Quantitative Techniques in
Research: Statistic in One day
Carlo Magno, PhD
Lasallian Institute for Development and Educational Research
Objectives
? Decide on what statistics to use given a set of data
? Use appropriate statistics in studies that will be
conducted (long term).
? Use statistica to conduct some statistical analysis
Outline
? Considerations in the selection of statistics to use.
? List of statistics
? Examples in using the statistics
? Read the article on CORI
Processing
? What was the aim of the study?
? What is the independent variable in the first study?
? What is the dependent variable it the first study?
? How many groups were used in the first study?
? How many levels of IV was used in the first study?
? How was the DV measured?
? How was the data analyzed? What statistics was
used?
? Why do you think this is the appropriate analysis?
? What is the difference between study 1 and 2?
Would the analysis change?
? When we analyzed the use of the statistics in the
study by Guthrie et al., what information did we
determine first?
What determines the use of statistics?
Variables Involved
•Independent
•Dependent
How many groups?
•Design
•Comparison
•Correlating
•Effect
Levels of
Measurement of the
variables (IV and DV)
Identify the IV, DV, and design
? Case 1: A study compared males and females. More
specifically, the study wanted to determine who is
higher in verbal ability between the two groups. A
test on verbal ability is given for the two groups and
the mean scores were compared.
? Case 2: The effect of Project-Based Learning (PBL)
on the grades of students was studied among
college students. It was hypothesized that students
will achieve more in the PBL as compared to a group
who received pure lecture. The grades of the
students were compared at the end of the term.
Identify the IV, DV, and design
? Case 3: Writing anxiety, writing metacognition, and
topic knowledge was used to predict students writing
proficiency. Students essays were scored which
served as indicator for their writing proficiency.
Scales were used to determine writing anxiety,
writing metacognition, and topic knowledge.
? Case 4: Neophyte and experienced principals,
coordinators, and directors were compared on their
degree of transformational leadership. A scale
measuring transformational leadership was
administered to the administrators across 200 school
in NCR.
Identify the IV, DV, and design
? Case 4: Filipino and Korean high school students
were compared on their oral proficiency (TOEFL),
vocabulary, and reading comprehension in English
(English test).
? Case 5: The effect of case study method on
students critical thinking was studied. The Watson
Glaser Critical Thinking Appraisal (WGCTA) was
administered as a pretest then the case study
method was implemented for the rest of the term.
Towards the end of the term, the WGCTA was
administered again.
? Case 6: The frequencies of SV agreement errors
were counted among high school students in the
public and private. The comparison was also done
among high and low ability students in these two
schools.
Levels of Measurement
A B C D
Type of school
Ethnicity
Gender
Socio-economic
status
Favorite movie
from like to least
like
Ranking of best
science fiction
stories
Perceived highest
to lowest
reputable
universities in
terms of research
English Ability
Math ability
Achievement in
Science
Motivation
Stress
Self-esteem
Self-efficacy
temperature
Height of children
Weight of first
graders
Length of travel
Width of the table
Brightness of light
Levels of Measurement
Nominal
Ordinal
Interval
Ratio
Levels of measurement
? Three important properties:
? Magnitude--property of “moreness”. Higher score
refers to more of something.
? Equal intervals--is the difference between any
two adjacent numbers referring to the same
amount of difference on the attribute?
? Absolute zero--does the scale have a zero point
that refers to having none of that attribute?
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
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
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.
16
Ordinal Scales
? Does not assume that the intervals between numbers are equal
Example:
finishing place in a race (first place, second place)
1 hour 2 hours 3 hours 4 hours 5 hours 6 hours 7 hours 8 hours
1st place 2nd place 3rd place 4th place
17
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!
18
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
19
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.
