Chapter 2 revised

Basic Assessment Principles

Chapter 2

Nominal

Ordinal

Interval

Ratio

Measurement Scales

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

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

Robert 72 Miles 96 Jason 68 Whitney 79Alice 82 Paul 59 Pedro 86 Jane

85Beth 94 John 82 Kelly 92 Michael

81Amy 77 Kevin 85 Justin 72 Rebecca

88Porter 62 Ling 98 Sherry 67 Maria

86

Norm-Referenced: Sample Scores

X 50-59 60-69 70-79 80-89 90-100

f 1 3 4 8 4

Frequency Distribution

Frequency Polygon

0123456789

50-59 60-69 70-79 80-89 90-100

Histogram

012345678

60-69 70-79 80-89 90-100

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: NX

M

Measures of Central Tendency

Example:

Sample scores – 98, 98, 97, 50, 49 Mode = 98 Median = 97 Mean = 78.4

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

NMX

s

Normal Distribution

Skewed Distribution

Raw scores Percentile scores/Percentile ranks Standard scores

z scores T scores Stanines Age/grade-equivalent scores

Types of Scores

X 50 60 70 80 90

f 1 3 4 9 4

% 5% 14% 19% 43% 19%

%ile 5 19 38 81 99*

Percentiles

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

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

Types of Standard Scores

z Scores

z score = X-M s Mean = 0

Standard deviation = 1

Mean = 50

Standard deviation = 10

T Scores

Stanines

Standard Scores: Summary

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

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

Methods for selecting norming group:

Simple random sample

Stratified sample

Cluster sample

Sampling Methods

Size Gender Race/ethnicity Educational background Socioeconomic status

Is the norming group appropriate for use with this client?

Norming Group Characteristics