1. Norms

2. Interpreting test results
If we assume that
Test is properly constructed
Test is reliable
Test is valid
How can we make our interpretation / inference?

3. Raw Score number (X) captures some aspect of a person’s performance
how fast task were solved (e.g. sum of seconds spend on each task)
how many task were solved (e.g. no task solved properly)
how well task were solved (e.g.
how many mistakes were made – (e.g. no errors)
how severe are symptoms – (e.g. no of symptoms)
How can we give meaning to the X? and interpret some number? For instance X = 20?

4. Most widely used frame of reference
Frames of reference
Norm-referenced test - standards based on the performance of specific groups of people to provide information for interpreting scores. useful for comparing individuals 1 vs 1 or 1 vs Group
Most widely used frame of reference

5. Frames of reference Norms
refer to the typical behavior of one or more reference groups
presented in the form of set of statistics summarizing performance of the group (normative or standardization samples)

6. Frames of reference
Criterion referenced test – standards based on test performance criteria, e.g. cutt-off point.
relationship between test and standard is demonstrable and well defined
designed to assess whether and to what extent the desired levels of mastery or performance criteria have been met.

7. Norms Within group norms Group or groups are point of reference
Placing test taker performance within normative distribution
Composition of normative sample (key issue)
Two main types based on
Uniform distribution
Normal distribution

8. NOTICE: Some vocabulary problems
Normative sample
Representative for the population (individuals that test is intended to)
Size – large = stability (usually ‘1000 +’)
Construct characteristics and amount of important factors
Demographic (gender, age…)
Purpose of the test
Special samples
NOTICE: Some vocabulary problems
Standardization sample: original sample for standardization and normalization
Normative sample: synonymous to previous but used also for any subsequent samples used for obtaining norms
Reference group: loose term -> any group used for score comparison

9. Normative sample
Reference groups – wide (nation wide representative) or specialized (clinical or occupational group)
Subgroup norms (usually by gender or age)
sufficient size
representative of their categories
Local norms
Based on local (e.g. geographical or organizational) groups
Convenience norms – convenient but not very useful

10. Assessing quality and Applicability of a Normative Sample
How large is the normative sample?
When was the sample gathered?
Where was the sample gathered?
How were individuals identified and selected for the sample?
Who tested the sample?
How did the examiner or examiners qualify to do the testing?
What was the composition of the normative sample (age, sex, ethnicity, race, linguistic background, education, SES, geographic distribution, ANY OTHER RELEVANT VARIABLE)

11. Norms – Percentiles
represent the percentage of persons in the reference group who scored at or below a given raw score
Percentile not to be confused with percent
most direct method
MAIN advantage – readily understood by test takers and applicable to most sorts of tests and test populations.

12. Transforming results
Ordering results in the normative sample from lowest thru highest

13. Percentiles No of units = 101 percentiles Range = 0 – 100. Median = 50
Transformation => Uniform (rectangular)distribution, is a distribution that has constant probability
No of units = 101 percentiles
Range = 0 – 100.
Median = 50
Each pecentile is equivalent to 1% of observations exept 0 & 100 = 0,5%
Disadvantage = unequal units

15. Norms – Normal distribution. Standard Scores
Transforming raw scores into standard score
Continuous variable
M = 0 and SD = 1
Range = unlimited
No of units = unlimited (unit as small as 0,01)
Used as a primary transformation

17. Formula for transforming z score into other derived standard scores
New standard score = (z score) (New SD) + New mean

18. STEN – Standard TEN Distribution normal Mean 5.5 (between 5th and 6th)
Range 1-10
SD = 2
No of units 10
1 unit (STEN) = 0,5 SD
Used for differentiating within -2 to +2 SD of normal distribution
STEN 1 and 10 used for scores above |2| SD of standard normal distribution

19. STANINE – STAndard NINE
Distribution normal
Mean 5 = 5th stanine
SD = 2
Range 1-9
No of units 9
1 unit (STEN) = 0,5 SD
Used for differentiating within -1,75 to +1,75 SD of normal distribution
STANINE 1 and 9 used for scores above |1,75| SD of standard normal distribution

20. T- Scores
Distribution normal Mean 50 = 50th T-score SD = 10 Range No of units unit (T-score) = 0,1 SD Used for differentiating within -5 to +5 SD of normal distribution 1th and 100th scores used for results above |5| SD of standard normal distribution Differentiating within norm and pathology

23. Other frequently used scales
Wechsler scale (M = 100, SD = 15). College Entrance Examination Board (CEEB) scores (M = 500, SD = 100), used by the College Board’s SAT as well as by the Educational Testing Service e.g. Graduate Record Exam (GRE)

24. Reasons behind norms selection
Distribution shape of raw data
different than normal (e.g. skew) uniform scales
Reliability of measurements and value of standard error of measurement
Utility of a test functioning within norm or pathology / extreme