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Handout (to be improved whilst sessions in progress)

Statistics for Research

The Graduate Program of English Studies

Sanata Dharma University

Feb 2014


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PREFACE

Why learn statistics for research in English language

studies? What for?

You are going to become an expert in English language

studies. You will become able to manage research to solve English

studies problems scientifically. Since all research involves logic and

observation, their coherence (validity) remains crucial for every

research project. Statistical concepts help clarify this, regardless

whether your research is with or without statistics

What do you compose this learning portfolio for?

To build your own perspectives of statistics for research, toenable you to describe and interpret a research validity, and improve

it.

What do you do?

You describe every issue briefly, state what it is for (the

goal), how to achieve the goal, and what is needed to process to

achieve the goal. All needs cross-checking with recent literature.

Which is most viable?

It is not the idea that every one of you shall elaborate every

issue, but only the most viable ones, given the allocated time and

your initial knowledge. The idea is that we make the most of the

time and other facilities at our disposal. We will at least spend

ample time on Part1, Part 2 Chapter IX: Validation of ResearchDiscovery, and electronic data processing (group project).These

having been done, it is reasonable to expect that you will be able tovalidate your own research.


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TABLE OF CONTENTS

PREFACE

TABLE OF CONTENTSPart 1 Research and Statistics

I. RESEARCHA. MEANING

B. FUNCTIONS AND TYPES

II. STATISTICS

A. MEANING

B. FUNCTIONS AND TYPESC. CONCEPT, OBSERVATION, AND EXPERIENCE

D. OBJECT, ATTRIBUTE, PHENOMENON, VARIABLE

E. MEASUREMENTF. DATA

G. INTERPRETATION

Part 2 Statistical Techniques

III. DESCRIPTIVE STATISTICS

A. MEANING

B. DATAB. MEASURES OF CENTRAL TENDENCY

C. MEASURES OF DISPERSION

D. CORRELATION

IV. INFERENTIAL STATISTICS

A. PARAMETRIC


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B. NON-PARAMETRIC

V. STATISTICS FOR SURVEY RESEARCH

A. SIMPLE CORRELATION

B. MULTIPLE CORRELATION

VI. STATISTICS FOR EXPERIMENTAL RESEARCH

A. SIMPLE COMPARISON

B. MULTIPLE COMPARISON

VII. STATISTICS FOR OTHER RESEARCH

A. EXPLORATORY RESEARCHB. RESEARCH AND DEVELOPMENTC. CONTENT ANALYSIS

VIII. SELECTION OF A STATISTICAL TECHNIQUE

A. KNOWLEDGE PRE-REQUISITES

B. PROCEDURE

IX. VALIDATION OF RESEARCH DISCOVERYA. VALIDITY

B. HYPOTHESIS FORMATION

C. EMPIRICAL VERIFICATION (HYPOTHESIS TESTING)

D. INTERPRETATION (OF DATA PROCESSING RESULTS)


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Part 1 Research and Statistics

I. RESEARCH

A. MEANING

A systematic investigation to discover the truth, the

scientific truth

Systematic investigation: think, plan, do

The scientific truth: logical and empirical/experiential

Logical truth: deductive, inductive

Empirical: about what you see using sensory organsConfirmatory (quantitative): deductive-inductive

Exploratory (qualitative): inductive-deductive

Experiential: see sensuously (statistically irrelevant)


EDUCATIONSystematic learning to improve life quality, empirical and

experiential

Empirical life-quality becoming more efficient and

effective (e.g. learners higher speaking ability, teachers

less preparation time, texts becoming more motivating)

Experiential life quality (statistically irrelevant)::

promotion of equity leading to self-actualization, personal

and social (= becoming excellent in ones own right)

C. ENGLISH

ELF, WE, IE, GE rather than EFL, ESOL, ESL

Focus: regional English; how to deploy it rather than

master it


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English education research is necessarily pragmatic. It is

not only to discover the scientific truth, but to imply a

contribution to life-quality improvement, empiric orexperiential.

