Statistical Guide T scores have a mean of 50 and a standard deviation of 10 for

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Statistical Guide
T scores have a mean of 50 and a standard deviation of 10 for the norm group on which a new test is standardized. Test makers prepare norm tables that allow us to convert a person’s raw score (points earned) to the T score equivalents that would have been obtained if that person had been in the norm group. Likewise, we can compare the mean and standard deviation of another group to the mean of 50 and standard deviation of 10 for the norm group.
Since there are about 3 standard deviation units on both sides of the mean in a normal distribution, in practice, T scores can range from 20-80 (i.e., 3 times the standard deviation of 10 = or – the mean of 50).
Note that the mean of 50 and the standard deviation of 10 are true of the norm group but not necessarily true of a subsequent group that is studied. Hence, if a study group has a mean of 55, the reader will immediately know that their mean is higher than the norm group’s mean. Also, for instance, if the study group’s standard deviation is 9, the reader will immediately know that their standard deviation is lower than the norm group’s standard deviation.

Excerpt from the Research Article*
Subjects consisted of 44 adolescents (17 males and 27 femailes) 12 to 18 years of age (who had a) minimum of 20% absences from school in the 4 weeks prior to evaluation for the study. (On average, they missed 72% of full or partial school days.) Subjects were recruited through biannual mailings sent to middle, junior high, and high schools in the seven-county metropolitan area surrounding Minneapolis and St. Paul. Referrals were made by school personnel, physicians, mental health workers, and family members.
Child Behavior Checklist. The CBCL is a report measure that the parent completes about the child… There are eight scales of CBCL (Withdrawn, Somatic Complaints (i.e., medical complaints about the body), Anxious/Depressed, Social Problems, Thought Problems, Attention Problems, Delinquent Behavior, and Aggressive Behavior). T scores of 70 (98th percentile) or greater are considered clinically significant.
In reporting their adolescents’ symptoms on the CBCL, mothers endorsed the Somatic Complaints scale as having the highest mean (T = 72.5, +- 11.4) (Table 4). The next highest group mean scores were on the Anxious/Depressed scale (T = 70.4 +- 10.7) and the Withdrawn scale (T = 69.8 +- 10.6). CBCL Scores Reported by Mothers

T scores
Scales
Withdrawn
69.8 means
10.6 SD
Somatic Complaints
72.5 mean
11.4 SD
Anxious/Depressed
70.4 mean
10.7 SD
Social Problems
62.6 mean
11.8 SD
Thought Problems
60.0 mean
8.7 SD
Attention Problems
64.1 mean
7.9 SD
Delinquent Behavior
63.1 mean
7.3 SD
Aggressive Behavior
61.0 mean
9.2 SD

based on the above t score
(1) what’s the lowest average score?
(2) what’s the most variability in their scores?
(3) the mean score on the anxious/ depressed scale is below the mean for the norm group is this true or false?
(4) how many of the scale is the mean for the adolescent in the study above the mean for the norm group Statistical Guide
T scores have a mean of 50 and a standard deviation of 10 for the norm group on which a new test is standardized. Test makers prepare norm tables that allow us to convert a person’s raw score (points earned) to the T score equivalents that would have been obtained if that person had been in the norm group. Likewise, we can compare the mean and standard deviation of another group to the mean of 50 and standard deviation of 10 for the norm group.
Since there are about 3 standard deviation units on both sides of the mean in a normal distribution, in practice, T scores can range from 20-80 (i.e., 3 times the standard deviation of 10 = or – the mean of 50).
Note that the mean of 50 and the standard deviation of 10 are true of the norm group but not necessarily true of a subsequent group that is studied. Hence, if a study group has a mean of 55, the reader will immediately know that their mean is higher than the norm group’s mean. Also, for instance, if the study group’s standard deviation is 9, the reader will immediately know that their standard deviation is lower than the norm group’s standard deviation.

