2. NORMS
The obtained scores on the test themselves convey no meaning
regarding the ability or trait being measured.
But when these are compared with the norms, a meaningful inference
can immediately be drawn.
Scores on psychological tests are most commonly interpreted by
reference to norm that represent the test performance of the
standardization sample.
In order to ascertain more precisely the individual’s exact position
with reference to the standardized sample, the raw score is converted
into some relative measure.
3. NORMS
These derived scores serve two purposes.
1.They indicate the individual’s relative standing in the normative
sample and facilitate evaluation of performance.
2.They provide comparable measures that permit a direct comparison of
the individuals’ performance on different tests.
4. NORMS
Statistical Concepts
• A major objective of statistical method is to organize and summarize
quantitative data in order to facilitate their understanding.
Frequency Distribution
It is prepared by grouping the scores into convenient class intervals and
tallying each score in the appropriate interval. When all scores are
centered, tallies are counted to find out frequencies in each class
interval.
5. NORMS
Histogram – the height of the column erected over each class interval
corresponds to the number of persons scoring in that interval.
Frequency Polygon – the number of persons in each interval is indicated
by a point in the center of the class interval and across from the
appropriate frequency. Successive points are then joined by straight
lines.
Normal curve - Normal curve has important mathematical properties and
provides the basis for many kinds of statistical analyses.
6. NORMS
Central tendency
Variability (range, variance, standard deviation)
• Further description of a set of test score is given by measures of
variability or extent of individual differences around the central
tendency.
• The most obvious and familiar way for reporting variability is in terms of
range between highest and lowest score.
• Range is extremely crude and unstable and insufficient description of test
score.
• A more precise method of measuring variability is based on the
difference between each individual’s score and the mean of the group.
7. NORMS
• The SD provide the basis for expressing an individual’s scores on
different tests in terms of norms.
• The interpretation of the SD is clear cut when applied to a normal
curve.
• Percentages of cases fall between Mean-1 and Mean +1 is 68.26%,
Mean-2 and Mean +2 is 95.44%, Mean-3 and Mean +3 is 99.72%.
8. NORMS
Developmental Norms
• One way in which meaning can be attached to test score is to
indicate how far along the normal developmental path the
individual progress.
• An 8-year-old child who performs as well as the average 10-
year-old on an intelligence test may be described as having
mental age of 10.
• They are very helpful for descriptive purpose but they are not
compatible to precise statistical treatment.
9. NORMS
Developmental Norms
• The types of developmental norms are
- Mental Age Norms,
- Grade Equivalent Norms and
- Ordinal Scale Norms.
10. NORMS
MentalAge
• Mental age norm is mainly employed to the age tests like
intelligence tests.
• A measure of an individual’s performance on an intelligence
test expressed in terms of years and months.
• A child’s mental age on the test is the sum of basal age and
the additional months of credit earned at higher age levels.
11. NORMS
MentalAge
• Mental age norms also have been employed with tests that are
not divided into year levels.
• The mean raw scores obtained by the children in each year
group within the standardization sample constitute the age
norms for such test.
12. NORMS
Grade Equivalents
• Scores on educational achievement tests are often interpreted
in terms of grad equivalents.
• We use this norm to describe students’ achievement as
equivalent i.e. 7th grade performance in spelling, 8th grade in
reading, 5th grade inarithmetic.
• Grade norm are found by computing the mean raw score
obtained by children in each grade.
13. NORMS
Grade Equivalents
• If the average number of problems solve correctly on an
arithmetic test by 4th graders in the standardized sample is 23,
then a raw score of 23 corresponds to a grade equivalent of 4.
• Garde norms generally applicable only common subjects
those are taught thorough out grades.
14. NORMS
Ordinal scales
• Ordinal scales are designed to identify stage reached by the child
in the development of specific behavior functions.
• The ordinality of such scales refers to the uniform progression of
development through successive stages.
• Although scores may be reported in terms of approximate age
levels, such scores are secondary to qualitative description of the
children characteristics behavior.
• These scales typically provide information about what the child
actually able to do in successive stages.
15. NORMS
Within-Group Norms
• Such type of norms helps in comparing the individual’s performance
with the most nearly comparable standardized group’s performance.
• For example – a child’s raw score is compared with that of children of
same chronological age or in the same school grade.
