this a psychometrics course lecture note for chapter 2

1. Chapter two
B a s i c s o f M e a s u r e m e n t
s c a l e

2. M e a s u r e m e n t
 Measurement is the assignment of numbers to
objects
 Many variables studied are straightforward and simple
to measure. E.g. include , age, height, weight, etc
 Other variables are not so straightforward or simple to
measure

3.  E.g we cannot accurately assess people’s level of self
esteem by looking at them.
 These kinds of variables are called constructs
 A construct is an idea or a concept that we wish to
explore
 Constructs include personality traits , emotional
states, attitudes and abilities etc.

4. O p e r a t i o n a l i z a t i o n
 Is the process by which we translate the construct or
idea into something we can measure.
 We transform the idea of constructs with the use of a
standardized tests
 Examples, organization commitment, job satisfaction,
self esteem scales, personality traits etc
 All these scales typically use the items with a five
point scale with scores of one to five representing
Strongly disagree, Disagree, Neither agree nor
disagree, Agree and Strongly agree.

5. J o b s a t i s f a c t i o n m e a s u r e m e n t
1. I enjoy my work most days
2. I do interesting and challenging work.
3. I am satisfied with my job.
4. I am noticed when I do a good job.
5. I get full credit for the work I do.
6. There is a lot of variety in my job.
7. I feel the level of responsibility I am given is acceptable.
8. My job fully uses my skills .
9. The major satisfaction in my life comes from my job.
10. I often think about leaving.
11. I know the standards of work expected of me.
12. I feel my opinion counts in the organisation.
13. I feel valued by senior management
14. I feel my colleagues treat me with respect.

6. O r g a n i z a t i o n a l C o m m i t m e n t s c a l e
1. I tell my friends this is a good organisation to work for.
2. I feel very little loyalty to this organization
3. I would accept almost any type of job assignment in order to keep working
for this organisation
4. I find that my values and the organisations values are very similar.
5. I understand how my job contributes to the organisations goals and
objectives
6. I have a good understanding of where the organisation is going
7. I am proud to tell others that I am part of this organisation.
8. My organisation is known as a good employer locally
9. I am willing to put in a great deal of extra effort to help this organisation be
successful.
10. I would be just as happy working for a different organisation if the work
was similar.
11. It would take very little change in my present circumstances to make me
to leave this organisation.
12. For me this is the best of all possible organisations for which to work.

7. S e l f - e s t e e m m e a s u r e m e n t
A 10-item scale that measures your self-esteem at a given point in time.
It is designed to measure what you are thinking at this moment.
• NB: All items are answered using a 5-point scale (1= not at all, 2= a
little bit, 3= somewhat, 4= very much, 5= extremely).
1. I feel confident about my abilities
2. I am worried about whether I am regarded as a success or failure
3. I feel satisfied with the way my body looks right now.
4. I feel frustrated or rattled about my performance.
5. I feel that I am having trouble understanding things that I read.
6. I feel that others respect and admire me.
7. I am dissatisfied with my weight.
8. I feel self-conscious.
9. I feel as smart as others.
10. I feel displeased with myself

8. V a r i a b l e s a n d C o n s t a n t s
Variables :-are characteristics that take different values in
different persons, places, or things; it is something that
varies
Example:
 Height is a variable which varies both from person to
person
 Sex is a variable, people being either male or female.
A constant is a number that does not change its value (is
constant) in a given situation

9. T y p e s o f v a r i a b l e s
1. Qualitative or categorical variables
2. Quantitative or numerical variables
 Discrete vs. continuous variables

10. Q u a l i t a t i v e o r c a t e g o r i c a l
v a r i a b l e s
• Type of variables, which cannot expressed in numbers
• consist of values representing counts
• They can only be sorted by name or categories
• Not able to be measured as we measure height or
weight
• The notion of magnitude is absent or implicit
• E.g ~ times of runners in a race, incomes of college
graduates, the number of students in different classes,
temperature, etc.

11. Q u a n t i t a t i v e o r n u m e r i c a l
v a r i a b l e s
• Type of variables, which can be measured and
expressed numerically;
• So, quantitative data are arise from counts or
measurements
• They provides information on amount

12. E x a m p l e 1
Classify each of the following sets of data as
either qualitative or quantitative
a) Brand names of shoes in a consumer
survey
• Qualitative; brands are categorical
b) Scores on a multiple choice exam
• Quantitative; the numbers represent a
count of how many questions were right

13. E x a m p l e …
c) Letter grades on an essay assignment
• Qualitative; letter grades categorize based on
ability level
d) Numbers on uniforms that identify basketball
players
• Qualitative; the numbers identify the player,
but wouldn’t be used to make computations

14. D i s c r e t e a n d c o n t i n u o u s v a r i a b l e s
 Discrete variables have a relatively small set of
possible values
 e.g, gender, marital status, religious affiliation
 Continuous variables can (theoretically) assume
any value between the lowest and highest
points on the scale
 e.g, time, distance, weight

15. E x a m p l e
For each data set, indicate whether the data are
discrete or continuous
1. Measurements of the time it takes to walk a mile
• Continuous
2. The numbers of calendar years (such as 2007, 2008,
2009)
• Discrete
3. The numbers of dairy cows on different farms
• Discrete
4. The amounts of milk produced by dairy cows on a
farm
• Continuous

16. T h e s c a l e s o f m e a s u r e m e n t
• Scales of measurement is how variables are defined
and categorized.
• Psychologist Stanley Stevens developed the four
common scales of measurement: nominal, ordinal,
interval and ratio.
• Each scale of measurement has properties that
determine how to properly analyze the data.
• The properties evaluated are identity, magnitude,
equal intervals and a minimum value of zero.