Excerpt from the Research Article*
Subjects consisted of 44 adolescents (17 males and 27 femailes) 12 to 18 years of age (who had a) minimum of 20% absences from school in the 4 weeks prior to evaluation for the study. (On average, they missed 72% of full or partial school days.) Subjects were recruited through biannual mailings sent to middle, junior high, and high schools in the seven-county metropolitan area surrounding Minneapolis and St. Paul. Referrals were made by school personnel, physicians, mental health workers, and family members.
Child Behavior Checklist. The CBCL is a report measure that the parent completes about the child… There are eight scales of CBCL (Withdrawn, Somatic Complaints (i.e., medical complaints about the body), Anxious/Depressed, Social Problems, Thought Problems, Attention Problems, Delinquent Behavior, and Aggressive Behavior). T scores of 70 (98th percentile) or greater are considered clinically significant.
In reporting their adolescents’ symptoms on the CBCL, mothers endorsed the Somatic Complaints scale as having the highest mean (T = 72.5, +- 11.4) (Table 4). The next highest group mean scores were on the Anxious/Depressed scale (T = 70.4 +- 10.7) and the Withdrawn scale (T = 69.8 +- 10.6). CBCL Scores Reported by Mothers

T scores
Scales
Withdrawn
69.8 means
10.6 SD
Somatic Complaints
72.5 mean
11.4 SD
Anxious/Depressed
70.4 mean
10.7 SD
Social Problems
62.6 mean
11.8 SD
Thought Problems
60.0 mean
8.7 SD
Attention Problems
64.1 mean
7.9 SD
Delinquent Behavior
63.1 mean
7.3 SD
Aggressive Behavior
61.0 mean
9.2 SD

based on the above t score
(1) what’s the lowest average score?
(2) what’s the most variability in their scores?
(3) the mean score on the anxious/ depressed scale is below the mean for the norm group is this true or false?
(4) how many of the scale is the mean for the adolescent in the study above the mean for the norm group Statistical Guide
T scores have a mean of 50 and a standard deviation of 10 for the norm group on which a new test is standardized. Test makers prepare norm tables that allow us to convert a person’s raw score (points earned) to the T score equivalents that would have been obtained if that person had been in the norm group. Likewise, we can compare the mean and standard deviation of another group to the mean of 50 and standard deviation of 10 for the norm group.
Since there are about 3 standard deviation units on both sides of the mean in a normal distribution, in practice, T scores can range from 20-80 (i.e., 3 times the standard deviation of 10 = or – the mean of 50).
Note that the mean of 50 and the standard deviation of 10 are true of the norm group but not necessarily true of a subsequent group that is studied. Hence, if a study group has a mean of 55, the reader will immediately know that their mean is higher than the norm group’s mean. Also, for instance, if the study group’s standard deviation is 9, the reader will immediately know that their standard deviation is lower than the norm group’s standard deviation.

Excerpt from the Research Article*
Subjects consisted of 44 adolescents (17 males and 27 femailes) 12 to 18 years of age (who had a) minimum of 20% absences from school in the 4 weeks prior to evaluation for the study. (On average, they missed 72% of full or partial school days.) Subjects were recruited through biannual mailings sent to middle, junior high, and high schools in the seven-county metropolitan area surrounding Minneapolis and St. Paul. Referrals were made by school personnel, physicians, mental health workers, and family members.
Child Behavior Checklist. The CBCL is a report measure that the parent completes about the child… There are eight scales of CBCL (Withdrawn, Somatic Complaints (i.e., medical complaints about the body), Anxious/Depressed, Social Problems, Thought Problems, Attention Problems, Delinquent Behavior, and Aggressive Behavior). T scores of 70 (98th percentile) or greater are considered clinically significant.
In reporting their adolescents’ symptoms on the CBCL, mothers endorsed the Somatic Complaints scale as having the highest mean (T = 72.5, +- 11.4) (Table 4). The next highest group mean scores were on the Anxious/Depressed scale (T = 70.4 +- 10.7) and the Withdrawn scale (T = 69.8 +- 10.6). CBCL Scores Reported by Mothers

