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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.
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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
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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.
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Variables
Discrete variable: no value can exist betweentwo neighboring categories.
Continues variable: there are infinite numberof possible values that fall between any twoobserved value
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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
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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.
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Interval Scale
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Ratio Scale
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DATA
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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.
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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