This document discusses key concepts in measurement scales and assessment instruments. It covers nominal, ordinal, interval, and ratio measurement scales. It describes norm-referenced instruments, which compare individuals to norms, and criterion-referenced instruments, which compare individuals to standards. It also discusses measures of central tendency like mean, median, and mode. Finally, it covers standard scores and different types of scores from assessments, as well as evaluating norming groups.

1. Basic Assessment
Principles
Chapter 2

2. ∗ Nominal
∗ Ordinal
∗ Interval
∗ Ratio
Measurement Scales

3. ∗ Individual’s score is compared to performance of
others who have taken the same instrument (norming
group)
∗ Example: personality inventory
∗ Evaluating the norming group
∗ size
∗ sampling
∗ representation
Norm-Referenced Instruments

4. ∗ Individual’s performance is compared to specific
criterion or standard
∗ Example: third-grade spelling test
∗ How are standards determined?
∗ common practice
∗ professional organizations or experts
∗ empirically-determined
Criterion-Referenced Instruments

5. Robert 72 Miles 96 Jason 68 Whitney 79
Alice 82 Paul 59 Pedro 86 Jane 85
Beth 94 John 82 Kelly 92 Michael 81
Amy 77 Kevin 85 Justin 72 Rebecca 88
Porter 62 Ling 98 Sherry 67 Maria 86
Norm-Referenced: Sample Scores

6. X 50-59 60-69 70-79 80-89 90-100
f 1 3 4 8 4
Frequency Distribution

7. Frequency Polygon
0
1
2
3
4
5
6
7
8
9
50-59 60-69 70-79 80-89 90-100

8. Histogram
0
1
2
3
4
5
6
7
8
60-69 70-79 80-89 90-100

9. Measures of Central Tendency
∗ Mode – most frequent score
∗ Median – evenly divides scores into two halves (50%
of scores fall above, 50% fall below)
∗ Mean – arithmetic average of the scores
∗ Formula:
N
X
M
∑=

10. Measures of Central Tendency
Example:
Sample scores – 98, 98, 97, 50, 49
∗ Mode = 98
∗ Median = 97
∗ Mean = 78.4

11. Measures of Variability
∗ Range – highest score minus lowest score
∗ Variance – sum of squared deviations from the mean
∗ Standard Deviation – square root of variance
∗ Formula:
( )2
N
MX
s
∑ −
=

12. Normal Distribution

13. Skewed Distribution

14. ∗ Raw scores
∗ Percentile scores/Percentile ranks
∗ Standard scores
∗ z scores
∗ T scores
∗ Stanines
∗ Age/grade-equivalent scores
Types of Scores

15. X 50 60 70 80 90
f 1 3 4 9 4
% 5% 14% 19% 43% 19%
%ile 5 19 38 81 99*
Percentiles

16. ∗ 98th
percentile
∗ 98% of the group had a score at or below this
individual’s score
∗ 32nd
percentile
∗ 32% of the group had a score at or below this
individual’s score
∗ If there were 100 people taking the assessment, 32 of
them would have a score at or below this individual’s
score
Interpreting Percentiles

17. ∗ Units are not equal
∗ Useful for providing information about relative
position in normative sample
∗ Not useful for indicating amount of difference
between scores
Interpreting Percentiles

18. Types of Standard Scores

19. z Scores
∗ z score = X-M
s
∗ Mean = 0
∗ Standard deviation = 1

20. ∗ Mean = 50
∗ Standard deviation = 10
T Scores

21. Stanines

22. Standard Scores: Summary

23. ∗ Possible problematic scores
∗ Age-equivalent scores
∗ Grade-equivalent scores
∗ Problematic because:
∗ These scores do not reflect precise performance on an instrument
∗ Learning does not always occur in equal developmental levels
∗ Instruments vary in scoring
Additional Converted Scores

24. ∗ Adequacy of norming group depends on:
∗ Clients being assessed
∗ Purpose of the assessment
∗ How information will be used
∗ Examine methods used for selecting group
∗ Examine characteristics of norming group
Evaluating the Norming Group

25. ∗ Methods for selecting norming group:
∗ Simple random sample
∗ Stratified sample
∗ Cluster sample
Sampling Methods

26. ∗ Size
∗ Gender
∗ Race/ethnicity
∗ Educational background
∗ Socioeconomic status
∗ Is the norming group appropriate for use with this
client?
Norming Group Characteristics