quantitative techniques in research: statistic in one day

7/22/2019 Quantitative Techniques in Research: Statistic in One day

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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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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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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.

16


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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

17


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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!

18


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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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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?



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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?



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Select the highest appropriate level of measurement:

Bicycle models:

1= Road

2 = Touring

3 = Mountain

4 = Hybrid5 = Comfort

6 = Cruiser



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Educational Level:

1 = Some High school

2 =High school Diploma3 = Undergraduate Degree

4 = Masters Degree

5 = Doctorate Degree



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Number of questions asked during a class lecture



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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



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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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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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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

quantitative techniques in research: statistic in one day

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