Here are the answers to the measurement scale questions: 1) Number of absences - Ordinal 2) Letter grade on exam - Ordinal 3) Room temperature - Interval 4) Productivity - Ratio 5) Bicycle models - Nominal 6) Educational level - Ordinal 7) Number of questions - Ratio 8) Likert scale categories - Ordinal The key things to remember are: - Nominal has no quantitative properties - Ordinal allows ranking but not equal intervals - Interval has equal intervals but no absolute zero - Ratio has all properties - magnitude, equal intervals, absolute zero Let me know if any of these need more explanation!

1. Introduction to the Practice of
Statistics
Carlo Magno, PhD
De la Salle University, Manila

2. The Process of Statistics
Step 1: Identify a Research Objective
• Researcher must determine question he/she
wants answered - question must be detailed.
• Identify the group to be studied. This group is
called the population.
• An individual is a person or object that is a
member of the population being studied

3. The Process of Statistics
Step 2: Collect the information needed to
answer the questions.
• In conducting research, we typically look at a
subset of the population, called a sample.
Step 3: Organize and summarize the
information.
• Descriptive statistics consists of organizing
and summarizing the information collected.
Consists of charts, tables, and numerical
summaries.

4. The Process of Statistics
Step 4: Draw conclusions from the
information.
• The information collected from the sample is
generalized to the population.
• Inferential statistics uses methods that
generalize results obtained from a sample to the
population and measure their reliability.

5. EXAMPLE The Process of Statistics
Many studies evaluate batterer treatment programs, but there are few
experiments designed to compare batterer treatment programs to
non-therapeutic treatments, such as community service. Researchers
designed an experiment in which 376 male criminal court defendants
who were accused of assaulting their intimate female partners were
randomly assigned into either a treatment group or a control group.
The subjects in the treatment group entered a 40-hour batterer
treatment program while the subjects in the control group received
40 hours of community service. After 6 months, it was reported that
21% of the males in the control group had further battering incidents,
while 10% of the males in the treatment group had further battering
incidents. The researchers concluded that the treatment was
effective in reducing repeat battering offenses.
Source: The Effects of a Group Batterer Treatment Program: A Randomized Experiment in
Brooklyn by Bruce G. Taylor, et. al. Justice Quarterly, Vol. 18, No. 1, March 2001.

6. Step 1: Identify the research objective.
To determine whether males accused of batterering
their intimate female partners that were assigned into
a 40-hour batter treatment program are less likely to
batter again compared to those assigned to 40-hours
of community service.

7. Step 2: Collect the information needed to answer the
question.
The researchers randomly divided the subjects into
two groups. Group 1 participants received the 40-hour
batterer program, while group 2 participants received
40 hours of community service. Group 1 is called the
treatment group and the program is called the
treatment. Group 2 is called the control group. Six
months after the program ended, the percentage of
males that battered their intimate female partner was
determined.

8. Step 3: Organize and summarize the information.
The demographic characteristics of the subjects in
the experimental and control group were similar.
After the six month treatment, 21% of the males in
the control group had any further battering
incidents, while 10% of the males in the treatment
group had any further battering incidents.

9. Step 4: Draw conclusions from the data.
We extend the results of the 376 males in the study
to all males who batter their intimate female
partner. That is, males who batter their female
partner and participate in a batter treatment
program are less likely to batter again.

10. What do we do in statistics?
• A sample of students from both public and private
schools were compared in their study habits. The
Survey of Study Habits (SSH) was administered
among 150 year 7 public HS students and 175
private HS students. The scores of the two samples
were separated. The means and standard deviations
were obtained for each group. The means were
compared using the t-test for two independent
samples. It was found in the study that private HS
students have significantly higher mean scores
than the public HS students.

11. Statistics is the science of collecting,
organizing, summarizing and analyzing
information in order to draw
conclusions.

12. Variables are the characteristics of the
individuals within the population
Key Point: Variables vary. Consider the
variable heights. If all individuals had the same
height, then obtaining the height of one
individual would be sufficient in knowing the
heights of all individuals. Of course, this is not
the case. As researchers, we wish to identify
the factors that influence variability.

