Week 1 - Introduction to Statistics.pdf

7/24/2019 Week 1 - Introduction to Statistics.pdf

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MPU1034

Application of

Statistic in Educational Research

Dr. Norazrena Abu Samah

Office: M39 Wing [email protected]

019-7103903
mailto:[email protected]:[email protected]


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Chapter 1: Introduction to Statistics


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Statistical Termspopulation

sample

parameter

statisticdescriptive

statistics

inferential

statistics

sampling error

Measurement Termsoperational definition

nominal

ordinal

intervalratio

discrete variable

continuous variable

real limits

Research Termscorrelational method

experimental method

independent variable

dependent variablenonexperimental

method

quasi-independent

variable

Students should be familiar with the terminology andspecial notation of statistical analysis


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Variables

A variableis a characteristic or condition that

can change or take on different values.

Most research begins with a general question

about the relationship between two variables

for a specific group of individuals. (eg: Male

and Female, x & y )


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Population

The entire group of individuals is called the

population.

For example, a researcher may be interested

in the relation between class size (variable 1)

and academic performance (variable 2) for the

population of third-grade children.


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Sample

Usually populations are so large that a

researcher cannot examine the entire group.

Therefore, a sampleis selected to represent

the population in a research study. The goal is

to use the results obtained from the sample to

help answer questions about the population.


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Types of Variables

Variables can be classified as discrete orcontinuous.

Discrete variables(such as class size) consist

of indivisible categories, and continuousvariables(such as time or weight) areinfinitely divisible into whatever units aresearcher may choose. For example, timecan be measured to the nearest minute,second, half-second, etc.



Real Limits

To define the units for a continuous variable, a

researcher must use real limitswhich are

boundaries located exactly half-way between

adjacent categories.

Example

Intervals 11-20,21-30,31-40.

Lower limit = 20.5

Upper limit = 30.5



Measuring Variables

To establish relationships between variables,researchers must observe the variables andrecord their observations. This requires that

the variables can be measured. The process of measuring a variable requires a

set of categories called a scale ofmeasurementand a process that classifieseach individual into one category.



Variables

Discrete variable: no value can exist betweentwo neighboring categories.

Continues variable: there are infinite numberof possible values that fall between any twoobserved value



4 Types of Measurement Scales

1. A nominal scaleis an unordered set ofcategories identified only by name. Nominalmeasurements only permit you to determine

whether two individuals are the same ordifferent.

2. An ordinal scaleis an ordered set ofcategories. Ordinal measurements tell youthe direction of difference between twoindividuals.


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Eg.2 Numbers assigned to specific categories of colours:

1 for Blue 2 for Brown 3 for Green

State 1 State 2 State 3

45 34 20

Nos. of Deaths for Three States

Eg. 3*: Numbers representing a list of rate of death for each category (e.g.

state)

Numbers are regarded as NOMINAL when they represent categories

for classificationof characteristics with no specific order.

Note: In general, the true order of magnitudescan be applied to these numbers,

i.e. 20 < 34 < 45 (so that 45, 34 and 20 are ordinal!)

However, the comparative orderingcannot be applied in this particular

case, as the rate of 45 deaths in State 1 perhaps is lower (in terms of

percentage of the population) as compared to 20 deaths in State 3!

Eg.1 Natural numbers in the general number system (0, 1, 2, 3,. )


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Numbers are regarded as ORDINALwhen they represent orderedrelations of some characteristic, with the order having unspecified intervals.

Eg.1 Grades obtained by students in a Maths Test

Eg.2 Mypre-school child watches television:1 very much

2 a little

3 not very much

4 not at all

Eg. 3 Suppose you conduct an Algebra Readiness Test to 3 different groups of

samples, namely Traditional Class, Hands-on Class and Prealgebra Class.Each of these classes comprises of 7 students. The scores obtained by

each student are shown below:

Note: In this case, the numbers 95, 94, 89,

84, can be ordered. Bearing in mind

the nature of interval scale, thesenumbers may be regarded as

INTERVAL



4 Types of Measurement Scales

3. An interval scaleis an ordered series of equal-sized

categories. Interval measurements identify the

direction and magnitude of a difference. The zero

point is located arbitrarily on an interval scale.4. A ratio scaleis an interval scale where a value of

zero indicates none of the variable. Ratio

measurements identify the direction and

magnitude of differences and allow ratiocomparisons of measurements.



15

Interval Scale



16

Ratio Scale



DATA



Correlational Studies

The goal of a correlationalstudy is to

determine whether there is a relationship

between two variables and to describe the

relationship.

A correlationalstudy simply observes the two

variables as they exist naturally.



Experiments

The goal of an experimentis to demonstrate acause-and-effect relationship between two

variables; that is, to show that changing the

value of one variable causes changes to occurin a second variable.


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Experiments (cont.)

In an experiment, one variable is manipulated tocreate treatment conditions. A second variable isobserved and measured to obtain scores for a groupof individuals in each of the treatment conditions.

The measurements are then compared to see if thereare differences between treatment conditions. Allother variables are controlled to prevent them frominfluencing the results.

In an experiment, the manipulated variable is calledthe independent variableand the observed variableis the dependent variable.


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Other Types of Studies

Other types of research studies, know as non-experimentalor quasi-experimental, aresimilar to experiments because they alsocompare groups of scores.

These studies do not use a manipulatedvariable to differentiate the groups. Instead,the variable that differentiates the groups isusually a pre-existing participant variable(such as male/female) or a time variable (suchas before/after).


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Other Types of Studies (cont.)

Because these studies do not use the

manipulation and control of true experiments,

they cannot demonstrate cause and effect

relationships. As a result, they are similar tocorrelational research because they simply

demonstrate and describe relationships.


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Data

The measurements obtained in a research

study are called the data.

The goal of statistics is to help researchers

organize and interpret the data.


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Two type of Statistics

Descriptive statisticsare methods fororganizing and summarizing data.

Inferential statisticsare methods for using

sample data to make general conclusions(inferences) about populations


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Descriptive Statistics

Descriptive statisticsare methods fororganizing and summarizing data.

For example, tables or graphs are used to

organize data, and descriptive values such asthe average score are used to summarize data.

A descriptive value for a population is called a

parameterand a descriptive value for asample is called a statistic.


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Inferential Statistics

Inferential statisticsare methods for using sample

data to make general conclusions (inferences) about

populations.

Because a sample is typically only a part of the wholepopulation, sample data provide only limited

information about the population. As a result,

sample statistics are generally imperfect

representatives of the corresponding populationparameters.


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Parameter Statistics

Number of cases N n

Mean x

Variance 2 s2

Standard division s

Correlation coefficient r


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Sampling Error

The discrepancy between a sample statistic

and its population parameter is called

sampling error.

Defining and measuring sampling error is a

large part of inferential statistics.


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Notation

The individual measurements or scores obtained fora research participant will be identified by the letterX (or X and Y if there are multiple scores for eachindividual).

The number of scores in a data set will be identifiedby N for a population or n for a sample.

Summing a set of values is a common operation instatistics and has its own notation. The Greek lettersigma, , will be used to stand for "the sum of." Forexample, X identifies the sum of the scores.


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X Y XY

72 5184 165 27225 11880

68 151

67 160

67 160

68 146

70 160

66 133

Also, find (x-1)2 and (x)

2

Week 1 - Introduction to Statistics.pdf

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