quantitative techniques in research: statistic in one day
TRANSCRIPT
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Quantitative Techniques in
Research: Statistic in One day
Carlo Magno, PhD
Lasallian Institute for Development and Educational Research
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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
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Outline
Considerations in the selection of statistics to use. List of statistics
Examples in using the statistics
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Read the article on CORI
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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?
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When we analyzed the use of the statistics in thestudy by Guthrie et al., what information did we
determine first?
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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)
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Identify the IV, DV, and design
Case 1: A study compared males and females. Morespecifically, 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 groupwho received pure lecture. The grades of the
students were compared at the end of the term.
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Identify the IV, DV, and design
Case 3: Writing anxiety, writing metacognition, andtopic 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 scalemeasuring transformational leadership was
administered to the administrators across 200 school
in NCR.
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Identify the IV, DV, and design
Case 4: Filipino and Korean high school studentswere 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 WatsonGlaser Critical Thinking Appraisal (WGCTA) wasadministered as a pretest then the case studymethod was implemented for the rest of the term.
Towards the end of the term, the WGCTA wasadministered again.
Case 6: The frequencies of SV agreement errorswere counted among high school students in thepublic and private. The comparison was also doneamong high and low ability students in these two
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Levels of Measurement
A B C DType 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
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Levels of Measurement
Nominal
Ordinal
Interval
Ratio
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Levels of measurement
Three important properties:
Magnitude--property of moreness. Higher scorerefers to more of something.
Equal intervals--is the difference between anytwo adjacent numbers referring to the sameamount of difference on the attribute?
Absolute zero--does the scale have a zero point
that refers to having none of that attribute?
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Types of Measurement Scales
Nominal Scales - there must be distinct classes but these classeshave no quantitative properties. Therefore, no comparison can be madein 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
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Nominal Scale Sometimes numbers are used to designate category
membership
Example:Country of Origin
1 = United States 3 = Canada2 = 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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Types of Measurement Scales
Ordinal Scales - there are distinct classes but theseclasses have a natural ordering or ranking. Thedifferences can be ordered on the basis of magnitude.
For example - final position of horses in athoroughbred 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.
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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
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Types of Measurement Scales (cont.)
Interval Scales - it is possible to compare differences in magnitude,but importantly the zero point does nothave a natural meaning. Itcaptures 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 tosay 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 anatural meaning. That is, 0 degrees Celsius does not mean the absenceof heat!
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Types of Measurement Scales (cont.)
Ratio Scales - captures the properties of the other types ofscales, but also contains a true zero, which represents theabsence 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 aratio variable. Again, the zero value is meaningful, zero gramsmeans 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 219
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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 scaleshave 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.
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Types of scales
Nominal scales--qualitative, not quantitativedistinction (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)
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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
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In the previous example, what is the measurement scale of
letter grade on the final exam?
a) Nominal b) Ordinal c) Interval d) Ratio
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A researcher is interested in studying the effect of room
temperature in degrees Fahrenheit on productivity of automobileassembly 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 lastgroup 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
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In the previous example, what is the measurement scale of
productivity?
a) Nominal b) Ordinal c) Interval d) Ratio
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Select the highest appropriate level of measurement:
Bicycle models:
1= Road
2 = Touring
3 = Mountain
4 = Hybrid5 = Comfort
6 = Cruiser
a) Nominal b) Ordinal c) Interval d) Ratio
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Select the highest appropriate level of measurement:
Educational Level:
1 = Some High school
2 =High school Diploma3 = Undergraduate Degree
4 = Masters Degree
5 = Doctorate Degree
a) Nominal b) Ordinal c) Interval d) Ratio
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Select the highest appropriate level of measurement:
Number of questions asked during a class lecture
a) Nominal b) Ordinal c) Interval d) Ratio
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Select the highest level of measurement:
Categories on a Likert-type scale measuring attitudes:
1 = Strongly Disagree
2 = Disagree
3 = Neutral4 = Agree
5 = Strongly Agree
a) Nominal b) Ordinal c) Interval d) Ratio
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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 studentswill 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.