13. Types of variables
• Intelligence test scores • Gender
• Spelling ability • Religious affiliation
• Personality test score • Socio-economic status
• Height
• Weight
• Heart rate
• Air pressure

14. Qualitative or Categorical variables allow for
classification of individuals based on some attribute or
characteristic.
Quantitative variables provide numerical measures
of individuals. Arithmetic operations such as addition
and subtraction can be performed on the values of the
quantitative variable and provide meaningful results.

15. EXAMPLE Distinguishing Between Qualitative and
Quantitative Variables
Determine whether the following variables are qualitative or
quantitative.
(a) Type of wood used to build a kitchen table.
(b) Number of yards Tiger Woods hits his drives.
(c) Number of times your Internet service goes down
in the next 30 days.

16. Exercise

17. Types of quantitative variable
• Chairs in a classroom • Height of a tree
• Rooms in hotel • Size of paper
• Plates in the kitchen • Salary of a supervisor
• Magazines in a table • Grams of
carbohydrates in
cereals

18. A discrete variable is a quantitative variable that either
has a finite number of possible values or a countable
number of possible values. The term “countable”
means the values result from counting such as 0, 1, 2, 3,
and so on.
A continuous variable is a quantitative variable that
has an infinite number of possible values it can take on
and can be measured to any desired level of accuracy.

19. EXAMPLE Distinguishing Between Continuous and
Discrete Variables
Determine whether the following quantitative variables
are continuous or discrete.
(a) Number of yards Tiger Woods hits his drives.
(b) Number of times your Internet service goes down
in the next 30 days.

20. The list of observations a variable assumes is called
data.
While gender is a variable, the observations, male or
female, are data.
Qualitative data are observations corresponding to a
qualitative variable.
Quantitative data are observations corresponding to a
quantitative variable.
•Discrete data are observations corresponding to
a discrete variable.
•Continuous data are observations
corresponding to a continuous variable.

21. Interval Ratio
A=50 A=5 feet
B=100 B=10 feet
Person B’s IQ is double the IQ Person B’s height is double the
of person A. height of person A.
Invalid Valid
0/20 spelling test (arbitrary) 0 gravity (floating)-absolute
IQ1=80, IQ2=100 WS1-40 kg, Ws2=40.1

22. Types of data
ID number Honor roll IQ score Height
Room Class Temperatur Length
number officers e
Religious Hardest to Spelling Weight
affiliation softest rock ability
Stock Top 10 Stress level Capacity
number billboard
list

23. Types of Measurement Scales
1. Nominal
2. Ordinal
3. Interval
4. Ratio
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24. Types of Measurement Scales
Nominal Scales - there must be distinct classes but these classes
have no quantitative properties. Therefore, no comparison can be made
in terms of one category being higher than the other.
For example - there are two classes for the variable gender -- males and
females. There are no quantitative properties for this variable or these
classes and, therefore, gender is a nominal variable.
Other Examples:
country of origin
biological sex (male or female)
animal or non-animal
married vs. single
24

25. Nominal Scale
• Sometimes numbers are used to designate category
membership
• Example:
Country of Origin
1 = United States 3 = Canada
2 = Mexico 4 = Other
• However, in this case, it is important to keep in
mind that the numbers do not have intrinsic meaning
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26. Types of Measurement Scales
Ordinal Scales - there are distinct classes but these
classes have a natural ordering or ranking. The
differences can be ordered on the basis of magnitude.
For example - final position of horses in a
thoroughbred race is an ordinal variable. The horses
finish first, second, third, fourth, and so on. The
difference between first and second is not necessarily
equivalent to the difference between second and third,
or between third and fourth.
26

