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This chapter covers measurement scales, norm-referenced and criterion-referenced instruments, frequency distributions, central tendency and variability measures, standard scores, and evaluating norming groups in assessment. Learn about different types of scores like raw, percentile, standard, z, and T scores. Interpret percentiles and understand the importance of evaluating norming group characteristics. Discover sampling methods like simple random, stratified, and cluster sampling and how characteristics such as size, gender, race/ethnicity, educational background, and socioeconomic status impact the norming group appropriateness.
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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 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
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:
Example: Sample scores – 98, 98, 97, 50, 49 Mode = 98 Median = 97 Mean = 78.4 Measures of Central Tendency
Measures of Variability • Range – highest score minus lowest score • Variance – sum of squared deviations from the mean • Standard Deviation – square root of variance • Formula:
Types of Scores • Raw scores • Percentile scores/Percentile ranks • Standard scores • z scores • T scores • Stanines • Age/grade-equivalent scores
Interpreting 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
z Scores • z score = X-M s • Mean = 0 • Standard deviation = 1
T Scores Mean = 50 Standard deviation = 10
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 • 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?
