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Table 2 Sample size and significance cut-points for (GLL-RUL) differences for a one-sample test, power (80%, 90%, 95%) and 1-tailed 5% significance level based on the binomial exact test

From: Determining sample size for progression criteria for pragmatic pilot RCTs: the hypothesis test strikes back!

RUL

GLL

α (0.05), β (0.2)

α (0.05), β (0.1)

α (0.05), β (0.05)

%

%

n

Ac (%)

n

Ac (%)

n

Ac (%)

10

20

78

13 (16.7)

109

17 (15.6)

135

20 (14.8)

15

25

101

22 (21.8)

136

28 (20.6)

176

35 (19.9)

15

30

48

12 (25.0)

64

15 (23.4)

85

19 (22.4)

20

30

116

31 (26.7)

160

41 (25.6)

204

51 (25.0)

20

35

56

17 (30.4)

77

22 (28.6)

98

27 (27.6)

20

40

35

12 (34.3)

47

15 (31.9)

60

18 (30.0)

25

35

129

41 (31.8)

179

55 (30.7)

230

69 (30.0)

25

40

62

22 (35.5)

83

28 (33.7)

107

35 (32.7)

25

45

36

14 (38.9)

49

18 (36.7)

62

22 (35.5)

25

50

26

11 (42.3)

33

13 (39.4)

42

16 (38.1)

30

40

144

53 (36.8)

193

69 (35.8)

248

87 (35.1)

30

45

67

27 (40.3)

93

36 (38.7)

114

43 (37.7)

30

50

39

17 (43.6)

53

22 (41.5)

67

27 (40.3)

30

55

25

12 (48.0)

36

16 (44.4)

44

19 (43.2)

30

60

17

9 (52.9)

25

12 (48.0)

28

13 (46.4)

35

45

148

62 (41.9)

206

84 (40.8)

262

105 (40.1)

35

50

68

31 (45.6)

96

42 (43.8)

119

51 (42.9)

35

55

41

20 (48.8)

53

25 (47.2)

68

31 (45.6)

35

60

26

14 (53.8)

36

18 (50.0)

45

22 (48.9)

35

65

19

11 (57.9)

24

13 (54.2)

29

15 (51.7)

40

50

158

74 (46.8)

214

98 (45.8)

268

121 (45.1)

40

55

71

36 (50.7)

94

46 (48.9)

119

57 (47.9)

40

60

42

23 (54.8)

56

29 (51.8)

67

34 (50.7)

40

65

28

16 (57.1)

34

19 (55.9)

45

24 (53.3)

40

70

19

12 (63.2)

25

15 (60.0)

28

16 (57.1)

45

55

154

80 (51.9)

220

112 (50.9)

269

135 (50.2)

45

60

70

39 (55.7)

98

53 (54.1)

119

63 (52.9)

45

65

42

25 (59.5)

54

31 (57.4)

68

38 (55.9)

45

70

25

16 (64.0)

36

22 (61.1)

44

26 (59.1)

45

75

16

11 (68.8)

23

15 (65.2)

29

18 (62.1)

50

60

158

90 (57.0)

213

119 (55.9)

268

148 (55.2)

50

65

69

42 (60.9)

93

55 (59.1)

119

69 (58.0)

50

70

37

24 (64.9)

53

33 (62.3)

67

41 (61.2)

50

75

23

16 (69.6)

33

22 (66.7)

42

27 (64.3)

55

65

150

93 (62.0)

210

128 (61.0)

262

158 (60.3)

55

70

70

46 (65.7)

92

59 (64.1)

114

72 (63.2)

55

75

37

26 (70.3)

50

34 (68.0)

62

41 (66.1)

60

70

143

96 (67.1)

197

130 (66.0)

248

162 (65.3)

60

75

62

44 (71.0)

85

59 (69.4)

107

73 (68.2)

60

80

36

27 (75.0)

45

33 (73.3)

60

43 (71.7)

65

75

133

96 (72.2)

180

128 (71.1)

230

162 (70.4)

65

80

55

42 (76.4)

75

56 (74.7)

98

72 (73.5)

65

85

31

25 (80.6)

42

33 (78.6)

52

40 (76.9)

70

80

119

92 (77.3)

164

125 (76.2)

204

154 (75.5)

70

85

49

40 (81.6)

69

55 (79.7)

85

67 (78.8)

75

85

103

85 (82.5)

139

113 (81.3)

176

142 (80.7)

75

90

45

39 (86.7)

55

47 (85.5)

70

59 (84.3)

80

90

82

72 (87.8)

112

97 (86.6)

135

116 (85.9)

  1. RUL upper limit of RED zone (expressed as percentage of total sample), GLL lower limit of GREEN zone (expressed as percentage of total sample), AC AMBER-statistical significance threshold (within the AMBER zone) where an observed estimate below the cut-point will result in a non-significant result (p ≥ 0.05) and figures at or above the cut-point will be significant (p < 0.05) (%, expressed as a percentage of sample size (n))