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