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)
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
In the previous example, what is the measurement scale of
letter grade on the final exam?
a) Nominal b) Ordinal c) Interval d) Ratio
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
In the previous example, what is the measurement scale of
productivity?
a) Nominal b) Ordinal c) Interval d) Ratio
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
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
Select the highest appropriate level of measurement:
Number of questions asked during a class lecture
a) Nominal b) Ordinal c) Interval d) Ratio
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
Identify the level of measurement
? Case 1: A study compared males and females on
their verbal ability. More specifically, the study
wanted to determine who is higher in verbal ability
between the two groups. A test on verbal ability is
given for the two groups and the mean scores were
compared.
? Case 2: The effect of Project-Based Learning (PBL)
on the grades of students was studied among
college students. It was hypothesized that students
will achieve more in the PBL as compared to a group
who received pure lecture. The grades of the
students were compared at the end of the term.
Identify the level of measurement
? Case 3: Writing anxiety, writing metacognition, and
topic knowledge was used to predict students writing
proficiency. Students essays were scored which
served as indicator for their writing proficiency.
Scales were used to determine writing anxiety,
writing metacognition, and topic knowledge.
? Case 4: Neophyte and experienced principals,
coordinators, and directors were compared on their
degree of transformational leadership. A scale
measuring transformational leadership was
administered to the administrators across 200 school
in NCR.
Identify the level of measurement
? Case 4: Filipino and Korean high school students
were compared on their oral proficiency (TOEFL),
vocabulary, and reading comprehension in English
(English test).
? Case 5: The effect of case study method on
students critical thinking was studied. The Watson
Glaser Critical Thinking Appraisal (WGCTA) was
administered as a pretest then the case study
method was implemented for the rest of the term.
Towards the end of the term, the WGCTA was
administered again.
? Case 6: The frequencies of SV agreement errors in
an essay were counted among high school students
in the public and private. The comparison was also
done among high and low ability students in these
two schools.
Statistics Used
Parametric Non-Parametric
•Enables researchers to make
assumptions about the population
•Large sample size is requires (N>30)
•Used for interval and ratio scales
•Difficult to make assumptions about
the population
•Large sample size is not a
requirement
•Used for nominal and ordinal scales
Statistics Used
Design Parametric Non-Parametric
One sample
-the mean of one sample is compared
with a standard
No. of comparisons:
nominal
DV: interval/ratio
One sample,
categories are
nominal/ordinal
One sample repeated measures
(dependent groups)
-One sample is studies but more
measured twice (2 set of data)
- e. g. pre and post test design
No. of comparisons:
nominal
DV: interval/ratio
No. of comparisons:
nominal
DV: nominal/ordinal
Two independent groups
-studying two distinct samples/groups
Groups/IV: nominal
DV: interval/ratio
Groups/IV: nominal
DV: nominal/ordinal
Comparing multiple groups
(independent or dependent groups)
Groups/IV: nominal
DV: interval/ratio
Groups/IV: nominal
DV: nominal
Relating one variable to another
Statistics Used
Design Parametric Non-Parametric
One sample
-the mean of one sample is
compared with a standard
z-test
t-test
One-way chi-square
Kolmogorov smirnov
One sample repeated measures
(dependent groups)
-One sample is studies but more
measured twice (2 set of data)
- e. g. pre and post test design
t-test for 2 dependent
samples
McNemar change test
Wilcoxon signed ranks
test
Two independent groups
-studying two distinct
samples/groups
t-test for 2
independent samples
Two-way chi-square
Mann Whitney U test
Comparing multiple groups
(independent or dependent groups)
Analysis of Variance
(ANOVA)
1 IV, 1 DV: one way
ANOVA
2 IV, 1 DV: two way
ANOVA
1 more IV, 2 or more
DV: MANOVA
Kruskal wallis test
Relating one variable to another Pearson r Spearman rho
Phi coefficient
Case 1
? It was hypothesized in a study that students ability in
school is related to procrastination. College students
were tested using the OTIS Lenon School Ablity Test
(OLSAT) and the perfectionism scale by Frost was
administered to the same group.
? How many variables are studied?
? What are the levels of measurement of the
variables?