• Within group norms have a uniform and clearly defined quantitative
meaning and can be appropriately employed in most types of statistical
analyses.
• Nearly all standardized tests provide some form of with-in group
norms.
16. NORMS
Percentiles
• Percentile scores are expressed in terms of the percentage of
persons in the standardization sample who fall below a given
raw score.
• A percentile indicates the individual’s relative position in the
standardized sample.
• It can be regarded as ranks in a group. Lower the percentile,
the poorer the individual’s standing.
17. NORMS
Percentiles
• The 50th percentile (P50) correspond to median. Percentiles
above 50 represent above-average performance and below 50
signify inferior performance.
Adv. –
• Percentiles
understood.
are easy to compute and can be readily
• It is universally applicable.
• It can be used equally well with adults and children and
suitable for any type of test.
18. NORMS
Percentiles
• The chief drawback of percentile scores arises from marked
inequality of their units, especially at the extremes of the
distribution.
• It is apparent that percentile show each individual’s relative
position in the normative sample but not the amount of
differences between scores.
19. NORMS
Standard Scores
• Standard scores are most satisfactory type of derived score
from most point of view.
• It expresses the individual’s distance from the Mean in terms
of the Standard Deviation of the distribution.
• They are obtained by linear or nonlinear transformation of the
original raw scores.
20. NORMS
Standard Scores
• When found by linear transformation, they retain the exact
numerical relations of the original raw scores.
• Because they computed by substracting a constant from each
raw score and then dividing the result by another constant.
• All properties are duplicated in the distribution of these
standard scores.
• Standard scores are often termed as z-score.
21. NORMS
Standard Scores
• To compute z-score, we find the differences between raw
score and the mean of normative group and then divide the
difference by SD of the normative group.
• Any raw score that is equal to mean is equivalent to a z-score
of 0.
• For occurrence of negative values and decimals, some further
linear transformations are usually applied.
22. NORMS
Standard Scores
• For example, scores on the Scholastic Assessment Test (SAT)
are standard scores adjusted to mean 500 and SD 100.
• Thus, standard score -1 on the test would be expressed as
500-100*1=400.
• Scores on separate subtests of the Wechsler Intelligence
Scales are converted to a distribution of mean 10 and SD 3.
23. Relativity of Norms
Interest Comparison
• Test scores cannot be properly interpreted in abstract; these
must be referred to particular tests.
• An individual’s relative standing in different functions may
be grossly misinterpreted through lack of comparability of
test norms.
• There are three principal reasons account for systematic
variations among the scores obtained by the same individual
on different tests.
24. Relativity of Norms
Interest Comparison
- Tests may differ in content despite their similar labels
- Scale units may not be comparable
-Composition of the standardized samples used in establishing
norms for different tests may vary.
25. Relativity of Norms
The Normative Sample
• Any norm is restricted to the particular normative population
from which it was derived.
• Psychological norms are in no sense absolute, universal, or
permanent.
• Norms merely represent the test performance of the persons
constituting the standardization sample.
• In the development and application of test norms,
considerable attention should be given to the standardization
of sample.
26. Relativity of Norms
The Normative Sample
• It is apparent that the sample on which the norms are based should be
large enough to provide stable values.
• Norms with a large sampling error would be of little value in the
interpretation of test scores.
• Requirements of selecting representative sample from the population
under consideration are also important.
• Subtle selective factors that might make the sample unrepresentative
should be carefully investigated.
• It is far better to redefine the population more narrowly than to report
norms on an ideal population that is not adequately represent by
standardized sample.
27. Relativity of Norms
National AnchorNorms
• One solution for the lack of comparability of norms is to use
an anchor test to work out equivalency tables for scores on
different tests.
• Such table are designed to show what score in Test A is
equivalent to each score in test B.
• This can be done by the equipercentile method. In this
method, scores are considered equivalent when they have
equal percentile in a given group.
28. Relativity of Norms
Specific Norms
• Another approach to the nonequivalence of existing norms is to
standardized tests on more narrowly defined populations.
• In such case, the limits of the normative population should be clearly
reported with the norms.
• For many testing purposes, highly specific norms are desirable.
• Even when representative norms are available for a broadly defined
population, it is often helpful to have separately reported subgroup
norms.
• The subgroup may be formed with respect to age, grade, type of
curriculum, sex, geographical region, urban, or rural environment,
socioeconomic level, and many other variables.
