns show the percentage of cases that the 95% confidence interval of the simulated result yields a significant treatment effect (i.e. excluding zero for MD and SMD, and one for RoM), with and without heterogeneity. The I^{2} column shows the degree of heterogeneity only for the scenarios in which heterogeneity was introduced. (For all the scenarios without heterogeneity, the ratio of Q/(k1) was close to unity as expected, corresponding to I^{2 }= 0 [data not shown].) Abbreviations for Table and Legend: contr – control, exp – experimental, I^{2 }– I^{2 }heterogeneity measure, k – number of trials in each metaanalysis, n – number of experimental or number of control patients per trial, Q – Cochran's Q statistic for heterogeneity, MD – mean difference, RoM – ratio of means, s – standard deviation units, SMD – standardized mean difference. 

Friedrich et al. BMC Medical Research Methodology 2008 8:32 doi:10.1186/14712288832 