? What is the purpose of the study?
? What statistics will be used?
Data
OLSAT (X) Procrastination (Y)
100 99
95 98
90 94
85 87
82 84
80 81
75 78
70 73
65 68
50 60
Regression Line between OLSAT and
perfectionism
Scatterplot: X vs. Y
Y = 14.379 + .85633 * X
Correlation: r = .98966
40 50 60 70 80 90 100 110
X
55
60
65
70
75
80
85
90
95
100
105
Y
95% confidence
Linear Regression
? There is a straight line relationship between
variables X and Y
? When X increases, Y also increases-positive
relationship
? When X increases, Y decreases or vice versa –
negative relationship
Correlational Techniques
? Pearson Product-Moment correlation – (r) used for
interval/ratio sets of variables
? Spearman Rank-order correlation – two sets of data
are ordinal
? Phi coefficient – each of the variables is a
dichotomy
OLSAT Perfectionism
100 35
95 40
90 45
85 50
75 55
70 60
65 64
60 70
55 76
50 80
Relationship between Laziness and
Perseverance
Scatterplot: Y vs. X
X = 139.94 - 1.138 * Y
Correlation: r = -.9959
30 40 50 60 70 80 90
Y
40
50
60
70
80
90
100
110
X
95% confidence
Magnitude of the Relationship
? Positive relationship – as one variable increases
the other variable also increases
? Ex. academic grades and intelligence
? Negative relationship – as one variable increases,
the other decreases or vice versa
? Ex. procrastination and motivation
? Absence of relationship between variables –
denoted by .00
Show computation in statistica
Strength of Relationship
? A correlation coefficient is computed for a
bivariate distribution using a statistical formula
Correlation Coefficient Value Interpretation
0.80 – 1.00 Very strong relationship
0.6 – 0.79 Strong relationship
0.40 – 0.59 Substantial/marked relationship
0.2 – 0.39 Low relationship
0.00 – 0.19 Negligible relationship
Variance
? How much of Y’s is explained/accounted for by X
? Proportion explained
? Square of the correlation coefficient value
Case 2: Spearman rho
? Students ranked their degree of importance on
poverty alleviation poverty and health policy.
Poverty alleviation policy Health policy
14 13
11 12
10 9
10 8
14 10
13 14
Case 3: Phi coefficient
High Low
Own choice 30 20
Others choice 10 40
Teaching Satisfaction
Becoming
a teacher
Case 4: One sample t-test
? 7 Filipino college students have taken the Test for
English as a Second Language (TESL). The
researcher wanted to determine if their scores are
far from the standard norm among speakers of ESL.
The standard norm in the manual is 40.5 with a
standard error of 4.54.
42
45
46
45
43
46
47
Case 5: one way chi-square
Errors found F Expected
frequency
Poor sentence
construction
26 21.11
Wrong choice of
word
32 21.11
Faulty parallelism 12 21.11
Wrong case 14 21.11
Wrong
punctuation
46 21.11
Fragment 8 21.11
Wrong article 16 21.11
Run-on sentence 27 21.11
Wrong verb 9 21.11
Total=190
Case 6: Kolmogorov smirnov
f
o
f
e
Asst. Instructor
25
15.6
Instructor
10
15.6
Ass. Prof
31
15.6
Prof
7
15.6
Full Prof 5 15.6
ft/? f
o
= 78
Case 7: t-test for 2 dependent samples
? A study investigated whether the effect of problem-
based teaching in mathematics would develop
students deep approach to learning. The students
were first given a pre test using the learning process
questionnaire (LPQ) that measures deep approach
to learning. The students are exposed to different
problems in mathematics before learning concepts
and algorithms. After the instruction, the LPQ was
again administered to the same 10 students.
