Basic Assessment Principles Chapter 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 Alice Beth Amy Porter 72 82 94 77 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 X f 50-59 60-69 70-79 80-89 90-100 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: X ∑ M= N Measures of Central Tendency Example: Sample scores – 98, 98, 97, 50, 49 ∗ Mode = 98 ∗ Median = 97 ∗ Mean = 78.4 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 X 50 60 70 80 90 f % 5% 14% 19% 43% 19% %ile 19 38 81 99* 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 Types of Standard Scores z Scores ∗ z score = X-M s ∗ Mean = ∗ Standard deviation = 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 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? [...]... 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:... 38 81 99* 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... 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 ∗...Measures of Variability ∗ Range – highest score minus lowest score ∗ Variance – sum of squared deviations from the mean ∗ Standard Deviation – square root of variance ∗ Formula: s= ∑( X − M ) N 2 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 X 50... 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? ... 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... 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:... 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