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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