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Standard Deviations. Standard Scores, T Score Conversion, and Percentiles

Tests by schools and professionals use various yardsticks to measure traits. The following measurements are frequently used. It is important to know what they mean.

Standard Deviations (SD): The general sense is that everything within one standard deviation of average is considered "within the normal range" or "within the average range." Notice that normal or average can range between the 16th percentile rank and the 84th percentile rank. Many people consider 1.5 SD’s as a position of a high probability of either significantly below or above average performance. This is comparable to either the 7th or 93rd percentile rank. When there is a deviation of 2 SD’s from the normal (or from ability) then almost everyone agrees that this is a very significant problem. A deviation of 2 SD’s places one at the 2nd or 98th percentile rank. When diagnosing for Attention Deficit Disorder, most professionals use 1.5 to 2 SD's from average  regarding various traits (such as hyperactivity, impulsivity or inattention) before deciding a person has ADD/ADHD.

Standard Scores(SS): These are used most often to measure ability (IQ tests) and achievement. Thus they are used to figure out if a person has some strong difference or discrepancy between ability and achievement. If it is severe enough, we consider that person to have a Learning Disability. But be careful with Standard Scores. Do not confuse them with grades on tests, where 100 is perfect, and 85 is a B. If you look at the chart below you discover that 100 is average (50th percentile rank, with half of the students better and half worse than your child). But an SS of 85 is a 16th percentile rank, meaning 84 out of 100 do that score or better and 16 out of 100 do that score or worse.

SS’s have a mean of 100 and a SD of 15.

T-Scores: These are usually technical scores, not used too much for parents, but they still get used nonetheless. T-Scores have a mean of 50 and a SD of 10.

Standard Score

T Score

Standard Deviation

Percentile Rank

55

20

-3.0

.13

 

21

-2.9

.19

58

22

-2.8

.26

 

23

-2.7

.35

61

24

-2.6

.47

 

25

-2.5

.62

64

26

-2.4

.82

 

27

-2.3

1.07

67

28

-2.2

1.39

 

29

-2.1

1.79

70

30

-2.0

2.28

 

31

-1.9

2.87

73

32

-1.8

3.59

 

33

-1.7

4.46

76

34

-1.6

5.48

 

35

-1.5

6.68

79

36

-1.4

8.08

 

37

-1.3

9.68

82

38

-1.2

11.51

 

39

-1.1

13.57

85

40

-1.0

15.87

 

41

-.9

18.41

88

42

-.8

21.19

 

43

-.7

24.20

91

44

-.6

27.43

 

45

-.5

30.58

94

46

-.4

34.46

 

47

-.3

38.21

97

48

-.2

42.07

 

49

-.1

46.02

100

50

-0

50.00

 

51

+.1

53.98

103

52

+.2

57.93

 

53

+.3

61.79

106

54

+.4

66.54

 

55

+.5

69.15

109

56

+.6

72.57

 

57

+.7

75.80

112

58

+.8

78.81

 

59

+.9

81.59

115

60

+1

84.13

 

61

+1.1

86.43

118

62

+1.2

88.49

 

63

+1.3

90.32

121

64

+1.4

91.92

 

65

+1.5

93.32

124

66

+1.6

94.52

 

67

+1.7

95.54

127

68

+1.8

96.41

 

69

+1.9

97.13

130

70

+2.0

97.72

 

71

+2.1

98.21

133

72

+2.2

98.61

 

73

+2.3

98.93

136

74

+2.4

99.18

 

75

+2.5

99.38

139

76

+2.6

99.53

 

77

+2.7

99.65

142

78

+2.8

99.74

 

79

+2.9

99.81

145

80

+3.0

99.87

 

© 2012  John E. Swank, MS, LPCC   Swank Counseling , 21 Robinhood Lane, Troy, OH 45373  

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