EDUCATIONAL STATISTICS

Rohani Ahmad Tarmizi - EDU5950

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EDUCATIONAL STATISTICS

- EDU 5950 -


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ABOUT THE INSTRUCTOR

ASSOC. PROF. DR. ROHANI AHMAD TARMIZI

Email: [email protected]

[email protected]

Tel: 89467005/0123100675

mailto:[email protected]

mailto:[email protected]


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Course Objective:

Students will be able to acquire statistical concepts and statistical methods in data analysis for social sciences research.

Students will be able to use statistical procedures for describing and interpreting social science research results.


Course Content:

1. Introduction to Educational Research & Basics to Statistics for Educational Research

2. Descriptive Statistics – Graphical Display of Data

3. Descriptive Statistics – Measures of Central Tendency

4. Descriptive Statistics – Measures of Variability

5. Inferential Statistics – Normal Curve and Introduction to Hypothesis Testing

6. Inferential Statistics: Hypothesis Testing – t- Test for a Single Sample and t Test for Dependent Means

7. Inferential Statistics: Hypothesis Testing – t- Test for a Single Sample and t Test for Two Independent Means

8. Inferential Statistics: Hypothesis Testing – Analysis of Variance

9. Inferential Statistics: Hypothesis Testing – Correlation Analysis

10. Inferential Statistics: Hypothesis Testing – Regression Analysis

11. Inferential Statistics: Hypothesis Testing – Chi-Square Analysis

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Course Evaluation:

1. Assignments 30%

2. Test I 30%

3. Final Examination 40%


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What is Research?• SYSTEMATIC AND SCIENTIFIC

INVESTIGATION in which the researchers want to – OBJECTIVES TO BE ACHIEVED– OBTAIN ANSWERS TO RESEARCH QUESTIONS,– GET HYPOTHESES TO BE TESTED AND

VALIDATED

• HENCE• The researcher collects data• The researcher indicates how the data answered

the question OR validate the hypotheses through STATISTICAL ANALYSES.


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EXAMPLES OF RESEARCH TOPICS• Effects of Graphic Calculator on Performance and

Mathematical Thinking Among Malaysian Mathematics Secondary School Learners

• Relationship Between Perceived Organizational Support, Leadership Style and Job Satisfaction

• Affective Commitment to the Organization and Job Satisfaction

• Influences of Leadership Styles on Employee Performance

• Transformational Leadership’s Impact on Higher Education Performance


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Importance of Research

• Reason 1: Research Adds Knowledge About Educational Issues– Addresses gaps in knowledge– Expands knowledge– Adds voices of individuals to knowledge


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• Reason 2: Research Helps Improve Practice– Educators gain new ideas– Educators gain new insight into methods– Educators gain new insight into students


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• Reason 3: Research Informs Policy Debates– Research helps people weigh different

perspectives on issues– Research helps people make informed

decisions regarding policy


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• Reason 4: Research Builds Student Research Skills– Organizational skills– Analytical skills– Writing skills– Presentation skills


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The Research Spiral

Write Report

Identify the Research Problem

Review theLiterature

Specify a Research Purpose

Collect Data

Analyze andInterpret

Data

Specify a problemJustify a problemSuggest a need to study it for audiences

Select and summarize the resources in a Literature Review

Determine the data collection method,Select the individuals to study,Design instruments, and outline procedures

Skills Needed for Research

• Curiosity to solve puzzles

• Lengthen attention span

• Using the library and computer resources

• Writing and rewriting

TYPES OF RESEARCH

• QUANTITATIVE RESEARCH

• QUALITATIVE RESEARCH


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Quantitative Research

♠ Are used in the systematic scientific investigation of

quantitative properties and phenomena and their relationships.

♠ Are widely used in both the natural and social sciences,

from physics and biology to sociology and journalism.

♠ The objective is to develop and employ mathematical

models, theories and hypotheses pertaining to natural phenomena

♠ The process of measurement is central to quantitative

research because it provides the fundamental connection

between empirical observation and mathematical expression of

quantitative relationships.


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Quantitative methods

♠ Are research methods dealing with numbers and anything that is measurable.

♠ Counting and measuring are common forms of quantitative methods.

♠ The modern tendency is to use statistical softwares to analyze the huge amount of data. Quantitative methods might be used with a global qualitative frame

♠ Using quantitative methods, it is possible to give precise and testable expression to qualitative ideas.


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Qualitative methods♠ Are research methods dealing with natural settings to

gather direct source of data for example in schools, community, company, etc

♠ The researcher is the key instrument who will be directly observing and interviewing individuals as people go about their daily routines.

♠ The data comes in the form of words, video recordings, documents, manuscripts, or pictures rather than numbers.

♠ Qualitative researchers are concerned with context, process as well as product. Their concerns – how things occur, how people’s attitudes are translated into actions, gestures, teacher’s mannerism, views, opinions, etc.


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Basic Statistical Concepts


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What is Statistics?

Statistics is the science of collecting, organizing, analyzing, and interpreting data in order to make decisions.


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Inferential Statistics Involves using sample data to draw conclusions about a population.

Branches of Statistics

• Descriptive Statistics Involves organizing, summarizing, and displaying data.


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Important Terms•Population

The collection of all responses, measurements, or counts that are of interest.

•SampleA portion or subset of the population.

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Important Terms

•Parameter:A number that describes a population characteristic.

•Statistic:

A number that describes a sample characteristic.

Average age of all peoplein the United States

Average age of people from a sample of three states.


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Random SamplesSimple Random Sample: Each member of the

population has an equal chance of being selected.