Case 7: t-test for 2 dependent samples
LPQ pre test LPQ post test
24 2
28 30
32 37
18 22
24 29
36 40
40 38
37 41
24 29
20 28
Case 8: Wilcoxon signed ranks test
? One group of pre-school students were asked to
rank a picture by giving the age of a very simple
person in a picture without make-up. On a second
occasion, the same person in the first picture was
again shown but with elaborate clothes and with
make-up. Is there a difference in the 2 sets of
rankings?
Case 8: Wilcoxon signed ranks test
Student No. 1
st
Pic 2
nd
Pic
1 12 12
2 14 16
3 15 14
4 12 11
5 16 14
6 15 18
7 13 16
8 10 11
Case 9: McNemar Change test
? An experiment was conducted to determine whether
hypnosis can be a clinical intervention to increase
students test performance. A test was given and
students who passed and failed were identified. The
students have undergone hypnosis and after session
they were again given an identical test. The students
who passed and failed were again identified.
Before hypnosis
Pass Fail
After
hypnosis
Fail 7 10
Pass 15 20
Case 10: t-test for 2 independent samples
? The effect of picture-taste association on memory
recall was investigated among 30 volunteer college
students. The 15 participants in the experiment
group looked at 20 pictures matched with the food
that they have to taste. The other 15 participants in
the control group just looked at the pictures. After
the procedure, both groups were tested in their
memory where they have to enumerate in order the
labels of the pictures they saw.
Case 10: t-test for 2 independent samples
Experimental group Control group
9 4
14 9
11 3
9 6
12 4
13 2
14 5
9 5
11 4
13 5
11 6
13 6
12 4
14 7
15 8
?x
1
= 180 ?x
2
= 78
1
= 12
2
= 5.2
Case 11: Mann-Whitney U test
? In the study, 8 single individuals and 7 married
individuals were asked to rank their life satisfaction
using a ranking scale. Test whether they differ in
their rankings.
Single Married
40 10
37 75
35 40
37 32
51 25
38 62
42 5
49
Case 12: Chi-square
? A survey was conducted among 29 prisoners in
manila city jail. They were asked crimes that they
committed and their educational attainment through
a checklist. The following data was tabulated
Crimes
Committed
Educational Attainment
Elementary HS College Total
Murder 3 7 1 11
Homicide 2 3 6 11
Robbery 1 2 5 8
Total 6 12 12 30
Case 13: One-Way ANOVA
? In an experiment, the effect of nonbehavioral
intervention techniques was investigated on the
computational ability of fourth year high school
students. The non-behavioral intervention
techniques has three levels: bibliotherapy, small
group interaction, and games. These techniques
were used as a teaching strategy in a lesson in a
math class for three sections. Each of the strategy
was used for each section. One section did not
receive any strategy which served as the control
group. After undergoing the strategy, the students
were tested where they answered a series of
computation items.
Case 13: One-Way ANOVA
Control bibliotherap
y
Small group Games
8 14 19 15
9 13 18 15
6 12 19 14
7 15 19 15
2 15 17 13
4 14 18 14
4 13 18 13
Self-efficacy
Achievement
Effect of Achievement and Type of school on self-efficacy
Low Achievers High Achievers
Type of school
Public
school
Private
School
Case 14: Two way ANOVA
Case 14: Two way ANOVA
low achiever high achiever
Public
10 15
9 16
5 17
6 15
5 16
Private
15 19
14 20
14 19
13 18
15 18
Case 15: MANOVA
? Public and Private schools were compared on their
self-monitoring and goal-setting
Self-monitoring goal-setting
Public 10 9
10 8
9 7
7 7
8 5
7 5
6 4
Private 18 17
19 19
18 19
17 18
17 18
18 17
18 18
Case 16: Multiple regression
? Goal-setting, self-evaluation, seeking assistance,
and environmental structuring were used to predict
learning responsibility.
Workshop
? Work with a team
? Make an outline of a study that will make use of
quantitative analysis
? State the purpose of the study (research question)
? Possible hypothesis (if there is)
? Framework that supports the study
? Research Design
? Participants
? Instruments
? Procedure
? Data Analysis
doc_478314551.pptx
Research: Statistic in One day
Carlo Magno, PhD
Lasallian Institute for Development and Educational Research
Objectives
? Decide on what statistics to use given a set of data
? Use appropriate statistics in studies that will be
conducted (long term).
