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TYPES OF SCORES(PP. 117-121 IN HUTCHINSON;MERRELL & PLANTE; SECOND PART OF HAYNES AND PINDZOLA )
TYPES OF SCORES
Item score
Raw score
Converted scores (See normal curve…) percentile rank Standard scores
z-scoresT-scoresStanine
age-equivalent and grade-equivalent scores
Examples of item scores
More examples of item scores. Items scores together allow us to calculate raw score
TYPES OF SCORES
Item score
Raw score
Converted scores (See normal curve…) percentile rank Standard scores (based on central tendency and distribution around measure
of central tendency)
z-scoresT-scoresStanine
age-equivalent and grade-equivalent scores
Converted scores all us to compare client’s score with that of the normative sample (sometimes called standardization sample)
PERCENTILE RANK
Tells us what proportion of the norming population scored lower than the subject
99th percentile means out of 100 children 99 scored lower.
10th percentile means out of 100 children 10 scored lower.
30
20
10
00 204
Example: 4:6 year olds
58
Measures of central tendency and variability……
Esp. mean and standard deviation
To understand standard scores, you need to understand..
30
20
10
00 204
Example: 4:6 year olds
58
To understand standard scores, you need to understand..
Standard deviation, in-class discussion(Standard deviation as the “average” distance of all deviations from the measure of central tendency)
In a normal (bell-shaped curve) 68% of the population will have a mean score between +/- 1 sd (e.g., b/w 85 and 115 on this sample IQ test)
95% of the population will have a mean score between +/- 2 sd (e.g., b/w 70 and 130 on this sample IQ test)
Note that standard deviation and percentile rank are related!
30
20
10
0
0
Example: 4:6 year olds
58
Standard scores
•Raw score transformed to standard scores…. (3 types)
100 115 1308570
76 954024
•Raw score transformed to standard scores…. (We’ll consider three types of standard scores)
Transform to a distribution of Z-scores
100 115115 1301307070 8585
Note that standard deviation and percentile rank AND z-scores are related!
Note that standard deviation and percentile rank are related. Standard scores like z-scores and t-scores say the same thing, just in a different language, as do stanines
TYPES OF SCORES:AGE/GRADE-EQUIVALENT SCORES (“DEVELOPMENTAL SCORES” LAWRENCE, 1992)
E.g. Jack’s raw score: 59
age-equivalent score “5;2”
Jack’s 59 is average (mean or median) raw score expected for child who is 5;2
(AGE EQUIVALENT SCORE, CONT.)
Problems? Age equivalent score doesn’t consider:Range of performance for that ageSomeone whose chronological age is higher than their age-equivalent score may still be performing normallye.g. child 6;2 with age-equivalent score of 5;2
Same score for kids of different ages may come from qualitatively different patterns of performance
(AGE EQUIVALENT SCORE, CONT.)
Useful to:Help parents understand extreme casesMeet agency requirements
BUT, rule of thumb: Don’t use these scores!
AGE EQUIVALENT FUNCTION
Norm-referenced tests will give you table with converted scores, and will give you place to record them