ENGLISH EDUCATION RESEARCH VALIDITYValidity = coherence between what is meant to investigate with

what actually is investigated

What is investigated = the scientific truth of English education =

a theory

A theory = a logical (and empirical) relation of concepts

Internal validity = degree of coherence between concepts and

data

External validity = the discovered theory and real life

(statistically: sampling and population)


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II. THE STRUCTURE AND FUNCTIONS OF

STATISTICS

A. RESEARCH VALIDITY AND STATISTICS

B. CONFIRMATORY RESEARCH(deductive-inductive; hypothesis testing)

a. Hypothesis of association

Ho: no associationH1: there is (only; positive; negative)

b. Hypothesis of difference

Ho: no difference

H1: there is; larger; smaller

C. EXPLORATORY RESEARCH

(theory generating; inductive-deductive)1. Non-inferential

2. Inferential


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II. STATISTICS

A. MEANINGTraditionally (mechanistic): statistics is the science of conductingstudies to collect, organize, summarize, analyze, and draw

conclusions from data (Bluman, 2000?)

Research related (conceptual): to ensure research validity,internal and external, i.e. by keeping consistent relation between

logic and observation, notably the essential components of scientific

research

1. Statistics

i. Observation

ii. Object, attribute, phenomenoniii. Data

iv. Organization

v. Process

vi. Interpretation

2. A statistic

i. indexii. analysis technique

iii. vs. parameteriv. ...


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1. Statistics

i. Observation

ii. Object, attribute, phenomenon

iii. Data

iv. Organizationv. Process

vi. Interpretation

2. A statistic

i. index

ii. analysis technique

iii. vs. parameter

iv. ...


C. CONCEPT, OBSERVATION, AND EXPERIENCE

1. Meaning

2. Procedure

i. Elicitation

ii. Measurementiii. Record

D. OBJECT, ATTRIBUTE, PHENOMENON, VARIABLE

E. MEASUREMENT

F. DATA1. Meaning

recorded result of observation

to represent a world reality2. Observation

3. Recording

4. Variable

5.


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G. INTERPRETATION


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Part 2 Statistical Techniques

III. DESCRIPTIVE STATISTICS

A. MEANING

B. DATA

B. MEASURES OF CENTRAL TENDENCY

C. MEASURES OF DISPERSION

D. CORRELATION


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IV. INFERENTIAL STATISTICS

A. PARAMETRIC

1. Correlational

i. Pearson r

ii. Regression

2. Comparative

the t-test

ANOVA

B. NON-PARAMETRICRequirements violated, or, nominal and ordinal data

1. Chi-square

2. Mann Whitney U-Test

3. Kruskal Wallis H Test

4. Wicoxon Test

5. Friedman Test


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V. STATISTICS FOR SURVEY RESEARCH

A. SIMPLE CORRELATION

B. MULTIPLE CORRELATION


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VI. STATISTICS FOR EXPERIMENTAL

RESEARCH

A. SIMPLE COMPARISON

B. MULTIPLE COMPARISON


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VII. STATISTICS FOR OTHER RESEARCH

A. EXPLORATORY RESEARCH

1. Descriptive (non-inferential): descriptive statistics

2. Inferential: Factor Analysis; SEM

B. RESEARCH AND DEVELOPMENT

(Validation of conceptual and iconic model)

1. Non-inferential: descriptive statistics

2. Inferential: Factor Analysis; SEM

C. CONTENT ANALYSIS


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VIII. SELECTION OF A STATISTICAL

TECHNIQUE

A. KNOWLEDGE PRE-REQUISITES

1. Variable

a. one: descriptive

b. two

1) descriptive: descriptive

2) inferential: inferentialc. more than two: multiple

2. Hypothesis (Variable relation)

a. Association

1) simple

2) multiple

b. Difference

1) simple2) multiple

c. Causal: independent-dependent; non-causal

3. Groups (within a variable)

a. Two or more

b. Independent (between subjects) or correlated (within subjects)

4. Data

a. Discrete or continuous

b. Data scales: nominal, ordinal, interval, ratioc. Standard scoring

c. Normal distribution

5. Parameter

a. Statistics and Parameters


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b. Definite and non-definite (hypothesis testing)

B. PROCEDURE

1. The nature of researcha. Descriptive, non-inferential

b. Inferential

2. Decide your hypothesis: association or difference

3. Data scale: nominal/ordinal, non-parametric; interval/ratio:

probably parametric

a. If normally distributed, linear, and homogeneous: parametric

b. If (a) strongly violated: non-parametric4. Measurement: correlated or independent5. Hypothesis of association

a. Data scale

b. Without prediction:

c. With prediction:

d.

