Application of Statistics in Research

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Application of Statistics in Research

• Dr.P.Muthupandi,
• Asst. Professor,
• Department of Education, DDE
• Madurai Kamaraj University,
• Madurai 625 021

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Research Educational Research

• Research is an intellectual activity in which
  systematic analysis is done.
• It is a systematized effort to acquire new
  knowledge.
• Research is simply one of many means by which
  human beings seeks answers to questions (may be
  personal or professional)
• Example a coworker who ask you for lunch. For
  this question u have to answer the questions like
  1. lunch already completed? 2. Money? 3. Time?
• Example Motivating a unmotivated student by
  applying various ideas till he motivated
• Research is undoubtedly an essential and powerful
  tool in leading man towards progress.
• According to John W. Best (1977) Research is
  considered to be the more formal, systematic
  intensive process of carrying on the scientific
  method of analysis.
• Educational Research is nothing but applying the
  scientific principles in the field of education
  in order to find the answers to the questions.

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Types of Research (in general)

• Quantitative Research
• where the data concerned can be analyzed in terms
  of numbers.
• Qualitative Research
• Which describes events, persons and so forth
  scientifically without utilizing numerical data.

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Research Methods (Major)

• Historical Research
• Survey
• Experimental
• Case study

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Population and Sample

• Population
• It is the entire group we are interested in,
  which we wish to describe or draw conclusions
  about
• Sample
• A sample is a group of units selected from a
  larger group (the population). By studying the
  sample it is hoped to draw valid conclusions
  about the larger group.
• A sample is generally selected for study because
  the population is too large to study in its
  entirety. The sample should be representative of
  the general population.
• This is often best achieved by random
  sampling.Survey

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Class 1 Class 2 Class 3
Student1 100 99 1
Student2 100 100 2
Student3 100 102 3
Student4 100 101 4
Student5 100 98 490

TOTAL 500 500 500

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Class 1 Class 2 Class 3
Student1 100 99 1
Student2 100 100 2
Student3 100 102 3
Student4 100 101 4
Student5 100 98 490

TOTAL 500 500 500

Average 100 100 100
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Significance of Standard Deviation

• So to determine the usefulness of an average , we
  have to calculate standard deviation.
• If the value of standard deviation is less then
  the usefulness of an average is more.
• If the value of standard deviation is more then
  the usefulness of an average is less.

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Class 1 Class 2 Class 3
Student1 100 99 1
Student2 100 100 2
Student3 100 102 3
Student4 100 101 4
Student5 100 98 490

TOTAL 500 500 500
Average 100 100 100
Standard Deviation 0 1.58 218.02
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TYPES OF DATA

• 1. NOMINAL DATA
• 2. ORDINAL DATA
• 3. INTERVAL DATA
• 4. RATIO DATA

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1. NOMINAL DATA (SCALE)

• A set of data is said to be nominal if the
  observations belonging to it can be assigned a
  code in the form of a number where the numbers
  are simply labels. You can count but not order or
  measure nominal data.
• Example
• Gender
• Female1, Male 2
• Marital status
• Married1 Unmarried2

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2. ORDINAL DATA (SCALE)

• A set of data is said to be ordinal if the values
  / observations belonging to it can be ranked (put
  in order) or have a rating scale attached. You
  can count and order, but not measure, ordinal
  data.
• Example
• Ranking information on the basis of importance.
• First rank for highest Importance
• Last Rank for least Importance

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3. INTERVAL DATA (SCALE)

• An interval scale is a scale of measurement where
  the distance between any two adjacent units of
  measurement (or 'intervals') is the same but the
  zero point is arbitrary. Scores on an interval
  scale can be added and subtracted but cannot be
  meaningfully multiplied or divided
• .
• Example
• Year 1990,1991,1992,1993,1994
• Strongly agree5,agree4,No opinion3,disagree2,s
  trongly disagree1

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4. Ratio data (scale)
A set of data is said to be Ratio if the values /
observations belonging to it may take on any
value within a finite or infinite interval. You
can count, order and measure continuous
data. Example For example height, weight,
temperature, the amount of sugar in an orange,
the time required to run a mile
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Stages of Data Analysis
EDITING
ERROR CHECKING AND VERIFICATION
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Editing