? Use statistica to conduct some statistical analysis
Outline
? Considerations in the selection of statistics to use.
? List of statistics
? Examples in using the statistics
? Read the article on CORI
Processing
? What was the aim of the study?
? What is the independent variable in the first study?
? What is the dependent variable it the first study?
? How many groups were used in the first study?
? How many levels of IV was used in the first study?
? How was the DV measured?
? How was the data analyzed? What statistics was
used?
? Why do you think this is the appropriate analysis?
? What is the difference between study 1 and 2?
Would the analysis change?
? When we analyzed the use of the statistics in the
study by Guthrie et al., what information did we
determine first?
What determines the use of statistics?
Variables Involved
•Independent
•Dependent
How many groups?
•Design
•Comparison
•Correlating
•Effect
Levels of
Measurement of the
variables (IV and DV)
Identify the IV, DV, and design
? Case 1: A study compared males and females. More
specifically, the study wanted to determine who is
higher in verbal ability between the two groups. A
test on verbal ability is given for the two groups and
the mean scores were compared.
? Case 2: The effect of Project-Based Learning (PBL)
on the grades of students was studied among
college students. It was hypothesized that students
will achieve more in the PBL as compared to a group
who received pure lecture. The grades of the
students were compared at the end of the term.
Identify the IV, DV, and design
? Case 3: Writing anxiety, writing metacognition, and
topic knowledge was used to predict students writing
proficiency. Students essays were scored which
served as indicator for their writing proficiency.
Scales were used to determine writing anxiety,
writing metacognition, and topic knowledge.
? Case 4: Neophyte and experienced principals,
coordinators, and directors were compared on their
degree of transformational leadership. A scale
measuring transformational leadership was
administered to the administrators across 200 school
in NCR.
Identify the IV, DV, and design
? Case 4: Filipino and Korean high school students
were compared on their oral proficiency (TOEFL),
vocabulary, and reading comprehension in English
(English test).
? Case 5: The effect of case study method on
students critical thinking was studied. The Watson
Glaser Critical Thinking Appraisal (WGCTA) was
administered as a pretest then the case study
method was implemented for the rest of the term.
Towards the end of the term, the WGCTA was
administered again.
? Case 6: The frequencies of SV agreement errors
were counted among high school students in the
public and private. The comparison was also done
among high and low ability students in these two
schools.
Levels of Measurement
A B C D
Type of school
Ethnicity
Gender
Socio-economic
status
Favorite movie
from like to least
like
Ranking of best
science fiction
stories
Perceived highest
to lowest
reputable
universities in
terms of research
English Ability
Math ability
Achievement in
Science
Motivation
Stress
Self-esteem
Self-efficacy
temperature
Height of children
Weight of first
graders
Length of travel
Width of the table
Brightness of light
Levels of Measurement
Nominal
Ordinal
Interval
Ratio
Levels of measurement
? Three important properties:
? Magnitude--property of “moreness”. Higher score
refers to more of something.
? Equal intervals--is the difference between any
two adjacent numbers referring to the same
amount of difference on the attribute?
? Absolute zero--does the scale have a zero point
that refers to having none of that attribute?
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
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
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.
16
Ordinal Scales
? Does not assume that the intervals between numbers are equal
Example:
finishing place in a race (first place, second place)
1 hour 2 hours 3 hours 4 hours 5 hours 6 hours 7 hours 8 hours
1st place 2nd place 3rd place 4th place
17
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!
18
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
19
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.
