Table 3 Shows the results of the hierarchical clustering analysis for skeletal class I patients. Cephalometric parameters, and age, descriptive statistics (mean, and standard deviation (SD)) for each cluster. Besides, the table presents the significance levels between the three clusters using ANOVA test (NS—not significant, * < 0.05, and ** < 0.01). The three clusters of class I varied significantly in the cephalometric parameters, and among these parameters were the most critical parameters for diagnosing skeletal malocclusion ANB, Calculated_ANB, and Wits appraisal

Age

13.03

5.22

12.11

2.50

13.45

3.66

NS

NL-ML angle [°]

24.00

5.38

28.66

5.04

20.94

4.23

**

NL-NSL angle [°]

9.54

2.85

7.01

3.22

6.00

3.50

**

PFH/AFH (%)

64.59

3.96

63.48

3.97

70.49

4.00

**

Gonial angle [°]

123.12

5.62

126.05

5.38

120.33

5.14

**

Facial axis

89.13

3.93

88.10

4.13

92.65

3.59

**

SNA angle [°]

77.88

3.03

81.47

2.44

83.81

3.02

**

SNB angle [°]

75.11

2.32

76.46

2.11

80.32

2.15

**

ANB angle [°]

2.77

1.38

5.00

1.16

3.49

1.46

**

ANB_ind [°]

2.70

1.22

4.54

1.16

3.75

1.24

**

Calculated_ANB (ANB – ANB_ind) [°]

0.07

0.85

0.41

0.78

−0.26

0.75

**

SN-Ba angle [°]

133.77

4.36

132.01

4.54

129.88

4.77

**

SN-Pg angle [°]

76.23

2.54

76.90

2.12

81.35

2.11

**

S–N (mm)

66.62

4.68

79.67

91.64

66.90

4.30

NS

Go-Me (mm)

66.01

5.52

78.63

89.69

68.36

5.30

NS

Wits appraisal (mm)

−0.55

2.26

0.30

5.26

0.33

2.08

*

ML-NSL angle [°]

33.56

4.66

35.67

5.09

26.93

4.29

**

 + 1/NL angle [°]

72.25

6.83

67.08

6.47

65.91

8.62

**

 + 1/SNL angle [°]

81.80

6.45

74.09

6.16

71.91

8.38

**

 + 1/NA angle [°]

20.32

7.49

24.44

6.52

24.27

8.61

**

 + 1/NA (mm)

2.90

2.56

4.90

6.68

4.05

2.56

NS

−1/ML (anatomic)

87.49

6.91

82.57

5.66

81.99

6.19

**

−1/NB angle [°]

21.18

6.77

29.56

4.70

25.27

6.49

**

−1/NB (mm)

2.66

2.17

6.75

6.72

3.64

2.10

NS

Interincisal angle [°]

135.74

12.19

120.99

8.74

126.97

10.82

**