application of statistics in research dr.p.muthupandi, asst. professor, department of education, dde...
TRANSCRIPT
Application of Statistics in Research
Dr.P.Muthupandi,Asst. Professor,
Department of Education, DDE
Madurai Kamaraj University,
Madurai – 625 021
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.
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.
Research Methods (Major)
Historical Research Survey Experimental Case study
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
Class 1 Class 2 Class 3Student1 100 99 1
Student2 100 100 2
Student3 100 102 3
Student4 100 101 4
Student5 100 98 490
TOTAL 500 500 500
Class 1 Class 2 Class 3Student1 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
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.
Class 1 Class 2 Class 3Student1 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
TYPES OF DATA
1. NOMINAL DATA
2. ORDINAL DATA
3. INTERVAL DATA
4. RATIO DATA
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 Female=1, Male =2
Marital status Married=1; Unmarried=2
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.
ExampleRanking information on the basis of importance.First rank for highest ImportanceLast Rank for least Importance
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.
ExampleYear: 1990,1991,1992,1993,1994Strongly agree=5,agree=4,No opinion=3,disagree=2,strongly disagree=1
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
DATA ANALYSIS
DATA ENTRY
ERROR CHECKING
ANDVERIFICATION
CODING
EDITING
Stages of Data Analysis
Editing
The process of checking and adjusting the data for omissions for legibility for consistency
And readying them for coding and storage
Coding
The process of identifying and assigning a numerical score or other character symbol to previously edited data
Dr.N.Ramkumar, Faculty, PSGIM
Data Entry
The process of transforming data from the research project to computers.
Optical scanning systems Marked-sensed questionnaires
Data Analysis
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
Sample Distribution1. Normal Distribution
2. Negatively Skewed3. Positively Skewed
4. Leptokutrtic5. Mesokurtic6. Platykurtic
Normal Distribution Norms
Skeweness - -2 to +2 Kurtoasis - -2 to +2
http://www.socialresearchmethods.net/
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-SquareSign TestMeanMedianModeRank Difference
Difference Between Parametric & Non parametric Tests
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
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 = (K)(SD)2 – M(K-M)
(SD)2 (K-1)
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
Cronbach’s Alpha
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
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.
U=Total number of pupils in both groups
Criteria for Selection
Discriminating Power 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
Distribution of Items based on Difficulty
50% of the items are of average difficulty, 25% are easy , 20% difficult and 05% are very difficult.
Finding Levels for the score
Description Level
Less than Mean-1sd Low
b/w (Mean-1sd) and (Mean+1sd)
Average
More than Mean+1sd High
Low HighAverage
Finding Levels for the score
Low High Average
Finding ‘t’ Test and ANOVA
ANOVA
Correlation by Using Ms.Excel
Enter the data
x y
22 31
44 40
48 52
50 34
52 55
64 52
60 35
42 26
45 43
54 50
Select the Cell where u want r value
Type the Formula =correl(Array1,Array2)
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.csbsju.edu/stats/contingency_NROW_NCOLUMN_form.html
