Chapter 8: Standard Error of Measurement

Internal consistency values provide an estimate of a test scores reliability, but these values also have practical applications in the calculation of the SEM, a statistic that quantifies the amount of error in the obtained scores. The formula for SEM is:

Internal consistency values provide an estimate of a test score’s reliability, but these values also have practical applications in the calculation ofthe SEM, a statistic that quantifies the amount of error in the obtained scores. The formula for SEM is:

SEM formula

SEM values were calculated for the Conners 4 scale scores using the standard deviation (SD) of the reference sample’s T-scores (i.e., SD = 10),along with the omega reliability coefficient. Overall, the median SEM was 2.60 for Parent, 2.36 for Teacher, and 2.36 for Self-Report in theNormative Samples, and 2.85 for Parent, 3.26 for Teacher, and 2.39 for Self-Report in the ADHD Reference Samples (see Table 8.7 for SEM values foreach scale for the Normative Samples, and Table 8.8 for the ADHD Reference Samples). The low values reported here indicate a very small SEM, or very little error in the estimated true scores.

Practical applications of SEM values for the Conners 4 include the calculation of confidence intervals (see chapter 4, Interpretation, for a description of how confidence intervals can be used in the interpretation of results). The confidence interval isa margin of error around the obtained score used to arrive at an estimate of a true score (Harvill, 1991). This margin provides a range of scores,at a particular level of probability, within which the true score is expected to fall. For the Conners 4, 90% and 95% confidence interval levelswere calculated based on the SEM for each scale (see appendix B; note that confidence intervals are automatically included in the digitalreports; see Scoring Options in chapter 3, Scoring and Reports).


Table 8.7a. Standard Error of Measurement for T-scores: Conners 4 Normative Samples Content Scales

