Transcript Lecture 30

Research Tools and Techniques
The Research Process: Step 7 (Data
Analysis Part C)
Lecture 30
Lecture Topics Covered Previously in the
Last Lecture
• Methods of Bivariate Analysis
• Contingency tables
• X2 Test
• Pearson’s Correlation
What we are going to Cover in this
Lecture
• Regression Analysis
• Paired Sample t-tests
• Independent Sample t-tests
• Contents of Research Proposal and Report
THE RESEARCH PROCESS
(1).
Observation
The Broad
Problem Area
(3).
(4).
Theoretical
Framework
Problem
Definition
Variables
Identification
(5)
(6).
Scientific
Research
Design
Generation
of
Hypothesis
(2).
Preliminary
Data
Gathering
Interviews
and Library
Search
(7).
Data
Collection
and
Analysis
(8)
Deduction
(9).
(10).
(11).
Report
Writing
Report
Presentation
Managerial
Decision
Making
Introduction to Data Analysis Process
Data Analysis Process
Interpretation of Results
Data Collection
Data Analysis
Discussion
Getting Data
Ready for
Analysis
Feel for
Data
1. Mean
Editing Data
2. Median
1. Incompleteness
/omissions
3. Mode
2. Inconsistencies
5. Frequency
Distribution
3. Legibility
4. Coding Data
5. Categorizing
6. Creating a Data
File
4. Variance
Recommendations
Hypotheses
Testing
Appropriate
Statistical
Manipulation
(Inferential
Statistics)
Goodness
of Data
1. Reliability
2. Validity
Tests of Statistical Significance
• Do our tests apply to general population or not (Confidence in
the Generalizability of findings)
• The mode of calculation of statistical significance hence prove
Ho or Ha
 Only for samples drawn from probability sampling.
 Determine level of statistical significance.

P < 0.05
 Find the test result using SPSS or any other software.
 If resulting value > table value (incase of chi square) you
accept alternate hypothesis.
 For Pearson’s r, Spearman’s Rho, Phi and Cramer’s V, SPSS
automatically generates statistical significance as shown in
table.
Regression Analysis
• Used to understand the nature of the
relationship between two or more variables
• A dependent or response variable (Y) is
related to one or more independent or
predictor variables (Xs)
• Object is to build a regression model
relating dependent variable to one or more
independent variables
• Model can be used to describe, predict, and
control variable of interest on the basis of
independent variables
Simple Linear Regression
• Yi = βo + β1 xi + εi
Where
• Y
• Dependent variable
• X
• Independent variable
• βo
• Intercept
• Mean value of dependent variable (Y) when the independent variable (X) is zero
• β1
• Model parameter
• Slope that measures change in mean value of dependent variable associated with a
one-unit increase in the independent variable
• εi
• Error term that describes the effects on Yi of all factors other than value of Xi
Model Summary with R Square and ANOVA table with F value and Significance.
Coefficientsa
• More
than
one
independent variable is
included in a multiple
linear regression model.
Model
1
(Cons tant)
PERFSALE
Uns tandardi zed
Coeffi cients
B
Std. Error
2.437
.253
.305
.073
a. Dependent Variabl e: PERFPROF
Standardi
zed
Coeffi cien
ts
Beta
.297
t
9.632
4.175
Sig.
.000
.000
ANOVA – Analysis of Variance between
Groups
• The reason for doing an ANOVA is to see if there is any difference between
groups on some variable.
• Example of Groups:
You might guess that the size of maple leaves depends on the location of the trees. For example, that
maple leaves under the shade of tall oaks are smaller than the maple leaves from trees in the prairie
and that maple leaves from trees in median strips of parking lots are smaller still. To test this
hypothesis you collect several (say 7) groups of 10 maple leaves from different locations.
• F=(Found variation of the group averages)/(Expected variation of the group averages).
Significant Mean Differences Between Two Groups – t-tests
Paired Sample t-tests
An independent testing agency is comparing the daily rental cost for
renting a compact car from Hertz and Avis. A random sample of eight
cities is taken and the following rental information obtained. At the .05
significance level can the testing agency conclude that there is a
difference in the rental charged?
City
Atlanta
Chicago
Cleveland
Denver
Honolulu
Kansas City
Miami
Seattle
•
•
•
•
•
Hertz ($)
42
56
45
48
37
45
41
46
Avis ($)
40
52
43
48
32
48
39
50
Step 1: Ho μd=0;
Ha μd ≠0
Step 2: The significance level is .05.
Step 3: H0 is rejected if t<-2.365 or t>2.365
Step 4: t=avg. of dif/[sd/√n] t=(1.00)/[3.162/√8]=0.89
Step 5: H0 is not rejected. There is no significant difference in the rental
charged.
Independent Sample t-test: Comparing Two Population Means
A recent EPA study compared the highway fuel economy of domestic
and imported passenger cars. A sample of 15 domestic cars revealed
a mean of 33.7 mpg with a standard deviation of 2.4 mpg. A sample
of 12 imported cars revealed a mean of 35.7 mpg with a standard
deviation of 3.9. At the .05 significance level can the EPA conclude
that the mpg is higher on the imported cars? (Let subscript 1 be
associated with domestic cars.)
Step 1: Ho μ2< μ1 Ha μ2> μ1
Step 2: The significance level is .05
Step 3: H0 is rejected if t<-1.708, df=25
Step 4: t= -1.64
Step 5: H0 is not rejected. There is
insufficient sample evidence to claim a
higher mpg on the imported cars.
Contents of the Research Proposal &
Report
1.A. Research Proposal
1.A.1. Problem Statement:
Background of the problem
1.A.2. Research Objective:
What the research is actually going to do
How it solves the problem
1.A.3. Importance/Benefits:
Mention in points
1.A.4. Research Design
1.A.4.1. Elements of research design in brief
1.A.4.2. Research Instrument:
Approximate number of questions, sample size, mail/hand
delivered, geographical premises
1.A.4.3. Pilot test if any
1.A.5. Data Analysis
1.A.6. Result & Deliverables
1.A.7. Budget
1.A.7.1. Time
1.A.7.2. Money
Writing Research Report
1.B. Abstract
1.B.1. Research Topic
1.B.2. Data and methods utilized
1.B.3. Summary
1.B.4 Conclusion
2. Research Topic and Introduction
3. Literature Review
4. Theoretical Framework
5. Hypotheses
6. Methodology
7. Data Findings and Analysis
8. Conclusion
9. Limitations
10. Discussion & Recommendations
11. References
12. Appendix
12.1. Research Correspondence if any
12.2. Research Instrument:
The Questionnaire
The End
Summary
• Regression Analysis
• Paired Sample t-tests
• Independent Sample t-tests
• Contents of Research Proposal and Report