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Foundations of
Psychological Testing
Interpreting Test Scores
Chapter 5
Levels of Measurement
• Nominal Scales
• Ordinal Scales
• Equal-Interval Scales
• Ratio Scales
Nominal Scales
• A system of measurement in which all
things measured are categorized based on
one or more distinguishing characteristics
and placed into mutually exclusive and
exhaustive categories
• Numbers are labels that identify data
• Usually used for demographic data
(gender, race, SES, place of residence…)
Nominal Scales
• Example of nominal scales for demographic
data
Race (0-Caucasian, 1-Hispanic, 2-African American…)
Gender (0-Female, 1-Male)
• Yields only categorical data, so there are few
ways the data can be described or manipulated
• Usually reported in terms of how many occur in
each category
Ordinal Scales
• System of measurement in which all things
measured are categorized based on one
or more distinguishing characteristics &
placed into mutually exclusive and
exhaustive categories
• Permits classification, rank-ordering from
greatest to least & vice versa
• Indicates an individual’s or object’s value
based on its relationship to others in the
group
Ordinal Scales
•
•
1.
2.
Uses of ordinal scales (Ranking employee sales,
student’s GPA, class standing, age & grade
equivalents, percentile scores)
Cannot add, subtract, multiply or divide ordinal scores
or compute means or standard deviation
Two Important Points
The number/rank has meaning only within the group
being compared & provides no information about the
group as a whole
Ordinal scales give no information about how closely 2
individuals or objects are related
Interval Scales
• Interval Scales – A system of measurement in
which all things measured can be rank-ordered,
where the rank-ordering contains equal
intervals, every unit on the scale is equal to
every other unit on the scale, & there is no
absolute zero point
• Mathematical operations may not be performed
on interval-level data because of the absence of
a true or absolute zero point (arbitrary)
Interval Scales
• Examples: Temperature scale, 5-point
rating scale “1=worst, 2=poor, 3=average,
4=good, 5=best”
• Allows us to compare the performance of
one group (or individual) to that of another
• Interval scales can be used to develop test
norms & standard scores
• No test taker possesses zero of the ability
or trait being measured
Ratio Scales
• A system of measurement in which all things
measured can be rank-ordered, the rankordering does imply something about exactly
how much greater one ranking is than another,
and equal intervals exist between each number
on the scale
• All mathematical operations can be meaningfully
performed because a true or absolute zero point
exists
• Few scales in psychology or education are ratio
scales
Ratio Scales
• Numbers are assigned to points with the
assumption that each point is an equal
distance from the adjacent numbers
• Examples: Bathroom scales, timed or
distance measures,
• Ratio Scales allow ratio comparisons
• Raw Scores – Basic scores calculated
from a psychological test
• Norm Group – A previously tested group of
individuals
Procedures for
Interpreting Test Scores
• Frequency Distributions
• The Normal Curve
• Descriptive Statistics
• Standard Scores
Frequency Distributions
• A tabular listing of scores along with the number
of times each score occurred
• An orderly arrangement of a group of numbers
(or test scores)
• Scores in frequency distributions are often
grouped in class intervals (for the purpose of
displaying them)
• Display on a horizontal (x) & vertical (y) axis
• Can be illustrated graphically (graph, histogram,
bar graph,etc.)
Frequency Distributions
• To determine size of the interval
1. take the highest score
2. subtract the lowest score
3. divide the result by 15 (number of
desired intervals)
= Yields the width of the interval
(If the width is an even number, add 1 to the
width so each interval will have a
midpoint)
The Normal Curve
• A bell-shaped, smooth, mathematically
defined curve highest at the center &
gradually tapered on both sides,
approaching but never actually touching
the horizontal axis
• Also referred to as the normal probability
distribution
Descriptive Statistics
• Describe or summarize a distribution of
scores numerically
• Measures of Central Tendency
• Measures of Variability
• Measures of Relationship
Measures of Central Tendency
• Mean – the average score in a distribution
• Median – the middle score in a distribution
• Mode – the most common score in a
distribution
• Outliers – a few values that are
significantly higher or lower than most of
the values
• Normal distribution – the mean, mode, &
median are equal
Measures of Variability
• Represent the spread of the scores in the distribution
and provide more information about individual
differences
• Range – the high score in a distribution minus the low
score
• Variance – tells whether individual scores tend to be
similar to or substantially different from the mean; equal
to the mean of the squares of the difference between the
scores in a distribution and their mean
• Standard Deviation – equal to the square root of the
averaged squared deviations about the mean; equal to
the square root of the variance
Measures of Relationship
• You must have two sets of scores to
calculate measures of relationship
• Correlation coefficient – describes the
relationship between two distributions of
scores
• Most common technique for computing
correlations yields an index called the
Pearson Product Moment Coefficient
Standard Scores
• A raw score that has been converted from one
scale into another, the latter scale (1) having
some arbitrarily set mean & standard deviation &
(2) being more widely used & readily
interpretable
• Examples of standard scores are z scores & T
scores
• Universally understood & allow the test user to
evaluate a person’s performance in reference to
other person’s who took the same test
Linear Transformations
• Change the unit of measurement but do not change the
characteristics of the raw data in any way
• Percentages – % of people whose score falls below a
particular raw score; divide the raw score by the total
number of question
• Standard Deviation Units – Refer to how many standard
deviations an individual falls away from the mean (mean
always has a standard deviation unit of zero)
• Example – mean of a distribution = 6, & standard
deviation = 2, then one standard deviation above = 8 &
one standard deviation below = 4
• Z scores – similar to standard deviation
units except they can be represented in
whole numbers & decimal points
Z=X–X
S
(refer to study sheet)
• T scores – unlike standard deviation units
& Z scores, T scores always have a mean
of 50 & a standard deviation of 10.
T = (Z x 10) + 50
Area Transformations
• Percentile Rank – the ordinal ordering of
person’s scores by percentile
• The mean of a distribution always has a
percentile rank of 50 (50% of the people scored
at or above the mean & 50% of the people
scored at or below the mean)
• Percentile Rank – Take the # of individuals that
scored below a specific raw score, + ½ (.5) of
those who scored exactly the same raw score,
then divide it by the total number of people who
took the test, multiply by 100 to make the
decimal number a whole number
The Role of Norms
• Types of Norms
Percentile Ranks
Age/Grade Norms
• The Careful Use of Norms
Types of Norms
• Percentile Rank – represents the
percentage of the norm group that scored
less than or equal to that individual
• Age & Grade Norms – allow test users to
compare an individual’s test score to the
scores of people of different ages & in
different grades; frequently used in
educational settings
Careful Use of Norms
• Use the appropriate norms when interpreting
test scores
• Use the norms correctly
• Use up-to-date norms
• Look at the size of the norm group (small is not
as representative of the entire population)
• When using age & grade norms, one test result
alone is not a good measure for advanced
educational placement