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•Assign a number to each member of the population. •Random numbers can be generated by a random number table, a software program or a calculator.•Members of the population that correspond to these numbers become members of the sample.•From the sample we obtain measurements -> variables or constructs


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Levels of Measurement

Categories, names, labels, or qualities. Cannot perform mathematical operations on this data.

Data can be arranged in order. You can say one data entry is greater than another.

1. Nominal:

Ex: type of car you drive, your major

2. Ordinal:

Ex: TV ratings, condition of patient in hospital.

1stplace


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Levels of Measurement

There is an inherent zero. Data can be ordered, differences can be found, and a ratio can be formed so you can say one data value is a multiple of another.

3. Interval:

4. Ratio:

Ex. Height, weight, age

Data can be ordered and differences between 2 entries can be calculated. There is no inherent zero (a zero that means “none”.) Ex: IQ, EQ, life satisfaction, marital happiness


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Statistic1.1. Can be viewed in two perspective:Can be viewed in two perspective:

►► Numerical factsNumerical facts

►► A fields discipline studyA fields discipline study

2.2. Decision making toolsDecision making tools

3.3. Types of statisticsTypes of statistics

► ► PurposePurpose

Descriptive vs InferentialDescriptive vs Inferential

►► AssumptionAssumption

Parametric vs Non parametricParametric vs Non parametric

►► Number of variablesNumber of variables

Univariate – Bivariate – Multivariate Univariate – Bivariate – Multivariate


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VariablesCharacteristic studied that assume different values for different elements

Demography:► Gender► Job tenure► Occupational status

Job characteristic:► Work condition► Job demand► Job control

Perceived quality of ICT facilities

Quality of work life

Independent Variables

Dependent Variable


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Sales of Measurement1. Nominal

► The lowest scale► Numbers assigned to identify attributes► No order/ sequence

2. Ordinal► Numbers assign in ranking order► Arrange from lowest to highest or vice versa

3. Interval► Arbitrary zero (no absolute zero)► Zero does not represents absence of the

characteristic4. Ratio

► The highest scale► True zero (represent absence of the

characteristic)


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Exercise:What are the scales of measurement for these variables?

1. Program of study

2. Speed (km/hr)

3. Motivation scores

4. Income categories

5. Number of SMS received

6. Marital Status

7. Quality of work life scores

8. Socio-economic status

9. Perception scores

10. Membership status


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Statistic Analyses and Scales of Measurement

Statistic Dependent Variables Independent Variablest-Test Interval / Ratio Nominal / Ordinal

(k=2)

ANOVA Interval / Ratio Nominal / Ordinal(k>2)

Chi-square Nominal / Ordinal Nominal / Ordinal

Spearman Rho Ordinal Ordinal

Interval / Ratio (Non-Normal) Interval / Ratio (Non-Normal)

Pearson correlation Interval / Ratio Interval / Ratio

Simple Linear Regression Interval / Ratio Interval / Ratio

(At least one of the scales is Nominal)

OR


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DOING RESEARCH MEANS YOU NEED DATA

• Data – organized information when researcher has undergone data collection phase

• Data can be organized and stored in various ways – softcopy/hardcopy, excell/spss/minitab/sas, etc


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SAMPLE OF DATA


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DATA - Aron, Paris and Aron (1995) study on 151 students on a question “How stressed have you been in the last 2 weeks, on a scale of 0 to 10, with 0 being not at all stressed and 10 being as stressed as possible”

4,7,7,7,8,8,7,8,9,4,,7,3,6,9,10,5,7,10,6,8,7,8,7,8,7,4,5,10,10,0,9,8,7,9,7,9,5,8,5,0,4,6,6,7,5,3,2,8,5,10,9,10,6,4,8,8,8,4,8,7,3,8,8,8,8,7,9,7,5,6,3,4,8,7,5,7,3,3,6,5,7,5,7,8,8,7,10,5,4,3,7,6,3,9,7,8,5,7,9,9,3,1,8,6,6,4,8,5,10,4,8,10,5,5,4,9,4,7,7,7,6,6,4,4,4,9,7,10,4,7,5,10,7,9,2,7,5,9,10,3,7,2,5,9,8,10,10,6,8,3.


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Types of Variables

VARIABLES – are the focus of a study or the things that we measure in a study/research

♠ Continuous vs Discrete► anxiety level – continuous

► anxiety categories – low or high

♠ Independent variable vs Dependent variable► variable manipulated by the researcher to investigate its effect (teaching approach, medication, counseling therapy, training modules)

► variables that are characteristic/inherent which the researcher wish to investigate (race, gender, program of studies)

► variable assumed dependent upon the value of independent variable. by the researcher to investigate its effect (achievement, sugar level, depression level, physical fitness)

► length, weight, speed, exam marks etc.


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Inferential Statistics Involves using sample data to draw conclusions about a population.

Branches of Statistics

• Descriptive Statistics Involves organizing, summarizing, and displaying data.


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MAJOR PURPOSE OF DESCRIPTIVE STATISTICS

1.Graphical Display of Data

2.Measures of Central Tendency

3.Measures of Variability


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TO COMPARE BETWEEN GROUPS► z-Test► t-Test – Independent or Dependent t-test► F-Test – Analysis of Variance

TO DETERMINE RELATIONSHIP Variables► Pearson correlation► Spearman correlation► Point Biserial correlation► Simple linear regression► Chi-square

MAJOR PURPOSE OF INFERENTIAL STATISTICS

Documents

EDUCATIONAL STATISTICS