Basic Assessment Principles Chapter 2 Measurement Scales Nominal
Basic Assessment Principles Chapter 2
Measurement Scales Nominal Ordinal Interval Ratio
Norm-Referenced Instruments 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
Criterion-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
Norm-Referenced: Sample Scores Robert 72 Alice 82 Beth 94 Amy 77 Porter 62 Miles Paul John Kevin Ling 96 59 82 85 98 Jason 68 Whitney 79 Pedro 86 Jane 85 Kelly 92 Michael 81 Justin 72 Rebecca 88 Sherry 67 Maria 86
Frequency Distribution
Frequency Polygon
Histogram
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:
Measures of Central Tendency Example: Sample scores – 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:
Normal Distribution
Skewed Distribution
Types of Scores Raw scores Percentile scores/Percentile ranks Standard scores z scores T scores Stanines Age/grade-equivalent scores
Percentiles
Interpreting Percentiles 98 th percentile 98% of the group had a score at or below this individual’s score 32 nd 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
Types of Standard Scores
z Scores z score = X-M s Mean = 0 Standard deviation = 1
T Scores Mean = 50 Standard deviation = 10
Stanines
Standard Scores: Summary
Additional Converted Scores 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
Evaluating the Norming Group 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
Sampling Methods for selecting norming group: Simple random sample Stratified sample Cluster sample
Norming Group Characteristics Size Gender Race/ethnicity Educational background Socioeconomic status Is the norming group appropriate for use with this client?
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