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Table 2 The probabilities of inequalities after simple randomization in groups of older men, based on scores of selected functional tests

From: Small samples and increased variability – discussing the need for restricted types of randomization in exercise interventions in old age

     Probability for inequalities between experimental groups (mean difference ± SD)
Functional test Sample Expected mean ± SD Participants per group 10% difference 15% difference 20% difference
Timed Up and Go 60+ years 10.8 ± 2.5 s Ibrahim et al., 2017 [26] 15 24.0% (1.5 ± .4) 7.8% (2.0 ± .3) 2.0% (2.5 ± .3)
20 17.5% (1.5 ± .3) 4.3% (1.9 ± .3) .7% (2.4 ± .2)
25 13.0% (1.4 ± .3) 2.3% (1.9 ± .2) .3% (2.3 ± .2)
Normal Walking Speed 70–79 years 120.0 ± 21.0 cm/s Atkinson, 2007 [27] 15 11.7% (15.3 ± 2.9) 2.0% (20.5 ± 2.4) .2% (25.9 ± 1.9)
20 7.1% (14.6 ± 2.4) .7% (19.9 ± 2) .03% (24.9 ± 1.4)
25 4.5% (14.2 ± 2.0) .3% (19.8 ± 1.8) .006% (25.1 ± 1.1)
Functional Reach Hypertensive 80.9 ± 4.3 29.3 ± 7.5 cm Bohannon et al., 2017 [28] 15 28.2% (4.3 ± 1.2) 11.0% (5.5 ± 1.0) 3.3% (6.8 ± .9)
20 22.0% (4.1 ± 1.0) 6.5% (5.3 ± .9) 1.4% (6.6 ± .7)
25 16.9% (3.9 ± .8) 3.9% (5.1 ± .7) .6% (6.4 ± .6)
Sit-to-Stand 60–94 years 14.2 ± 4.6 reps/30s Rikli and Jones, 1999 [29] 15 39.9% (2.4 ± .8) 20.9% (2.9 ± .7) 9.3% (3.5 ± .6)
20 32.8% (2.2 ± .7) 14.5% (2.8 ± .6) 5.2% (3.4 ± .5)
25 27.5% (2.1 ± .6) 10.4% (2.7 ± .5) 3.0% (3.3 ± .4)
Handgrip Strength 75–79 years 81.9 ± 9.94 pounds Jansen et al., 2008 [30] 15 2.4% (9.4 ± 1.2) .07% (13.1 ± .9) 0% (NA)
20 .9% (9.1 ± .9) .01% (12.8 ± .6) 0% (NA)
25 .4% (9.0 ± .8) .002% (12.26 ± .1) 0% (NA)
Unipedal Balance Testa 65–69 years 26.3 ± 18.4 s Lohne-Seiler et al., 2016 [31] 15 64.1% (9.7 ± 4.5) 48.4% (11.1 ± 4.2) 35.1% (12.7 ± 4)
20 59.3% (8.7 ± 3.8) 42.1% (10.3 ± 3.5) 28.6% (11.8 ± 3.3)
25 54.6% (8.1 ± 3.4) 36.6% (9.7 ± 3.1) 23.0% (11.2 ± 2.8)
  1. aCalculated with the assumption of non-normal distribution due to the large SD