• The process of checking and adjusting the data
• for omissions
• for legibility
• for consistency
• And readying them for coding and storage

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Coding

• The process of identifying and assigning a
  numerical score or other character symbol to
  previously edited data

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Data Entry

• The process of transforming data from the
  research project to computers.
• Optical scanning systems
• Marked-sensed questionnaires

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Data Analysis
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Construction of Master Table

• Assign Numbers for each level to the background
  variable
• Define Variable in the variable view
• Define the categories of the background variable
• Enter the data on the table
• Example

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Sample Distribution

1. Normal Distribution

• Negatively Skewed
• Positively Skewed

• Leptokutrtic
• Mesokurtic
• Platykurtic

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Normal Distribution Norms

• Skeweness - -2 to 2
• Kurtoasis - -2 to 2
• http//www.socialresearchmethods.net/

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Difference Between Parametric Non parametric
Tests
Parametric Statistics Non-Parametric Statistics
Scale Interval (or) Ratio Any Scale of Measurement
Distribution Normal Distribution Any Distribution
Power More Power Less Power
Example t Test, ANOVA, ANCOVA, PM Correlation, Regression, Trend Analysis Chi-Square Sign Test Mean Median Mode Rank Difference

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WHEN SHOULD SELECT A NONPARAMETRIC TEST

1. The outcome is a rank or a score and the
   population is clearly not Normal.
2. Some values are "off the scale," that is, too
   high or too low to measure
3. The data are measurements, and you are sure that
   the population is not distributed in a Normal
   manner

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Reliability of the tool

• In statistics, reliability is the consistency of
  a set of measurements or of a measuring
  instrument.
• Methods used for reliability
• Test-Retest method (Correlation between Test
  Retest)
• Split half method (Correlation between odd and
  even numbers scores)
• Internal consistency (Kuder Richardson Formula)
• (KR-21 formula)

r Reliability index K Number of Item on
the test M Mean
SD Standard Deviation
Example 40 items, mean of 27.3 SD is 4.64 0.64
Cronbachs Alpha
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Item Analysis

• For refinement of the tool item validity was
  calculated. This is also known as internal
  validity of an instrument. It refers to the
  interconnectedness of different items in the same
  tool.
• According to Borg and Gall (1979), item
  reliability and item validity play a vital role
  in selecting items to form the final tool.
• How can we find out item analysis
• Statistical assistance from internet
• Experimental Design

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Discriminating Power Difficulty Index

• Discriminating power Ph-Pl
• U
• Difficulty level (Ph Pl )
  
• U
• Ph the proportion of pupils in the high
  achieving group who answered the items correctly.
• Pl the proportion of pupils in the low achieving
  group who answered the items correctly.
• UTotal number of pupils in both groups

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Criteria for Selection
Discriminating Power Discriminating Power Difficulty Level Difficulty Level
.4 above Excellent item Between .4 .6 Average difficulty
Between .4 .3 Good Between .2 .4 Difficult item
Between .2 .3 Average item Between .6 .8 Easy item
Between .2 .1 Requires improvement Between .8 1 Very easy item
Less than .1 Item to be dropped Between 0 .2 Very difficult item
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Distribution of Items based on Difficulty

• 50 of the items are of average difficulty,
• 25 are easy ,
• 20 difficult and
• 05 are very difficult.

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Finding Levels for the score
Description Level
Less than Mean-1sd Low
b/w (Mean-1sd) and (Mean1sd) Average
More than Mean1sd High
Low
High
Average
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Finding Levels for the score
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Finding t Test and ANOVA
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ANOVA
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Correlation by Using Ms.Excel
x y
22 31
44 40
48 52
50 34
52 55
64 52
60 35
42 26
45 43
54 50
Enter the data
Select the Cell where u want r value
Type the Formula correl(Array1,Array2)
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Online Chi-Square Calculator

• Find the level from Ms.Excel
• Number of Low Level Sample
• Number of Average Level Sample
• Number of High Level Sample
• Put the Count of the data on http//www.physics.cs
  bsju.edu/stats/contingency_NROW_NCOLUMN_form.html

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For Further Contact

• E-mail ID
• haimuthupandi_at_yahoo.com
• Web page
• www.muthupandi.co.in