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)
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
In the previous example, what is the measurement scale of
letter grade on the final exam?
a) Nominal b) Ordinal c) Interval d) Ratio
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
In the previous example, what is the measurement scale of
productivity?
a) Nominal b) Ordinal c) Interval d) Ratio
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
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
Select the highest appropriate level of measurement:
Number of questions asked during a class lecture
a) Nominal b) Ordinal c) Interval d) Ratio
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
Identify the level of measurement
? Case 1: A study compared males and females on
their verbal ability. More specifically, the study
wanted to determine who is higher in verbal ability
between the two groups. A test on verbal ability is
given for the two groups and the mean scores were
compared.
? Case 2: The effect of Project-Based Learning (PBL)
on the grades of students was studied among
college students. It was hypothesized that students
will achieve more in the PBL as compared to a group
who received pure lecture. The grades of the
students were compared at the end of the term.
Identify the level of measurement
? Case 3: Writing anxiety, writing metacognition, and
topic knowledge was used to predict students writing
proficiency. Students essays were scored which
served as indicator for their writing proficiency.
Scales were used to determine writing anxiety,
writing metacognition, and topic knowledge.
? Case 4: Neophyte and experienced principals,
coordinators, and directors were compared on their
degree of transformational leadership. A scale
measuring transformational leadership was
administered to the administrators across 200 school
in NCR.
Identify the level of measurement
? Case 4: Filipino and Korean high school students
were compared on their oral proficiency (TOEFL),
vocabulary, and reading comprehension in English
(English test).
? Case 5: The effect of case study method on
students critical thinking was studied. The Watson
Glaser Critical Thinking Appraisal (WGCTA) was
administered as a pretest then the case study
method was implemented for the rest of the term.
Towards the end of the term, the WGCTA was
administered again.
? Case 6: The frequencies of SV agreement errors in
an essay were counted among high school students
in the public and private. The comparison was also
done among high and low ability students in these
two schools.
Statistics Used
Parametric Non-Parametric
•Enables researchers to make
assumptions about the population
•Large sample size is requires (N>30)
•Used for interval and ratio scales
•Difficult to make assumptions about
the population
•Large sample size is not a
requirement
•Used for nominal and ordinal scales
Statistics Used
Design Parametric Non-Parametric
One sample
-the mean of one sample is compared
with a standard
No. of comparisons:
nominal
DV: interval/ratio
One sample,
categories are
nominal/ordinal
One sample repeated measures
(dependent groups)
-One sample is studies but more
measured twice (2 set of data)
- e. g. pre and post test design
No. of comparisons:
nominal
DV: interval/ratio
No. of comparisons:
nominal
DV: nominal/ordinal
Two independent groups
-studying two distinct samples/groups
Groups/IV: nominal
DV: interval/ratio
Groups/IV: nominal
DV: nominal/ordinal
Comparing multiple groups
(independent or dependent groups)
Groups/IV: nominal
DV: interval/ratio
Groups/IV: nominal
DV: nominal
Relating one variable to another
Statistics Used
Design Parametric Non-Parametric
One sample
-the mean of one sample is
compared with a standard
z-test
t-test
One-way chi-square
Kolmogorov smirnov
One sample repeated measures
(dependent groups)
-One sample is studies but more
measured twice (2 set of data)
- e. g. pre and post test design
t-test for 2 dependent
samples
McNemar change test
Wilcoxon signed ranks
test
Two independent groups
-studying two distinct
samples/groups
t-test for 2
independent samples
Two-way chi-square
Mann Whitney U test
Comparing multiple groups
(independent or dependent groups)
Analysis of Variance
(ANOVA)
1 IV, 1 DV: one way
ANOVA
2 IV, 1 DV: two way
ANOVA
1 more IV, 2 or more
DV: MANOVA
Kruskal wallis test
Relating one variable to another Pearson r Spearman rho
Phi coefficient
Case 1
? It was hypothesized in a study that students ability in
school is related to procrastination. College students
were tested using the OTIS Lenon School Ablity Test
(OLSAT) and the perfectionism scale by Frost was
administered to the same group.
? How many variables are studied?
? What are the levels of measurement of the
variables?
? What is the purpose of the study?
