Interpreting Test Results using the Normal Distribution Dr. Amanda Hilsmier

Major Purposes of Assessment Gather information Answer important questions Instructional planning Monitor student program Evaluate program effectiveness

Guidelines for Assessment Nondiscriminatory Focused on educational needs Comprehensive Technically adequate tools and administered by trained professionals Protect rights of students and parents

Comprehensive assessment IQ test Achievement test Rating scales (behavior, attentional, emotional, &/or adaptive behavior) Classroom observations Parent interviews Work samples Assessments from other personnel (speech-language pathologist, occupational therapist, physical therapist, nurse/doctor, etc. Hearing/vision, if necessary

Measurement Error Assessment has room for measurement error Scores would differ when administering the same instrument to the same student with the same examiner Test scores are observed scores that are made up of 2 scores: a hypothetical true score and an error component The standard error of measurement estimates the amount of error in a score The confidence interval uses the measurement error +/- the obtained score to give a range for where the true score could fall

Descriptive Statistics Measures of central tendency Measures of variability Measures of correlation

Measures of Central Tendency The mean is the arithmetic average from a set of values The mode is the most frequently occurring score among a set of values The median is the middle score in a set of values

Measures of Variability The range is the difference between the highest and lowest score The standard deviation accounts for the relationship of the score from the mean

Results from Informal Measures Frequency counts (number of questions, items, or problems answered correctly) Percentages out of number answered correctly and total attempted Duration measures the time elapse

Results from Norm- referenced Measures Raw score: number of items answered correctly Age/Grade scores: express test performance in terms of grade or age in school Percentile ranks: percentage of individuals in the norm group who achieved the specific raw score or a lower one Standard Scores: raw scores transformed to a new scale with a set mean and standard deviation

What do derived scores tell us? How do we know what a standard score or percentile rank means? We must look at the mean and standard deviation for that test score.

Which is better a grade equivalent score or a standard score? What do you feel more comfortable interpreting? Why? What tells us more a 3 rd grader with a standard score of 84 on letter-word identification or a grade equivalency score of 1.7? Let’s examine the difference between these two scores with the grade equivalency exercise.

Considerations when evaluating grade and/or age equivalent scores Does not provide information on whether student’s performance is within average limits (hard to discern if one-year difference in reading is enough to rule a child eligible for services) Only provides precise information about a student’s instructional or developmental level (often means raw score is equivalent to that particular age or grade group) Grade scores do not describe the student’s current instructional level.

What is the normal distribution? IQ scores and other standard scores are normally distributed The standard normal distribution is a bell-shaped curve which represents the percentage of students that score in a particular range The standard normal distribution has a mean of 0 and a standard deviation of 1. The mean is usually 100 and the standard deviation is typically 15.

Why do you need to know about the normal distribution? Why would it be important?

What does an IQ score of 89 tell me about a student? The student is in the low average IQ range is average is low average while is high average The student is in the 23 rd percentile The means that this student scored at or above 23% of the students in his/her age range Can we know anything else from this score alone?

Not really we need more information What is the students’ current academic performance? What are his/her grades in school? Is he failing a course? If so, what course? Has he/she been retained?

Sample score results for Susie 7 th grade student Has a D in social studies Failing Math, Science, and Reading Held back in the 1 st grade because socially immature and behind peers academically Not a behavioral problem-very shy and insecure

Sample score results for Susie WISC- III VIQ WISC- III PIQ WISC- III FSIQ WJ-III L-W ID WJ-III Pass Comp WJ-III Math Calc WJ-III Math Reas 90 (25%) 72 (3%) 78 (7%) 65 (1%) 78 (7%) 56 (<1%) 73 (4%)

What do these scores mean? How do you explain these scores to a parent? What makes sense to a parent or a regular education teacher? What if you do not have the grade or age equivalents on the students’ score report?