Scale

Number of Items

Age Group

Parent

Teacher

Self-Report

Combined Gender

Males

Females

Combined Gender

Males

Females

Combined Gender

Males

Females

Inattention/
Executive
Dysfunction

20

6 to 7

1.71

1.90

1.78

1.37

1.53

1.55

—

—

—

8 to 9

1.64

1.49

1.84

1.51

1.49

1.62

2.38

2.20

2.59

10 to 11

1.80

1.85

1.74

1.43

1.45

1.48

2.48

2.44

2.48

12 to 13

1.59

1.45

1.76

1.53

1.50

1.59

2.06

1.93

2.17

14 to 15

1.72

1.74

1.68

1.43

1.45

1.51

2.01

1.90

2.10

16 to 18

1.73

1.70

1.76

1.50

1.56

1.48

2.33

2.23

2.42

Hyperactivity

11

6 to 7

2.70

2.71

2.64

2.08

2.14

2.05

—

—

—

8 to 9

2.72

2.54

2.91

2.17

2.05

2.38

3.10

2.83

3.43

10 to 11

2.68

2.72

2.58

2.12

2.10

2.31

3.31

3.58

3.00

12 to 13

2.68

2.53

2.86

2.42

2.45

2.36

3.00

2.73

3.40

14 to 15

2.49

2.39

2.53

1.98

1.99

2.01

3.06

3.06

3.00

16 to 18

2.93

2.99

2.82

2.51

2.54

2.40

3.27

3.45

3.12

Impulsivity

9

6 to 7

2.78

2.75

2.76

2.13

2.25

2.03

—

—

—

8 to 9

2.88

2.63

3.22

2.31

2.25

2.42

3.70

3.63

3.78

10 to 11

2.90

3.01

2.83

2.32

2.30

2.51

3.59

3.41

3.73

12 to 13

2.72

2.66

2.79

2.30

2.40

2.19

3.66

3.71

3.53

14 to 15

2.32

2.17

2.43

2.24

2.16

2.38

3.13

2.94

3.29

16 to 18

2.96

3.04

2.86

2.48

2.45

2.50

3.54

3.24

3.80

Emotional
Dysregulation

8

6 to 7

2.55

2.59

2.49

1.66

1.55

1.83

—

—

—

8 to 9

2.41

2.32

2.51

1.59

1.41

1.89

3.54

3.39

3.66

10 to 11

2.38

2.25

2.48

1.58

1.36

2.00

3.11

3.05

3.11

12 to 13

2.16

2.15

2.17

1.80

1.62

1.95

2.92

2.81

2.93

14 to 15

2.13

1.85

2.49

1.85

1.84

1.82

2.90

2.80

2.97

16 to 18

2.12

2.13

2.09

2.02

1.93

2.13

3.04

2.69

3.37

Depressed Mood

6

6 to 7

2.89

3.28

2.55

2.84

2.58

3.17

—

—

—

8 to 9

3.15

2.78

3.59

2.94

2.98

2.87

3.97

4.25

3.73

10 to 11

3.31

3.25

3.39

2.57

2.52

2.53

3.89

4.43

3.35

12 to 13

3.13

3.18

3.02

2.72

2.87

2.54

3.18

3.06

3.25

14 to 15

2.54

2.41

2.64

3.01

3.06

2.92

2.93

3.10

2.68

16 to 18

2.96

2.59

3.36

3.17

3.27

3.02

3.12

3.41

2.81

Anxious Thoughts

5

(6 for SR)

6 to 7

3.44

3.73

3.15

2.60

2.57

2.60

—

—

—

8 to 9

3.05

2.77

3.28

3.20

3.20

3.18

3.07

2.79

3.29

10 to 11

3.26

3.39

3.23

3.11

3.02

3.12

3.22

3.43

3.01

12 to 13

2.86

2.63

3.06

3.72

2.93

4.32

2.84

3.04

2.67

14 to 15

2.77

2.54

2.96

3.29

3.49

3.13

2.58

2.62

2.61

16 to 18

3.05

3.01

3.07

3.26

3.39

3.03

2.93

3.38

2.57

Note. SR = Self-Report.


Table 8.7b. Standard Error of Measurement for T-scores: Conners 4 Normative Samples Impairment & Functional Outcome Scales

Scale

Number of Items

Age Group

Parent

Teacher

Self-Report

Combined Gender

Males

Females

Combined Gender

Males

Females

Combined Gender

Males

Females

Schoolwork

6

6 to 7

3.06

2.68

3.34

2.61

2.60

2.71

—

—

—

8 to 9

2.95

2.80

3.29

2.41

2.39

2.50

4.14

3.79

4.51

10 to 11

2.98

2.78

3.05

2.37

2.63

2.14

4.17

4.01

4.31

12 to 13

2.84

2.73

3.15

2.36

2.28

2.51

3.62

3.55

3.61

14 to 15

2.95

2.80

3.05

2.24

2.24

2.41

3.81

3.93

3.60

16 to 18

3.43

3.17

3.72

2.48

2.48

2.66

3.82

3.87

3.75

Peer Interactions

6

6 to 7

3.47

3.57

3.34

2.41

2.51

2.23

—

—

—

8 to 9

3.05

2.88

3.27

2.33

2.24

2.49

4.03

4.19

3.80

10 to 11

2.83

3.20

2.59

2.26

2.25

2.26

4.32

4.31

4.24

12 to 13

2.57

2.40

2.85

2.61

2.54

2.64

4.44

4.47

4.36

14 to 15

2.56

2.23

2.89

3.46

3.44

3.57

4.24

4.05

4.31

16 to 18

2.44

2.46

2.48

2.94

2.94

2.97

4.49

4.65

4.31

Family Life

7

6 to 7

2.22

2.09

2.27

—

—

—

—

—

—

8 to 9

2.43

2.32

2.53

—

—

—

4.10

4.05

4.16

10 to 11

2.24

2.19

2.30

—

—

—

3.52

3.57

3.42

12 to 13

2.17

2.09

2.16

—

—

—

4.10

3.76

4.45

14 to 15

2.16

1.90

2.39

—

—

—

3.29

3.08

3.51

16 to 18

2.41

2.14

2.68

—

—

—

3.71

3.38

3.86


Table 8.7c. Standard Error of Measurement for T-scores: Conners 4 Normative Samples DSM Symptom Scales