-
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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 scalemeasuring transformational leadership was
administered to the administrators across 200 school
in NCR.
-
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Identify the level of measurement
Case 4: Filipino and Korean high school studentswere 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 WatsonGlaser Critical Thinking Appraisal (WGCTA) wasadministered as a pretest then the case studymethod was implemented for the rest of the term.
Towards the end of the term, the WGCTA wasadministered again.
Case 6: The frequencies of SV agreement errors inan essay were counted among high school studentsin the public and private. The comparison was alsodone among high and low ability students in these
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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
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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: nominalDV: interval/ratio
Groups/IV: nominalDV: nominal
Relating one variable to another
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Statistics UsedDesign Parametric Non-Parametric
One sample
-the mean of one sample iscompared 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
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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?
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Data
OLSAT (X) Procrastination (Y)100 99
95 98
90 94
85 87
82 84
80 81
75 7870 73
65 68
50 60
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Regression Line between OLSAT and
perfectionismScatterplot: X vs. Y
Y = 14.379 + .85633 * XCorrelation: 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
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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 versanegative relationship
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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 adichotomy
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OLSAT Perfectionism
100 35
95 40
90 45
85 50
75 55
70 60
65 64
60 70
55 76
50 80
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Relationship between Laziness and
Perseverance Scatterplot: Y vs. XX = 139.94 - 1.138 * YCorrelation: r = -.9959
30 40 50 60 70 80 90
Y
40
50
60
70
80
90
100
110
X
95% confidence
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Magnitude of the Relationship
Positive relationship as one variable increasesthe 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 variablesdenoted by .00
Show computation in statistica
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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
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Variance
How much of Ys is explained/accounted for by X
Proportion explained
Square of the correlation coefficient value
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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 1210 9
10 8
14 10
13 14
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Case 3: Phi coefficient
High Low
Own choice 30 20
Others choice 10 40
Teaching Satisfaction
Becoming
a teacher
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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
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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
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Case 6: Kolmogorov smirnov
fo feAsst. Instructor
25 15.6
Instructor
10 15.6Ass. Prof
31 15.6
Prof
7 15.6
Full Prof 5 15.6ft/ fo = 78
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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.
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Case 7: t-test for 2 dependent samples
LPQ pre test LPQ post test
24 2
28 30
32 37
18 2224 29
36 40
40 38
37 4124 29
20 28
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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?
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Case 8: Wilcoxon signed ranks test
Student No. 1st Pic 2nd Pic
1 12 12
2 14 16
3 15 144 12 11
5 16 14
6 15 18
7 13 16
8 10 11
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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
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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.
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Case 10: t-test for 2 independent samples
Experimental group Control group
9 414 9
11 3
9 6
12 4
13 214 5
9 5
11 4
13 5
11 6
13 6
12 4
14 7
15 8
x1 = 180 x2= 78
1 = 12 2 = 5.2
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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 1037 75
35 40
37 32
51 25
38 62
42 5
49
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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
CrimesCommitted
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
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Case 13: One-Way ANOVA
In an experiment, the effect of nonbehavioral
intervention techniques was investigated on thecomputational ability of fourth year high schoolstudents. The non-behavioral interventiontechniques has three levels: bibliotherapy, small
group interaction, and games. These techniqueswere used as a teaching strategy in a lesson in amath class for three sections. Each of the strategywas used for each section. One section did notreceive any strategy which served as the control
group. After undergoing the strategy, the studentswere tested where they answered a series ofcomputation items.
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Case 13: One-Way ANOVA
Control bibliotherapy
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
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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
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Case 14: Two way ANOVA
low achiever high achiever
Public
10 15
9 16
5 176 15
5 16
Private
15 19
14 20
14 19
13 18
15 18
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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 77 7
8 5
7 5
6 4
Private 18 17
19 19
18 19
17 18
17 18
18 17
18 18
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Case 16: Multiple regression
Goal-setting, self-evaluation, seeking assistance,
and environmental structuring were used to predict
learning responsibility.
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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