? What statistics will be used?
Data
OLSAT (X) Procrastination (Y)
100 99
95 98
90 94
85 87
82 84
80 81
75 78
70 73
65 68
50 60
Regression Line between OLSAT and
perfectionism
Scatterplot: X vs. Y
Y = 14.379 + .85633 * X
Correlation: r = .98966
40 50 60 70 80 90 100 110
X
55
60
65
70
75
80
85
90
95
100
105
Y
95% confidence
Linear Regression
? There is a straight line relationship between
variables X and Y
? When X increases, Y also increases-positive
relationship
? When X increases, Y decreases or vice versa –
negative relationship
Correlational Techniques
? Pearson Product-Moment correlation – (r) used for
interval/ratio sets of variables
? Spearman Rank-order correlation – two sets of data
are ordinal
? Phi coefficient – each of the variables is a
dichotomy
OLSAT Perfectionism
100 35
95 40
90 45
85 50
75 55
70 60
65 64
60 70
55 76
50 80
Relationship between Laziness and
Perseverance
Scatterplot: Y vs. X
X = 139.94 - 1.138 * Y
Correlation: r = -.9959
30 40 50 60 70 80 90
Y
40
50
60
70
80
90
100
110
X
95% confidence
Magnitude of the Relationship
? Positive relationship – as one variable increases
the other variable also increases
? Ex. academic grades and intelligence
? Negative relationship – as one variable increases,
the other decreases or vice versa
? Ex. procrastination and motivation
? Absence of relationship between variables –
denoted by .00
Show computation in statistica
Strength of Relationship
? A correlation coefficient is computed for a
bivariate distribution using a statistical formula
Correlation Coefficient Value Interpretation
0.80 – 1.00 Very strong relationship
0.6 – 0.79 Strong relationship
0.40 – 0.59 Substantial/marked relationship
0.2 – 0.39 Low relationship
0.00 – 0.19 Negligible relationship
Variance
? How much of Y’s is explained/accounted for by X
? Proportion explained
? Square of the correlation coefficient value
Case 2: Spearman rho
? Students ranked their degree of importance on
poverty alleviation poverty and health policy.
Poverty alleviation policy Health policy
14 13
11 12
10 9
10 8
14 10
13 14
Case 3: Phi coefficient
High Low
Own choice 30 20
Others choice 10 40
Teaching Satisfaction
Becoming
a teacher
Case 4: One sample t-test
? 7 Filipino college students have taken the Test for
English as a Second Language (TESL). The
researcher wanted to determine if their scores are
far from the standard norm among speakers of ESL.
The standard norm in the manual is 40.5 with a
standard error of 4.54.
42
45
46
45
43
46
47
Case 5: one way chi-square
Errors found F Expected
frequency
Poor sentence
construction
26 21.11
Wrong choice of
word
32 21.11
Faulty parallelism 12 21.11
Wrong case 14 21.11
Wrong
punctuation
46 21.11
Fragment 8 21.11
Wrong article 16 21.11
Run-on sentence 27 21.11
Wrong verb 9 21.11
Total=190
Case 6: Kolmogorov smirnov
f
o
f
e
Asst. Instructor
25
15.6
Instructor
10
15.6
Ass. Prof
31
15.6
Prof
7
15.6
Full Prof 5 15.6
ft/? f
o
= 78
Case 7: t-test for 2 dependent samples
? A study investigated whether the effect of problem-
based teaching in mathematics would develop
students deep approach to learning. The students
were first given a pre test using the learning process
questionnaire (LPQ) that measures deep approach
to learning. The students are exposed to different
problems in mathematics before learning concepts
and algorithms. After the instruction, the LPQ was
again administered to the same 10 students.