17. P r o p e r t i e s o f M e a s u r e m e n t
• Identity: Identity refers to each value having a unique
meaning.
• Magnitude: Magnitude means that the values have an
ordered relationship to one another, so there is a specific
order to the variables.
• Equal intervals: Equal intervals mean that data points along
the scale are equal, so the difference between data points
one and two will be the same as the difference between
data points five and six.
• A minimum value of zero: A minimum value of zero means
the scale has a true zero point. Degrees, for example, can
fall below zero and still have meaning. But if you weigh
nothing, you don’t exist.

18. N o m i n a l s c a l e E x a m p l e s
• The nominal scale of measurement defines
the identity property of data.
• This scale has certain characteristics, but
doesn’t have any form of numerical
meaning.
• The data can be placed into categories but
can’t be multiplied, divided, added or
subtracted from one another.
• It’s also not possible to measure the
difference between data points.
• You can categories your data in labeling
them in mutually exclusive groups, but there
is no order between the categories
City of birth
Gender
Ethnicity
Region
Martial status

19. O r d i n a l S c a l e E x a m p l e s
• You can categories and rank your
data in order, but you cannot say
anything about the intervals
between the rankings
• These values can’t be added to or
subtracted from.
e.g. Where someone finished in a
race also describes ordinal data.
While first place, second place or
third place shows what order the
runners finished in, it doesn’t specify
how far the first-place finisher was in
front of the second-place finisher.
• Language ability( e.G
beginner, intermediate,
fluent)
• Job satisfaction level
• Pain level ratings,
• Letter grades on a test,
etc.

20. I n t e r v a l S c a l e E x a m p l e s
• Data points on the interval scale
can be ordered and have the
same difference between them.
The difference on the scale
between 10 and 20 degrees is the
same between 20 and 30 degrees
• But there is no true zero point.
E.g. zero degree doesn’t mean an
absolute absence of temperature
• They can be added to or
subtracted from each other, but
not multiplied or divided. For
example, 40 degrees is not 20
degrees multiplied by two.
• Test score(e.g IQ or
exams)
• Personality inventories
• Temperature in
Fahrenheit or Celsius

21. R a t i o s c a l e E x a m p l e s
• Ratio scales of measurement
include properties from all four
scales of measurement
• You can categorize, rank, and infer
equal intervals between
neighboring data points, and there
is a true zero point.
• A true zero means there is an
absence of the variable of interest.
• Ratios(division) are meaningful-10
KM is twice as far as 5 KM and we
can say that 20 seconds is twice as
long as 10 seconds
• Height
• Age
• Weight
• Time
• Length
• Speeds
• Incomes and volume
are ratio scales

22. E x a m p l e
• Identify the level of measurement for each of the
following sets of data
• Numbers on uniforms that identify players on a
basketball team
• Nominal
 Student rankings of cafeteria food as excellent, good, fair,
or poor
• Ordinal
 Calendar years of historical events, such as 1776, 1945, or
2001
Interval; They are not significant at the ratio level
because there is no “true” zero. The year 0 is not the
beginning of time

23. E x a m p l e
 Temperatures on the Celsius scale
 Interval; the differences are meaningful,
but ratios are not. There is no “true” zero
point – 0 degrees Celsius does not
represent a state of no heat.
 Runners’ times in the Boston Marathon
 Ratio; time has a true zero. A time of 0
hours is the start of the race and it would
be meaningful to say that 6 hours really
is twice as long as 3 hours.

24. T h e H i e r a r c h y o f L e v e l s
Nominal

25. T h e H i e r a r c h y o f L e v e l s
Nominal Attributes are only named; weakest

26. T h e H i e r a r c h y o f L e v e l s
Nominal Attributes are only named; weakest
Ordinal

27. T h e H i e r a r c h y o f L e v e l s
Nominal Attributes are only named; weakest
Attributes can be ordered
Ordinal

28. T h e H i e r a r c h y o f L e v e l s
Nominal
Interval
Attributes are only named; weakest
Attributes can be ordered
Ordinal

29. T h e H i e r a r c h y o f L e v e l s
Nominal
Interval
Attributes are only named; weakest
Attributes can be ordered
Distance is meaningful
Ordinal

30. T h e H i e r a r c h y o f L e v e l s
Nominal
Interval
Ratio
Attributes are only named; weakest
Attributes can be ordered
Distance is meaningful
Ordinal

31. Nominal
Interval
Ratio
Attributes are only named; weakest
Attributes can be ordered
Distance is meaningful
Absolute zero
Ordinal
Going from lowest to highest, the 4
levels of measurement are
cumulative. This means that they
each take on the properties of
lower levels and add new
properties.

32. S u m m a r y

33. W h y I s L e v e l o f M e a s u r e m e n t
I m p o r t a n t ?
• The level at which you measure a variable determines
how you can analyze your data.
• The different levels limit which descriptive statistics
you can use to get an overall summary of your data,
and which type of inferential statistics you can
perform on your data to support or disprove your
hypothesis.
• In many cases, your variables can be measured at
different levels, so you have to choose the level of
measurement you will use before data collection
begins.