ESE633�STATISTICS IN EDUCATION ��Video A�Chapter 1 & 2

Dr Kim Teng Siang

kskim2007@gmail.com

012-4661131

WHAT IS STATISTICS?

Let us start with an activity:

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Tell us your favourite numbers from 1 to 9

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Your Favourite numbers – �(from every person in your class)

This is

Called

Data-

What

is that?

How?

Meaning?

How to find meaning from Data?

• You arrange and tally the numbers using frequency table (organizing)
• plot a graph about the distribution of numbers (processing)
• Extracting further information (interpreting)

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• Note: Step 1 & 2 can be done using computer software like SPSS

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Data

N

POPULATION

What can you see? Meanings?

WHAT IS STATISTICS?

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Statistic is the study about the ways of collecting, organizing, processing and interpreting of numerical data (information)

or

ways to give meanings to the data in a research.

Some Definitions

• A branch of mathematics dealing with the collection, interpretation and presentation of masses of numerical data (The Merriam-Webster’s Collegiate Dictionary)

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• The science of learning from data (Jon Kettenring, President of the American Statistics Association)

Course Content

Inferential

Statistics:

Parametric

Tests

Chapter 1: �Basic Concepts in Statistics

• Descriptive and Inferential Statistics
• Construct and Variables
• Independent Variable (IV)
• Dependent Variable (DV)
• Measurement and Scales
• Nominal
• Ordinal
• Interval
• Population
• Sample and Sampling Techniques

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Types of Statistics

a) Descriptive = just make know what the data is

• Describe the basic features of the data
• The centre of the distribution (most common value) and
• The spread (how it varies)
• Provide simple summaries about the sample or measure
• With simple graphics analysis, they form the basis of virtually every quantitative analysis of data

Data from population or sample

Summaries

of data

b) Inferential = induction = make an inference from __ to ___

(sample – population)

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n

Parameters

SAMPLEL

Statistics

Represent by

Make inference or draw conclusion about

µ, σ

Mue , Sigma

, S

N

POPULATION

b) Inferential = induction = make an inference from __ to ___

(sample – population)

• Inference is the act or process of deriving a conclusion (about unknown value in a population) based solely on what one already know (from sample).
• Specially develop statistical techniques (t-test, ANOVA, ANCOVA…) based on sound maths theories are able to do this inference with accuracy

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VARIABLES

• A certain characteristic that has at least TWO of More values or types
• The characteristic could be either naturally in existence or measure by a certain tool or scale
• E.g.
• Sex or Gender
• Ethnic group
• Height of a person
• IQ
• Opinion Ranking

Types of Variables

Dependent

Variable

(DV)

(Academic Achievement)

Independent Variable A

(IV)

(Gender)

Independent Variable B

(IV)

(IQ)

Construct and Variable

• Construct = a crude or general concept or idea that is not clearly define or measurable (e.g . Attitude, Intelligent)
• This concept need to be operationalised or make it measurable ( or be a variable) to be useful in an analysis (using Attitudinal Inventory, IQ Test)
• Thus a variable is a deliberate constructed entity for a specific purpose

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Questions

• Why variable is important in a research?

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• We usually study relationships between two variables, can we study one variable?

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• Why should a variable be operationally defined?

Types of Value or Measurement

• Nominal (type, category)
• Gender, Ethnic Group, Class
• Ordinal (order, level)
• Rank or order, arbitrary divided group e.g good, intermediate, and poor, Likert Scale
• Interval (measurement, score)
• A range of value that is divided into equal quantities or intervals, e.g. ruler, test scores
• Ratio (measurement in science)
• Similar as interval but with an absolute zero

Types of Value

• E.g.
• Sex or Gender (Natural - Nominal /

category)

• Ethnic group ( Natural - Nominal)
• Height of a person (Measure – interval)
• IQ Test score (Measure – interval)
• Math Test score (Measure – interval)
• Opinion Ranking (level based on

perception- Ordinal)

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Population and Sample

• A population is a collection of data whose properties are analyzed. The population is the complete collection to be studied, it contains all subjects of interest.�
• A sample is a part of the population of interest, a sub-collection selected from a population.

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Sample & Population

n

N

POPULATION

Parameters

SAMPLEL

Statistics

Represent by

Make inference or draw conclusion about

µ, σ

Mue , Sigma

, S

X bar

Mean = X bar or mue

Std. Dev. = S, or sigma

Sampling Techniques

• Sample is supposed to be a true representation of a population despite its small in size or subjects’ number
• What constitute a true Sample or true representation of a population?
• Its selection must based on the principle of

Random selection = ALL subjects in a population are given equal and independence chance to be selected

• Simple Random Sampling

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Random Selection �(by chance)

• How to do it?