Case 7: t-test for 2 dependent samples
LPQ pre test LPQ post test
24 2
28 30
32 37
18 22
24 29
36 40
40 38
37 41
24 29
20 28
Case 8: Wilcoxon signed ranks test
? One group of pre-school students were asked to
rank a picture by giving the age of a very simple
person in a picture without make-up. On a second
occasion, the same person in the first picture was
again shown but with elaborate clothes and with
make-up. Is there a difference in the 2 sets of
rankings?
Case 8: Wilcoxon signed ranks test
Student No. 1
st
Pic 2
nd
Pic
1 12 12
2 14 16
3 15 14
4 12 11
5 16 14
6 15 18
7 13 16
8 10 11
Case 9: McNemar Change test
? An experiment was conducted to determine whether
hypnosis can be a clinical intervention to increase
students test performance. A test was given and
students who passed and failed were identified. The
students have undergone hypnosis and after session
they were again given an identical test. The students
who passed and failed were again identified.
Before hypnosis
Pass Fail
After
hypnosis
Fail 7 10
Pass 15 20
Case 10: t-test for 2 independent samples
? The effect of picture-taste association on memory
recall was investigated among 30 volunteer college
students. The 15 participants in the experiment
group looked at 20 pictures matched with the food
that they have to taste. The other 15 participants in
the control group just looked at the pictures. After
the procedure, both groups were tested in their
memory where they have to enumerate in order the
labels of the pictures they saw.
Case 10: t-test for 2 independent samples
Experimental group Control group
9 4
14 9
11 3
9 6
12 4
13 2
14 5
9 5
11 4
13 5
11 6
13 6
12 4
14 7
15 8
?x
1
= 180 ?x
2
= 78
1
= 12
2
= 5.2
Case 11: Mann-Whitney U test
? In the study, 8 single individuals and 7 married
individuals were asked to rank their life satisfaction
using a ranking scale. Test whether they differ in
their rankings.
Single Married
40 10
37 75
35 40
37 32
51 25
38 62
42 5
49
Case 12: Chi-square
? A survey was conducted among 29 prisoners in
manila city jail. They were asked crimes that they
committed and their educational attainment through
a checklist. The following data was tabulated
Crimes
Committed
Educational Attainment
Elementary HS College Total
Murder 3 7 1 11
Homicide 2 3 6 11
Robbery 1 2 5 8
Total 6 12 12 30
Case 13: One-Way ANOVA
? In an experiment, the effect of nonbehavioral
intervention techniques was investigated on the
computational ability of fourth year high school
students. The non-behavioral intervention
techniques has three levels: bibliotherapy, small
group interaction, and games. These techniques
were used as a teaching strategy in a lesson in a
math class for three sections. Each of the strategy
was used for each section. One section did not
receive any strategy which served as the control
group. After undergoing the strategy, the students
were tested where they answered a series of
computation items.
Case 13: One-Way ANOVA
Control bibliotherap
y
Small group Games
8 14 19 15
9 13 18 15
6 12 19 14
7 15 19 15
2 15 17 13
4 14 18 14
4 13 18 13
Self-efficacy
Achievement
Effect of Achievement and Type of school on self-efficacy
Low Achievers High Achievers
Type of school
Public
school
Private
School
Case 14: Two way ANOVA
Case 14: Two way ANOVA
low achiever high achiever
Public
10 15
9 16
5 17
6 15
5 16
Private
15 19
14 20
14 19
13 18
15 18
Case 15: MANOVA
? Public and Private schools were compared on their
self-monitoring and goal-setting
Self-monitoring goal-setting
Public 10 9
10 8
9 7
7 7
8 5
7 5
6 4
Private 18 17
19 19
18 19
17 18
17 18
18 17
18 18
Case 16: Multiple regression
? Goal-setting, self-evaluation, seeking assistance,
and environmental structuring were used to predict
learning responsibility.
Workshop
? Work with a team
? Make an outline of a study that will make use of
quantitative analysis
? State the purpose of the study (research question)
? Possible hypothesis (if there is)
? Framework that supports the study
? Research Design
? Participants
? Instruments
? Procedure
? Data Analysis
doc_478314551.pptx