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Table 3 Calculation of between-group effect sizes, based on information provided in eight randomized sham-controlled studies included in a previous review on pressure pain threshold changes after spinal manipulation

From: How big is the effect of spinal manipulation on the pressure pain threshold and for how long does it last? – secondary analysis of data from a systematic review

First author
Year
1) What is the number of participants of the experimental group (NE) and the control group (NC) and are they equal?
- NE = NC
NE ≠ NC
2) Are the standard deviations of the experimental group (SDE) and the control group (SDC) equal?
- SDE = SDC
- SDE ≠ SDC
3) Which type of effect size coefficient should be used?
- Cohen’s d coefficient (if NE = NC and SDE = SDC or SDE ≠ SDC)
- Hedges’ g coefficient (if NE ≠ NC and SDE ≠ SDC)
4) Give the equations that would be used:
- Effect size (d/g)
- Standard deviation of PPT values used to calculate the effect size (SD* or SD pooled)
- Standard deviation of the effect size (SD(d))
- Confidence interval of the effect size (95% CI)
What are the reported mean PPT values for the experimental group (ME) and for the control group (MC) with their standard deviation (+/− SD), at each follow-up time (units)? At each follow-up time, what are the:
- Effect size (d/g),
- Its standard deviation (SD(d))
- Its confidence interval
(95% CI)
- p value between groups
Effect sizes of clinical significant findings at each follow-up:
0.2 to 0.49 (small)
- 0.5 to 0.79 (medium)
- 0.8 to 1.00 (large)
Ruiz Saez
2007
1) NE = NC = 36
2) SDE ≠ SDC
3) Cohen’s d coefficient
4)
-\( d=\frac{M_E-{M}_C}{SD^{\ast }} \)
- \( \mathrm{SD}\ast =\sqrt{\frac{{SD_E}^2+{SD_C}^2}{2}} \)
- \( \mathrm{SD}(d)=\sqrt{\frac{N_E+{N}_C}{N_E\times {N}_C}+\frac{d^2}{2\left({N}_E+{N}_C\right)}} \)
- 95% CI: [d − 1.96 × SD (d); d + 1.96 × SD(d)]
-T0:
ME = + 1.35 +/−  0.5 Kg/cm2
MC = + 1.27 +/−  0.4 Kg/cm2
-T + 5:
ME = + 1.38 +/−  0.5 Kg/cm2
MC = +  1.15 +/−  0.4 Kg/cm2
-T + 10:
ME = + 1.39 +/−  0.5 Kg/cm2
MC = + 1.1 +/−  0.5 Kg/cm2
-T0:
-d = 0.17
-SD(d) = 0.24
- 95% CI: [− 0.29; + 0.63]
- p value: NS
-T + 5:
-d = 0.51
-SD(d) = 0.24
- 95% CI: [+ 0.04; + 0.98]
- p < 0.01
-T + 10:
-d = 0.58
-SD(d) = 0.24
- 95% CI: [+ 0.11; +  1.05]
-p < 0.01
T0: small
T + 5: medium
T + 10: medium
Srbely
2013
1) NE = NC = 18
2) SDE ≠ SDC
3) Cohen’s d coefficient
4)
-\( d=\frac{M_E-{M}_C}{SD^{\ast }} \)
-\( \mathrm{SD}\ast =\sqrt{\frac{{SD_E}^2+{SD_C}^2}{2}} \)
-\( \mathrm{SD}(d)=\sqrt{\frac{N_E+{N}_C}{N_E\times {N}_C}+\frac{d^2}{2\left({N}_E+{N}_C\right)}} \)