27. Ordinal Scales
• Does not assume that the intervals between numbers are equal
Example:
finishing place in a race (first place, second place)
1st place 2nd place 3rd place 4th place
1 hour 2 hours 3 hours 4 hours 5 hours 6 hours 7 hours 8 hours
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28. Types of Measurement Scales (cont.)
Interval Scales - it is possible to compare differences in magnitude,
but importantly the zero point does not have a natural meaning. It
captures the properties of nominal and ordinal scales -- used by most
psychological tests.
Designates an equal-interval ordering - The distance between, for
example, a 1 and a 2 is the same as the distance between a 4 and a 5
Example - Celsius temperature is an interval variable. It is meaningful to
say that 25 degrees Celsius is 3 degrees hotter than 22 degrees Celsius,
and that 17 degrees Celsius is the same amount hotter (3 degrees) than
14 degrees Celsius. Notice, however, that 0 degrees Celsius does not
have a natural meaning. That is, 0 degrees Celsius does not mean the
absence of heat!
28

29. Types of Measurement Scales (cont.)
Ratio Scales - captures the properties of the other types of
scales, but also contains a true zero, which represents the
absence of the quality being measured.
For example - heart beats per minute has a very natural zero
point. Zero means no heart beats. Weight (in grams) is also a
ratio variable. Again, the zero value is meaningful, zero grams
means the absence of weight.
Example:
the number of intimate relationships a person has had
0 quite literally means none
a person who has had 4 relationships has had twice as
many as someone who has had 2 29

30. Types of Measurement Scales (cont.)
• Each of these scales have different properties (i.e.,
difference, magnitude, equal intervals, or a true zero point)
and allows for different interpretations.
• The scales are listed in hierarchical order. Nominal scales
have the fewest measurement properties and ratio having the
most properties including the properties of all the scales
beneath it on the hierarchy.
• The goal is to be able to identify the type of measurement
scale, and to understand proper use and interpretation of the
scale.
30

31. Types of scales
• Nominal scales--qualitative, not quantitative
distinction (no absolute zero, not equal intervals, not
magnitude)
• Ordinal scales--ranking individuals (magnitude, but
not equal intervals or absolute zero)
• Interval scales--scales that have magnitude and equal
intervals but not absolute zero
• Ratio scales--have magnitude, equal intervals, and
absolute zero (so can compute ratios)
31

32. Test Your Knowledge:
A professor is interested in the relationship between the number
of times students are absent from class and the letter grade that
students receive on the final exam. He records the number of
absences for each student, as well as the letter grade
(A,B,C,D,F) each student earns on the final exam. In this
example, what is the measurement scale for number of
absences?
a)Nominal b) Ordinal c) Interval d) Ratio
32

33. In the previous example, what is the measurement scale of
letter grade on the final exam?
a) Nominal b) Ordinal c) Interval d) Ratio
33

34. A researcher is interested in studying the effect of room
temperature in degrees Fahrenheit on productivity of automobile
assembly workers. She controls the temperature of the three
manufacturing facilities, such that employees in one facility work
in a room temperature of 60 degrees, employees in another
facility work in a room temperature of 65 degrees, and the last
group works in a room temperature of 70 degrees. The
productivity of each group is indicated by the number of
automobiles produced each day. In this example, what is the
measurement scale of room temperature?
a) Nominal b) Ordinal c) Interval d)Ratio
34

35. In the previous example, what is the measurement scale of
productivity?
a) Nominal b) Ordinal c) Interval d) Ratio
35

36. Select the highest appropriate level of measurement:
Bicycle models:
1= Road
2 = Touring
3 = Mountain
4 = Hybrid
5 = Comfort
6 = Cruiser
a) Nominal b) Ordinal c) Interval d) Ratio
36

37. Select the highest appropriate level of measurement:
Educational Level:
1 = Some High school
2 =High school Diploma
3 = Undergraduate Degree
4 = Masters Degree
5 = Doctorate Degree
a) Nominal b) Ordinal c) Interval d) Ratio
37

38. Select the highest appropriate level of measurement:
Number of questions asked during a class lecture
a) Nominal b) Ordinal c) Interval d) Ratio
38

39. Select the highest level of measurement:
Categories on a Likert-type scale measuring attitudes:
1 = Strongly Disagree
2 = Disagree
3 = Neutral
4 = Agree
5 = Strongly Agree
a) Nominal b) Ordinal c) Interval d) Ratio
39