Scale

Number of Items

Age Group

Parent

Teacher

Self-Report

Combined Gender

Males

Females

Combined Gender

Males

Females

Combined Gender

Males

Females

DSM ADHD Inattentive Symptoms

11

6 to 7

2.53

2.61

2.45

2.01

2.02

2.06

—

—

—

8 to 9

2.33

2.10

2.68

2.02

2.00

2.15

3.20

2.97

3.49

10 to 11

2.41

2.52

2.29

1.88

1.92

1.95

3.37

3.35

3.32

12 to 13

2.18

2.01

2.39

1.97

1.94

2.07

2.85

2.66

3.03

14 to 15

2.33

2.38

2.26

1.89

1.89

2.04

2.71

2.57

2.83

16 to 18

2.35

2.34

2.38

1.92

1.99

1.96

3.06

3.00

3.13

DSM ADHD Hyperactive/Impulsive
Symptoms

13

6 to 7

2.47

2.51

2.41

1.85

1.93

1.80

—

—

—

8 to 9

2.53

2.33

2.77

2.00

1.94

2.11

3.02

2.83

3.24

10 to 11

2.58

2.59

2.51

1.96

1.94

2.17

3.23

3.48

2.95

12 to 13

2.49

2.44

2.54

2.17

2.30

1.98

3.22

2.92

3.60

14 to 15

2.19

2.16

2.19

1.84

1.83

1.95

3.01

2.95

3.03

16 to 18

2.84

2.84

2.79

2.24

2.29

2.16

3.39

3.42

3.39

DSM Total ADHD Symptoms

24

6 to 7

1.89

1.92

1.84

1.52

1.55

1.55

—

—

—

8 to 9

1.91

1.74

2.18

1.70

1.70

1.78

2.33

2.14

2.58

10 to 11

2.02

2.14

1.89

1.59

1.61

1.72

2.53

2.58

2.44

12 to 13

1.85

1.77

1.97

1.67

1.77

1.59

2.33

2.17

2.52

14 to 15

1.85

1.86

1.80

1.56

1.61

1.61

2.19

2.13

2.22

16 to 18

2.07

2.06

2.07

1.80

1.86

1.82

2.48

2.49

2.48

DSM
Oppositional Defiant Disorder Symptoms

10

6 to 7

2.34

2.21

2.45

1.71

1.78

1.64

—

—

—

8 to 9

2.31

2.17

2.51

1.82

1.94

1.72

3.22

3.15

3.35

10 to 11

2.34

2.34

2.31

1.51

1.41

1.76

3.00

2.95

3.02

12 to 13

1.98

2.00

2.02

1.72

1.85

1.55

2.87

2.72

2.98

14 to 15

2.18

2.02

2.33

2.00

2.02

1.98

2.85

2.73

2.91

16 to 18

2.23

2.10

2.38

1.97

2.03

1.94

3.15

2.88

3.46

DSM Conduct Disorder
Symptoms

15

6 to 7

2.00

4.54

2.05

2.18

2.25

3.22

—

—

—

8 to 9

1.74

2.34

2.03

2.18

3.47

2.72

2.73

3.19

2.83

10 to 11

1.75

2.54

2.00

1.84

1.77

3.80

2.46

3.72

2.35

12 to 13

1.96

3.00

2.37

1.83

2.89

1.72

2.64

3.70

2.96

14 to 15

1.62

3.54

1.47

2.06

3.23

2.27

2.10

3.23

4.81

16 to 18

2.11

3.23

4.32

1.90

2.05

3.27

2.17

3.04

3.44


Table 8.8. Standard Error of Measurement for T-scores: Conners 4 ADHD Reference Samples

Note. SR = Self-Report. Age Group intervals are 6 to 12 years and 13 to 18 years for Parent and Teacher, and 8 to 12 years and 13 to 18 years for Self-Report.


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