- 95% CI: [d − 1.96 × SD (d); d + 1.96 × SD(d)]
-T + 1:
ME = + 34.4 +/−  9.6 N
MC = +  30.7 +/−  7.5 N
-T + 5:
ME = + 37.5 +/−  11.9 N
MC = + 28.7 +/−  6.0 N
-T + 10:
ME = + 37.9 +/−  14.4 N
MC = + 28.9 +/−  6.3 N
-T + 15:
ME = + 34.3 +/−  11.5 N
MC = + 28.6 +/− 7.0 N
-T + 1:
-d = 0.42
-SD(d) = 0.34
- 95% CI: [− 0.24; + 1.08]
-p < 0.01
-T + 5:
-d = 0.93
-SD(d) = 0.35
− 95% CI: [+ 0.24; + 1.62]
-p < 0.01
-T + 10:
-d = 0.80
-SD(d) = 0.35
- 95% CI: [+ 0.12; + 1.48]
-p < 0.01
-T + 15:
-d = 0.59
-SD(d) = 0.34
- 95% CI: [−  0.08; + 1.26]
-p < 0.01
T + 1: small
T + 5: large
T + 10: large
T + 15: medium
Fernandez de la Penas
2008
1) NE = NC = 10
2) SDE ≠ SDC
3) Cohen’s d coefficient
4)
- \( d=\frac{M_E-{M}_C}{SD^{\ast }} \)
- \( \mathrm{SD}\ast =\sqrt{\frac{{SD_E}^2+{SD_C}^2}{2}} \)
- \( \mathrm{SD}(d)=\sqrt{\frac{N_E+{N}_C}{N_E\times {N}_C}+\frac{d^2}{2\left({N}_E+{N}_C\right)}} \)
- 95% CI: [d − 1.96 × SD (d); d + 1.96 × SD(d)]
-T + 5:
(dominant side/dominant side)
ME = + 387.6 +/−  70.9 kPa/s
MC = + 312.3 +/−  47.7 kPa/s
-T + 5:
-d = 1.24
-SD(d) = 0.49
- 95% CI: [+ 0.28; + 2.20]
-p < 0.05
T + 5: large
Fernandez de la Penas
2007
1)NE = NC = 15
2) SDE ≠ SDC
3) Cohen’s d coefficient
4)
- d = \( \frac{M_E-{M}_C}{SD^{\ast }} \)
- SD*= \( \sqrt{\frac{{SD_E}^2+{SD_C}^2}{2}} \)
- SD(d)=\( \sqrt{\frac{N_E+{N}_C}{N_E\times {N}_C}+\frac{d^2}{2\left({N}_E+{N}_C\right)}} \)
- 95% CI: [d − 1.96 × SD (d); d + 1.96 × SD(d)]
-T + 5:
ME = + 2.9+/− 0.6 Kg/cm2
MC = + 2.3+/− 0.5 Kg/cm2
-T + 5:
-d = 1.08
-SD(d) = 0.48
− 95% CI: [+ 0.14; + 2.02]
-p < 0.01
T + 5: large
Hamilton
2007
1) NE ≠ NC
- NE = 35
- NC = 25
2) SDE ≠ SDC
3) Hedge’ g coefficient
4)
\( {\mathrm{SD}}_{\mathrm{pooled}}=\sqrt{\frac{\left({\mathrm{N}}_{\mathrm{E}}\hbox{-} 1\right){\mathrm{SD}}_{{\mathrm{E}}^2}+\left({\mathrm{N}}_{\mathrm{C}}\hbox{-} 1\right){\mathrm{SD}}_{{\mathrm{C}}^2}}{{\mathrm{N}}_{\mathrm{E}}+{\mathrm{N}}_{\mathrm{C}}\hbox{-} 2}} \)
- \( \boldsymbol{g}=\frac{{\boldsymbol{M}}_{\boldsymbol{E}}-{\boldsymbol{M}}_{\boldsymbol{C}}}{{\boldsymbol{SD}}_{\boldsymbol{Pooled}}} \)
-\( \mathrm{SD}\left(\mathrm{g}\right)=\sqrt{\frac{N_E+{N}_C}{N_E\times {N}_C}+\frac{d^2}{2\left({N}_E+{N}_C\right)}} \)
- 95% CI: [d − 1.96 × SD (d); d + 1.96 × SD(d)]
-T + 5:
ME = +  398.06 +/−  133.51 kPa/s
MC = + 368.44 +/−  208.16 kPa/s
-T + 30:
ME = + 374.58 +/−  127.50 kPa/s
MC = + 368.68 +/−  192.62 kPa/s
-T + 5:
-g = 0.17
-SD(g) = 0.26
− 95% CI: [− 0.34; +  0.68]
-p < 0.01
-T + 30:
-g = 0.03
-SD(g) = 0.26
− 95% CI: [− 0.48; + 0.54]
-p value: NS
