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Table 3 The probabilities of inequalities after simple randomization in groups of older women, 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

11.5 ± 2.7 s

Ibrahim et al., 2017 [26]

15

24.3% (1.6 ± .4)

8.2% (2.1 ± .4)

2.0% (2.6 ± .3)

20

18.2% (1.5 ± .4)

4.4% (2.0 ± .3)

.8% (2.5 ± .3)

25

13.3% (1.5 ± .3)

2.4% (2.0 ± .3)

.3% (2.5 ± .2)

Normal Walking Speed

70–79 years

111.0 ± 21.0 cm/s

Atkinson, 2007 [27]

15

14.9% (14.5 ± 3.1)

3.1% (19.4 ± 2.6)

.4% (24.2 ± 2.3)

20

9.5% (13.8 ± 2.5)

1.3% (18.7 ± 2.0)

.1% (23.7 ± 1.8)

25

6.2% (13.4 ± 2.1)

.5% (18.3 ± 1.8)

.01% (22.7 ± 1.5)

Functional Reach

Hypertensive 80.3 ± 3.9 years

26.1 ± 6.5 cm

Bohannon et al., 2017 [28]

15

27.4% (3.8 ± 1.0)

10.0% (4.9 ± .9)

2.8% (6.0 ± .8)

20

20.4% (3.6 ± .9)

5.7% (4.7 ± .7)

1.2% (5.8 ± .6)

25

15.8% (3.4 ± .7)

3.3% (4.6 ± .6)

.5% (5.7 ± .5)

Sit-to-Stand

60–94 years

12.7 ± 4.0 reps/30s

Rikli and Jones, 1999 [29]

15

38.8% (2.1 ± .7)

19.4% (2.6 ± .6)

8.5% (3.1 ± .6)

20

31.8% (1.9 ± .6)

13.5% (2.4 ± .5)

4.7% (3.0 ± .4)

25

26.3% (1.8 ± .5)

9.3% (2.4 ± .4)

2.6% (2.9 ± .4)

Handgrip Strength

75–79 years

48.2 ± 10.3 pounds

Jansen et al., 2008 [30]

15

20.0% (6.6 ± 1.6)

5.6% (8.6 ± 1.3)

1.1% (10.7 ± 1.1)

20

13.9% (6.3 ± 1.3)

2.7% (8.3 ± 1.1)

.34% (10.5 ± 1.0)

25

9.7% (6.0 ± 1.1)

1.3% (8.1 ± .9)

.1% (10.3 ± .8)

Unipedal Balance Testa

65–69 years

28.2 ± 18.2 s

Lohne-Seiler et al., 2016 [31]

15

64.1% (9.8 ± 4.6)

48.6% (11.3 ± 4.3)

35.3% (12.8 ± 4.0)

20

59.0% (8.9 ± 3.9)

42.2% (10.4 ± 3.6)

28.1% (12.0 ± 3.4)

25

55.0% (8.2 ± 3.4)

36.4% (9.8 ± 3.1)

22.9% (11.4 ± 2.9)

  1. aCalculated with the assumption of non-normal distribution due to the large SD