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• What it means by random?

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• How to use random table (pg 9)?

(random selection in SPSS)?

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Other Sampling Techniques

• Sometime other methods are used to satisfied certain needs of the study or to adjust to certain conditions of population that render the ideal technique unsuitable

Types of Sampling Techniques

• Simple Random
• Systematic
• Stratified
• Cluster
• Or mixture of two or more above

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Question

• Why do we use sample in a research?

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Exam Question 6

• How to do a simple random selection of 100 Chemistry teachers out of 5000?

Nonprobability Sampling�(not by chance)

• In general, researchers prefer probabilistic or random sampling methods over non-probabilistic ones, and consider them to be more accurate and rigorous.

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• However, in applied social research there may be circumstances where it is not feasible, practical or theoretically sensible to do random sampling. Here, we consider a wide range of non-probabilistic alternatives.

Nonprobability Sampling

• Purposive Sampling
• we sample with a purpose in mind. We usually would have one or more specific predefined groups we are seeking.

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• Accidental, Haphazard or Convenience Sampling
• the traditional "man on the street" (TV3 interview)

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• In clinical practice, we might use clients who are available to us as our sample e.g. volunteers.

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Chapter 2 �DESCRIPTIVE STATISTICS

• To describe

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• To tell

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• To summarize a set of data

�

Example

• You are called by your head master to tell (describe) him the results of Chinese test from the class you teach

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• What to tell him in one sentence?

Data from population or sample

Summaries

of data

So, What to tell?�

• The Center of the distribution (Location)

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• The Spread of the distribution

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• Type of Distribution (Shape)

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Centre of Distribution

• Analogy : Ants and sweet
• Where is the centre?
• Plot a graph of the distribution of these ants in relation to the centre
• What do you get?
• Can you tell why in statistics the centre is called the measure of central tendency?

a) Measures of Central Tendency

• 3 Types = Mean, Mode , Median

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• Why 3?

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• Is one is enough to show the central tendency of a distribution?

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Activity 2.1

• Find the Mean, mode and median of the following set of data:

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• 2, 5, 4, 4, 3, 4, 3, 5, 10

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• Compare these 3 measures, is one measure enough? Which measure indicates the centre best? Which is not, Why?

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• Use SPSS to plot the graph to help you to compare

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Mean = 4.44

Mode = 4

Median = 4

Mean = 4

Mode = 4

Median = 4

Normally Distributed

Not Normally Distributed

- skew

• If the value 10 is replace by 6

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• What happen?

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• What shape is the distribution?

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• Under what condition, mean is preferred?

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Question

b) Measures of Variability or Dispersion

• The spread of the values around the centre of distribution

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• Common measures:
• Range = Maximum and Minimum
• Variance= total square deviation from the

centre

• Standard deviation = average deviation

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Learning Activity 2.2

• Compute the variance and std deviation of the data below manually

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• 2, 5, 4, 4, 3, 4, 3, 5, 6

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Deviation

Use Table Below

Frequency Distribution

• It displays the number of times a value (or range of value or interval class) occur in an organized manner.

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• It can be in the form of:
• Frequnecy table
• Graph
• Bar Chart
• Histogram
• Line Graph
• Stem and Leaf

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Learning Activity 2.3

• Enter the data from Activity 2.2 into SPSS
• Plot the graph (histogram) for the set of data
• What is the shape of the distributions ?
• Find the means, and std deviations of the data
• What is Kurtosis, Skewness? (pg 10)

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Learning Activity 2.4

• Generate Frequency Table, Graphs and Boxplots using the same data in Activity 2.2 (use SPSS procedure pg 10)

HOW TO DESCRIBE A DISTRIBUTION of a Variable?

a) Graphically Using

• Graph/ Picture (Shape)
• Frequency Table
• Descriptive Statistics

Values:

• Suitable Central tendency measures (mean,

mode, median)

• Suitable measures of variability (Std. Dev., range)

b) Describing a distribution with numbers (Quantitative Variable)

• Centre - mean & median

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• Spread - range, interquartile range (middle 50%) & standard deviation

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• Shape - skewness, kurtosis (height)

Summary:�Describing a Variable