T + 5: small
T + 30: small
Yu
2012
1) NE = NC = 30
2) SDE ≠ SDC
3) Cohen’s d coefficient
4)
- d = \( \frac{M_E-{M}_C}{SD^{\ast }} \)
- SD*= \( \sqrt{\frac{{SD_E}^2+{SD_C}^2}{2}} \)
- SD(d)=\( \sqrt{\frac{N_E+{N}_C}{N_E\times {N}_C}+\frac{d^2}{2\left({N}_E+{N}_C\right)}} \)
- 95% CI: [d − 1.96 × SD (d); d + 1.96 × SD(d)]
-L5-S1 PD side
T0:
ME = + 5.64+/− 1.13 Kg/cm2
MC = + 4.85+/− 1.12 Kg/cm2
-L5-S1 OPD side
T0:
ME = + 5.56+/− 1.17 Kg/cm2
MC = + 4.91+/− 1.13 Kg/cm2
-L5 dermatome PD side
T0:
ME = + 4.77+/− 0.96 Kg/cm2
MC = + 4.14+/− 1.13 Kg/cm2
-L5 dermatome OPD side
T0:
ME = + 4.63+/− 0.95 Kg/cm2
MC = + 4.09+/− 0.82 Kg/cm2
-L5-S1 PD side
T0
-d = 0.70
-SD(d) = 0.27
− 95% CI: [+ 0.18; +  1.22]
-p < 0.05
-L5-S1 OPD side
T0
-d = 0.56
-SD(d) = 0.26
− 95% CI: [+ 0.04; +  1.08]
-p < 0.05
- L5 dermatome PD side
T0
-d = 0.60
-SD(d) = 0.26
− 95% CI: [+ 0.08; +  1.12]
-p < 0.05
- L5dermatome OPD side
T0
-d = 0.60
-SD(d) = 0.26
− 95% CI: [+ 0.08; +  1.12]
-p < 0.05
-L5-S1 PD side
T0: medium
-L5-S1 OPD side
T0: medium
- L5 dermatome PD side
T0: medium
- L5dermatome OPD side
T0: medium
Thomson
2009
1) NE ≠ NC
- NE = 19
- NC = 13
2) SDE ≠ SDC
3) Hedge’g coefficient
4)
- g = \( \frac{M_E-{M}_C}{SD_{Pooled}} \)
\( {\mathrm{SD}}_{\mathrm{pooled}}=\sqrt{\frac{\left({\mathrm{N}}_{\mathrm{E}}\hbox{-} 1\right){\mathrm{SD}}_{{\mathrm{E}}^2}+\left({\mathrm{N}}_{\mathrm{C}}\hbox{-} 1\right){\mathrm{SD}}_{{\mathrm{C}}^2}}{{\mathrm{N}}_{\mathrm{E}}+{\mathrm{N}}_{\mathrm{C}}\hbox{-} 2}} \)
-\( \mathrm{SD}\left(\mathrm{g}\right)=\sqrt{\frac{N_E+{N}_C}{N_E\times {N}_C}+\frac{d^2}{2\left({N}_E+{N}_C\right)}} \)
- 95% CI: [d − 1.96 × SD (d); d + 1.96 × SD(d)]
(Approximate data)
-T0:
ME = + 2.2 +/−  1.1 Kg/cm2
MC = + 2.1 +/−  0.8 Kg/cm2
-T0:
-g = 0.10
-SD(g) = 0.36
− 95% CI: [− 0.61; + 0.81]
-p value: NS
T0: small
Fryer
2004
1) NE = NC = 32
2) SDE ≠ SDC
3) Cohen’s d coefficient
4)
-\( d=\frac{M_E-{M}_C}{SD^{\ast }} \)
-\( \mathrm{SD}\ast =\sqrt{\frac{{SD_E}^2+{SD_C}^2}{2}} \)
-\( \mathrm{SD}\left(\mathrm{g}\right)=\sqrt{\frac{N_E+{N}_C}{N_E\times {N}_C}+\frac{d^2}{2\left({N}_E+{N}_C\right)}} \)
- 95% CI: [d − 1.96 × SD (d); d + 1.96 × SD(d)]
-T0:
ME = + 216.51 +/−  90.50 kPa
MC = + 244.64 +/−  91.59 kPa
-T0:
-d = 0.30
-SD(d) = 0.25
− 95% CI: [− 0.19; + 0.79]
-p value: NS
T0: medium
  1. NS: not significant; T0: Values at baseline; T + 1: Values after one minute; T + 5: Values after five minutes; T + 10: Values after ten minutes; T + 15: Values after fifteen minutes; T + 30: Values after thirty minutes; PD: Pelvic Deficiency; OPD: Opposite Pelvic Deficiency