basic assessment principles chapter 2. nominal ordinal interval ratio measurement scales
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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 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
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
XM
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
N
MXs
Raw scores
Percentile scores/Percentile ranks
Standard scores z scores T scores Stanines Age/grade-equivalent scores
Types of Scores
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
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