6. Hypothesis of difference

a. Data scaleb. Number of independent variablesc. Correlated data

d.

7.

Table 1.Statistical Technique-Selection: Descriptive, Non-

Inferential Research*)

Measure

Data

Nominal Ordinal Interval &

Ratio

Central

tendency

mode median average

Dispersion label range standard

deviation;


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variance

Location label percentile z-score; T-

score

Association: point biserial;

biserial

Spearman rho Pearson r

*)Povisional. Please cross-check with references for correction and

completion

Table 2.Statistical Technique-Selection: Inferential Research*)

Hypothesis Correlated IndependentParamtrc Non-Par Paramtric Non-Par

ASSOCIATION

2 Var

predict

Pearson r

Simple

Reg

Spearma

n rho;Chi-

square

- -

> 2 Var Multiple

Reg

Chi-

square

- -

DIFFERENCE

1IV

2 groups

> 2 groups

t-test (cor)

Anova

Wilcoxon

Test

FriedmanTest

t-test (ind)

Anova (1-way)

Chi-

square;

Mann

Whitney

KuskallWallis

2IV Anova (2-

way)

Anova (2-

way)

*)Povisional. Please cross-check with references for correction andcompletion


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IX. VALIDATION OF RESEARCH

DISCOVERY

A. VALIDITY

Validity: coherence of what you do with what you have intended to

do

Research-project validity: coherence of the research project with theparticipation in improving life quality

Validity of scientific (logical positivistic) research-project: whetheryou discover a theory (which is verified or generated)

Why theory? Because theory explains, predict, and control better, so

you can perform better.

A theory: a relation of variables (logical and empirical)

A variable, and variable relation, is a construct (= concept). It is

abstract. It exists in your mind only.

There are a countless number of variables in any academic

discipline, English education being no excempt. To make sense,

every one of them needs defining, discernedlyfrom others. This iswhat is called construct validity. Reading ability, for example, has to

be reading ability, and not other variables like grammar ability,vocabulary, or general intelligence. Construct validity is the most

important validity.

Again, your research discovery is a theory. In general, you will

verify (or test) a theory, mainly for two reasons. First, it is not easy

to identify an English education issue the theory of which is still


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scarce. Secondly, theory generation needs a wide and large data

size, which is unlikely accessible withion your time allocation.

A theory, as stated before, is a relation variables. Understandably,

for a relation to exist there must at least two variables (Please note,

that the relation itself is also a variable). A theory is also called athesis. It is a construct (= concept) which is both logically true and

empirically true. When it is logically true only, it is called a

hypothesis. Coincidentally your hypothesis is also the answer

(logical only) of your research question.

Validity of research discovery

Logically true variablesLogically true relationsLogically true variable operationalization

Logically true relation operationalization

Data representativeness

Coherent (methodologically correct) data processing

Coherent (methodologically correct) interpretation of data

processing result

Internal validity = validity of research discovery

External validity = applicability in a similar context other than the

research setting

B. HYPOTHESIS FORMATION

1. Clarification of variables and relevant concepts, including

working definitions of variables and variable relations2. Statement of universal theory

3. Clarification of local context

4. Logical relation of 2 and 3 = conceptual hypothesis5. Statistical hypothesis

C. EMPIRICAL VERIFICATION (HYPOTHESIS TESTING)

1. Variable operationalization

a. Construct validation (blueprint)


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b. Data: nature, types

c. Data gathering instruments (including their validation)

2. Data presentation

3. Data processing: computation, conclusion, decision

D. INTERPRETATION (OF DATA PROCESSING RESULTS)

1. Statistical: descriptive statistics, inferential statistic values,

significance level, hypothesis acception/rejection

2. Scientific: conceptual hypothesis

3. Recommendation


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SCORING

No Statistics &

Research

Competence

Know-ledge

Skill

Attitude

Con-science

Compas-sion

1 2 3 4

1 Research x

2 Statistics

3 Statistics &

Research

x

4 DescriptiveStatistics

5 Inferential

Statistics

11 Research knowledge

12 Research skill (NA)21

2231

32

41

42

51

52

12345.3 Conscience

Primacy of genuine progress rather than formality (contribution

to progress: self-, group, and class; absence of plagiarism and

cut-and-paste work).

12345.4 Compassion


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Show the implications of statistics and statistical research to the

promotion of human dignity and suggest how to offset

potentially negative effects

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