T scores
Scales
Withdrawn
69.8 means
10.6 SD
Somatic Complaints
72.5 mean
11.4 SD
Anxious/Depressed
70.4 mean
10.7 SD
Social Problems
62.6 mean
11.8 SD
Thought Problems
60.0 mean
8.7 SD
Attention Problems
64.1 mean
7.9 SD
Delinquent Behavior
63.1 mean
7.3 SD
Aggressive Behavior
61.0 mean
9.2 SD
Statistical Guide
T scores have a mean of 50 and a standard deviation of 10 for the norm group on which a new test is standardized. Test makers prepare norm tables that allow us to convert a person’s raw score (points earned) to the T score equivalents that would have been obtained if that person had been in the norm group. Likewise, we can compare the mean and standard deviation of another group to the mean of 50 and standard deviation of 10 for the norm group.
Since there are about 3 standard deviation units on both sides of the mean in a normal distribution, in practice, T scores can range from 20-80 (i.e., 3 times the standard deviation of 10 = or – the mean of 50).
Note that the mean of 50 and the standard deviation of 10 are true of the norm group but not necessarily true of a subsequent group that is studied. Hence, if a study group has a mean of 55, the reader will immediately know that their mean is higher than the norm group’s mean. Also, for instance, if the study group’s standard deviation is 9, the reader will immediately know that their standard deviation is lower than the norm group’s standard deviation.

Excerpt from the Research Article*
Subjects consisted of 44 adolescents (17 males and 27 femailes) 12 to 18 years of age (who had a) minimum of 20% absences from school in the 4 weeks prior to evaluation for the study. (On average, they missed 72% of full or partial school days.) Subjects were recruited through biannual mailings sent to middle, junior high, and high schools in the seven-county metropolitan area surrounding Minneapolis and St. Paul. Referrals were made by school personnel, physicians, mental health workers, and family members.
Child Behavior Checklist. The CBCL is a report measure that the parent completes about the child… There are eight scales of CBCL (Withdrawn, Somatic Complaints (i.e., medical complaints about the body), Anxious/Depressed, Social Problems, Thought Problems, Attention Problems, Delinquent Behavior, and Aggressive Behavior). T scores of 70 (98th percentile) or greater are considered clinically significant.
In reporting their adolescents’ symptoms on the CBCL, mothers endorsed the Somatic Complaints scale as having the highest mean (T = 72.5, +- 11.4) (Table 4). The next highest group mean scores were on the Anxious/Depressed scale (T = 70.4 +- 10.7) and the Withdrawn scale (T = 69.8 +- 10.6). CBCL Scores Reported by Mothers

T scores
Scales
Withdrawn
69.8 means
10.6 SD
Somatic Complaints
72.5 mean
11.4 SD
Anxious/Depressed
70.4 mean
10.7 SD
Social Problems
62.6 mean
11.8 SD
Thought Problems
60.0 mean
8.7 SD
Attention Problems
64.1 mean
7.9 SD
Delinquent Behavior
63.1 mean
7.3 SD
Aggressive Behavior
61.0 mean
9.2 SD
CBCL Scores Reported by Mothers

T scores
Scales
Withdrawn
69.8 means
10.6 SD
Somatic Complaints
72.5 mean
11.4 SD
Anxious/Depressed
70.4 mean
10.7 SD
Social Problems
62.6 mean
11.8 SD
Thought Problems
60.0 mean
8.7 SD
Attention Problems
64.1 mean
7.9 SD
Delinquent Behavior
63.1 mean
7.3 SD
Aggressive Behavior
61.0 mean
9.2 SD

based on the above t score
(1) what’s the lowest average score?
(2) what’s the most variability in their scores?
(3) the mean score on the anxious/ depressed scale is below the mean for the norm group is this true or false?
(4) how many of the scale is the mean for the adolescent in the study above the mean for the norm group

Explanation / Answer

Solution:

(1) The lowest average score is 50 from norm group after that lowest score is 60 from Thought Problems.

(2) The standard deviation of the social problem is 11.8 so there is most variability in their score.

(3) False, Because the mean score on the anxious/ depressed scale is high the mean for the norm group.

(4) 72.5-50 = 22.5 is the mean above for the adolescent in the study form the mean of the norm group.

Cheers!!

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