This document provides an overview of quantitative data analysis techniques for hypothesis testing, including types of errors, statistical power, and tests for single and multiple sample means. It also discusses regression analysis, issues of multicollinearity, and other multivariate tests such as discriminant analysis, logistic regression, and canonical correlation.

1. Research Methodology
Chapter 12
Quantitative Data Analysis: Hypothesis
Testing

2. Types I errors, Type II
Errors &statistical Power
Type I error
: the probability of rejecting
the null hypothesis when it
is actually true.
Type II error
the probability of failing to
reject the null hypothesis
given that the alternative
hypothesis is actually true.

3. Statistical power
(1 - ):
 the probability
of correctly
rejecting the null
hypothesis.
alpha
Sample size
Effect
size

5. Testing Hypotheses on a Single Mean
 One sample t-test: statistical
technique that is used to test the
hypothesis that the mean of the
population from which a sample is
drawn is equal to a comparison
standard.

6. Testing hypothesis about two
related means
 Paired sample t-test to examine the differences
in the same group before and after treatment.
 The Wilcoxon signed-rank test: a nonparametric test for examining significant
differences between two related samples or
repeated measurements on a single sample.
Used as an alternative for a paired samples ttest when the population cannot be assumed to
be normally distributed.

7. RESEARCH METHODOLOGY OF TEN STUDENTS
IN THE FIRST WEEK AND LAST WEEK OF
SEMESTER

8. Testing hypothesis about two related
means
 McNemar's test: non-parametric method used on
nominal data. It assesses the significance of the
difference between two dependent samples when
the variable of interest is dichotomous. It is used
primarily in before-after studies to test for an
experimental effect.

9. Performance of student before and after
extra class

10. Testing hypothesis about two unrelated
means
• Independent samples t-test: is done to see
if there are any significant differences in
the means for two groups in the variable
of interest.

11. Testing hypothesis about several
means
• Analysis Of Variance (ANOVA) helps to examine
the significant mean differences among more than
two groups on an interval or ratio-scaled
dependent variable.

12. Regression Analysis
• Simple regression analysis is used in a
situation where one metric
independent variable is hypothesized
to affect one metric dependent
variable.

13. Scatter plot
100
LKLHD_DATE
80
60
40
20
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50
60
PHYS_ATTR
70
80
90

14. Simple Linear Regression
Yi
0
1
Xi
i
Y
ˆ
ˆ
ˆ
1
0
`0
1
0
X

15. Standardized regression coefficients
 Standardized regression coefficients or beta
coefficients are the estimates resulting from a
multiple regression analysis performed on
variable that have been standardized. This is
usually done to allow the researcher to compare
the relative effects of independent variable on
the dependent variable, when independent
variable are measured in different unit of
measurement.

16. Regression with dummy
variable
• A dummy variable (also known as an
indicator variable, design variable,
categorical variable, binary variable, or
qualitative variable)
• Dummy variable allow to use nominal or
ordinal variable as independent variable
to explain, understand, or predict the
dependent variable.

17. MULTICOLLINEARITY
• Encountered statistical phenomenon in which two or more independent
variables in a multiple regression model are highly correlated.
• It makes the estimation of the regression coefficients impossible and
sometimes unreliable.
• To detect multicollinearity, we must check the correlation matrix for the
independent variables.
• The high correlations is first sign of sizeable multicollinearity.
TWO MEASURES :
Tolerance value
Variance inflation factor ( VIF )
To measure indicate the degree to which one independent variable and explained
by the other independent variable.

18. A display of the FEV data in SPSS

19. • To fit multiple linear regression model in SPSS using the FEV
data do the following:
• Analyze > Regression > Linear and then move forced
expiratory volume into the dependent box and Smoke and age
into independent(s) box. Then Click OK.
• This will give you the model summary table, ANOVA table
and the regression coefficients table in the output window.

20. A demonstration of how to start fitting the multiple
regression model in SPSS

21. A demonstration of how to select the dependent and
independent variable(s) for fitting multiple regression in SPSS.

22. A demonstration of how to select diagnostic statistic for
checking outliers and
multicollinearity issues in SPSS.

23. Multicollinearity is not a serious problem, because the
estimation of the regression coefficients may be unstable.
But when the objective of the study is to reliably estimate the
individual regression coefficients, multicollinearity is a
problem.
The Methods to Reduce
Reduce the set of independent variables to a set that are not
collinear.
Use more sophisticated ways to analyze the data, such as
ridge regression.
Create a new variable that is a composite of the highly
correlated variables.

24. Testing moderating using regression
analysis : interaction effects
It is effect one variable ( X1 ) on Y depends on the value of
another variable ( X2 ).
Moderating variable as a variable that modifies the original
relationship between an independent variable and dependent
variable.
Example :
H1 : The students’ judgement of the university’s library is
affected by the students’ judgement of the computers.
-It’s means the relationship between the judgement of computers
in the library and the judgement of the library is affected by
computer ownership.
H2 : The relationship between the judgement of computers in the
library is moderated by computer ownership.

26. Other multivariate tests and
analysis
•
•
•
•
•
•
Discriminant analysis
Logistic regression
Conjoint analysis
Two-way ANOVA
MANOVA
Canonical correlation

27. Other multivariate tests and
analysis
• Discriminant analysis
-help to identify IV that discriminate a
normally scaled DV of interest.

28. Other multivariate tests and
analysis
• Logistic regression
-used when the DV is nonmetric
-always used when DV has only 2
groups.
-it allows researcher to predict discrete
outcome.

29. Other multivariate tests and
analysis
• Conjoint analysis
-statistical technique used in many fields.
-used to understand how consumers develop
preferences for product/services
-built on the idea that consumers evaluate
the value of a product or service by
combining the value that is provided by each
attribute.

30. Other multivariate tests and
analysis
• Two-way ANOVA
-used to examine the effect of two non
metric IV on a single metric DV
-enable us to examine main effects &
also interaction effects that exist
between the independent variables.

31. Other multivariate tests and
analysis
• Two-way ANOVA
-example
DV : Satisfy with toy
IV : i) toy colour (pink & blue)
ii) gender (male & female)
 Main effect of toy colour. Pink toys significantly more
satisfaction than the blue toys.
 Main effect of gender. The female are more satisfy with the
toy than the male

32. Other multivariate tests and
analysis
• Multivariate Analysis of Variance
(MANOVA)
-is a multivariate extension of analysis of
variance.
-the IV measured on a nominal scale & the
DV on interval/ratio scale
i) The null hyphothesis:
Hₒ
:µ1=µ2=µ3... µn
ii) The alternate hyphothesis:
HA:µ1≠µ2≠µ3≠... µn

33. Other multivariate tests and
analysis
• Canonical correlation
-examine the relationship between two or
more DV & several IV

34. Data warehousing
•
Most companies are now aware of the benefits of
creating a data warehouse that serves as the central
repository of all data collected from disparate
sources including those pertaining to the company's
finance, manufacturing, sales, and the like.

35. Data Mining
• Complementary to the functions of data
warehousing, many companies resort to data
mining as a strategic tool for reaching new levels of
business intelligence.
• Using algorithms to analyze data in a meaningful
way, data mining more effectively leverages the
data warehouse by identifying hidden relations and
patterns in the data stored in it.

36. Operations Research
• Operations research (OR) or management science
(MS) is another sophisticated tool used to simplify
and thus clarify certain types of complex problem
that lend themselves to quantification.