Types of Scores & Types of Standard Scores

TYPES OF SCORES
MR. CRISALDO H. CORDURA
 TYPES OF STANDARD
SCORES

WHAT IS ATEST SCORE?
•A test score is a piece of information, usually a number,
that conveys the performance of an examinee on a test.
• One formal definition is that it is "a
summary of the evidence
contained in an examinee's
responses to the items of a test
that are related to the construct or
constructs being measured."

Types of scores
Raw Scores
Percentage Scores
Derived Scores
Developmental Scores
Scores of Relative

WHAT IS A RAW SCORE?
The raw score is the number of items a
student answers correctly without
adjustment for guessing.
For example, if there are 15 problems on
an arithmetic test, and a student
answers 11 correctly, then the raw score
is 11. Raw scores, however, do not
provide us with enough information to
describe student performance.

Percentage
Scores
A percentage score is the percent
of test items answered correctly.
These scores can be useful when describing a
student's performance on a teacher-made
test or on a criterion-referenced test.
However, percentage scores have a
major disadvantage:We have no way of
comparing the percentage correct on
one test with the percentage correct on
another test. Suppose a child earned a
score of 85 percent correct on one test
and 55 percent correct on another test.
The interpretation of the score is related
to the difficulty level of the test items on
each test. Because each test has a
different or unique level of difficulty, we
have no common way to interpret these
scores; there is no frame of reference.

Derived Scores  Derived scores are a family of
scores that allow us to make
comparisons between test scores.
 Raw scores are
transformed to
derived scores.
Developmental scores and scores
of relative standing are two types of
derived scores. Scores of relative
standing include percentiles,
standard scores, and stanines.

Developmental
Scores
Sometimes called age and grade
equivalents, developmental scores are
scores that have been transformed from
raw scores and reflect the average
performance at age and grade levels.
Thus, the student's raw score
(number of items correct) is the same
as the average raw score for students
of a specific age or grade. Age
equivalents are written with a hyphen
between years and months (e.g., 12–4
means that the age equivalent is 12
years, 4 months old). A decimal point
is used between the grade and month
in grade equivalents (e.g., 1.2 is the
first grade, second month).

Scores of Relative
A percentile rank is the point in a
distribution at or below which the scores
of a given percentage of students fall.
Percentiles provide information about
the relative standing of students when
compared with the standardization
sample. Look at the following test
scores and their corresponding
percentile ranks.

What is a Standard Score?
Standard score is the name
given to a group or category
of scores. Each specific type
of standard score within this
group has the same mean
and the same standard
deviation.

The different types of Standard Scores:
Z-Scores
T-Scores
Deviation IQ Scores
Normal Curves Equivalents
Stanines
Percentile Ranks

Z-Scores
Have a mean of 0 and a
standard deviation of 1.

Calculating Z-Scores
z =
(raw score – mean)
standard deviation
raw score = 31, mean =27, S = 6.
z =
(31 – 27)
6
= 4/6 or .67
Interpretation
The person scored .67
standard deviations
above the mean.

How to Identify Z-Scores?
Positive and Negative Z-Scores
Some z-scores will be positive
whereas others will be negative. If
a z-score is positive, its’
corresponding raw score is above
(greater than) the mean. If a z-
score is negative, its’
corresponding raw score is below
(less than) the mean.
http://statistics-help-for-students.com/How_do_I_interpret_Z_score_data_in_SPSS.htm#.W1I4vbgRXIU

T-Scores
A t score is one form of a
standardized test statistic (the other
you’ll come across in elementary
statistics is the z-score). The t score
formula enables you to take an
individual score and transform it
into a standardized form>one which
helps you to compare scores.
http://www.statisticshowto.com/probability-and-statistics/t-
distribution/t-score-formula/
have a mean of
50 and a
standard
deviation of 10.

Formula forT-Scores:
If you have only one item in
your sample, the square root in
the denominator becomes √1.
This means the formula
becomes:

Sample question:
A law school claims it’s graduates earn an
average of $300 per hour. A sample of 15
graduates is selected and found to have a
mean salary of $280 with a sample standard
deviation of $50. Assuming the school’s claim
is true, what is the probability that the mean
salary of graduates will be no more than $280?

Step 1: Plug the information into the
formula and solve:
x̄ = sample mean = 280
μ0 = population mean = 300
s = sample standard deviation = 50
n = sample size = 15

t = (280 – 300)/ (50/√15) = -20 / 12.909945 = -1.549.
Step 2: Subtract 1 from the sample size to get the
degrees of freedom:
15 – 1 = 14.The degrees of freedom lets you know
which form of the t distribution to use (there are
many, but you can solve these problems without
knowing that fact!).

Step 3: Use a calculator to find the probability using your
degrees of freedom (8).You have several options, including
theTI-83 (see How to find a t distribution on aTI 83) and
this online calculator. Here’s the result from that
calculator. Note that I selected the radio button under the
left tail, as we’re looking for a result that’s no more than
$280:
https://surfstat.anu.edu.au/surfstat-home/tables/t.php

Types of Scores & Types of Standard Scores

Converting Z-score toT-score
http://w
ww.statis
ticshowt
o.com/pr
obability
-and-
statistics/
t-
distributi
on/t-
score-
formula/

Deviation IQ scores:
have a mean of 100 and a standard
deviation of 15 or 16.

Deviation IQ scores are frequently used to report
the performance of students on norm-referenced
standardized tests. The deviation scores of the
Wechsler Intelligence Scale for Children–III and the
Wechsler Individual Achievement Test–II have a
mean of 100 and a standard deviation of 15, while
the Stanford-Binet Intelligence Scale–IV has a mean
of 100 and a standard deviation of 16. Many test
manuals provide tables that allow conversion of raw
scores to deviation IQ scores.

Normal curve equivalents:
Have a mean of 50 and a
standard deviation of 21.06.

Normal curve equivalents (NCEs) a type
of standard score with a mean of 50 and a
standard deviation of 21.06. When the
baseline of the normal curve is divided into
99 equal units, the percentile ranks of 1,
50, and 99 are the same as NCE units
(Lyman, 1986). One test that does report
NCEs is the Developmental Inventory-
2.However, NCEs are not reported for
some tests.

Stanines
Standard score bands divide a
distribution of scores into nine
parts.

Stanines are bands of standard scores that have a mean
of 5 and a standard deviation of 2. Stanines range from
1 to 9. Despite their relative ease of interpretation,
stanines have several disadvantages. A change in just a
few raw score points can move a student from one
stanine to another. Also, because stanines are a general
way of interpreting test performance, caution is
necessary when making classification and placement
decisions. As an aid in interpreting stanines, evaluators
can assign descriptors to each of the 9 values:

9—very superior
8—superior
7—very good
6—good
5—average
4—below average
3—considerably below average
2—poor
1—very poor

Percentile ranks
Point in a distribution at or below
which the scores of a given percentage
of students fall.

References:
Excerpt from Assessment of Children & Youth with Special Needs, by L.G. Cohen, L.J.
Spenciner, 2007 edition, p. 57-62
http://www.statisticshowto.com/probability-and-statistics/t-distribution/t-score-formula/
https://surfstat.anu.edu.au/surfstat-home/tables/t.php

Types of Scores & Types of Standard Scores

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