Download Basic Quantitative Data Analysis: Statistics

Research Design: Quantitative
Methods:
Elementary Statistics
Dr Sng Bee Bee
Taught by Dr. Sng Bee Bee • Singapore Bible College
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Lecture Objectives
Describe the experimental and quasiexperimental research approaches
Formulate appropriate questions and
hypothesis
Identify populations and samples
Describe the principles of research
tool design
A Research Design
collection
Describe the
purpose of study
and kinds of
questions being
addressed
A Research
Design is an
overarching
plan for
Analysis of
data
measurement
The Structure of
Experimental Design
Involves THREE Steps
STEP
ONE
Planning Stage
• Research Aim and
questions posed
• Relevant theories and
literature investigated
• Formulate research
hypothesis
• Identify dependent and
independent variables
STEP
TWO
Operational
Stage
Conduct of
the
experiment
STEP
THREE
Analysis of the
data
• Descriptive
statistics
• Inferential
statistics
Stages in planning of experimental and quasiexperimental research
Planning Stage
Identify the issue or questions of
interest
Review relevant literature and
theories
Develop questions and hypothesis
Identify independent and dependent
variables
Source: Gray, D.E. (2009), Doing Research in the Real
World (2nd ed.). London: Sage
Stages in planning of experimental and
quasi-experimental research
Operational Stage
Conduct the study
Use descriptive statistics to describe data
Develop questions and hypothesis
Accept or reject hypothesis
Source: Gray, D.E. (2009), Doing Research in the Real
World (2nd ed.). London: Sage
Statistics
Statistics concerned with the
collection, organization, and
interpretation of data according to
well-defined procedures.
Population and sample
Descriptive statistics methods
summarize, organize, and simplify
data.
 Inferential statistics consist of
techniques that allow us to study
samples and then make
generalizations about the population
from which they were selected.
Descriptive Statistics: Frequency
Distribution
Frequency distribution : A record of
the number of individuals located in
each category on the scale of
measurement.
Proportion
Percentages
Central tendency
Central tendency is a statistical measure that
identifies a single score as representative of
an entire distribution. The goal of central
tendency is to find the single score that is
most typical or most representative of the
entire group.
Central tendency
Central tendency: mean, median and mode
1. Mode
Most frequently occurring score(s)
Example:
3 5 9 6 8 8 5 4 5 7
Mode = ?
3 4 5 5 5 6 7 8 8 9
Mode = 5
Mode (continue)
It is a fast way to obtain central tendency but
it is not reliable.
3 4 5 5 5 6 7 8 8 9
Mode = 5
3 4 5 5 8 6 7 8 8 9
Mode = 8
Measure Central Tendency
2. Mean
Average: Add up all the scores and divide by
number of scores.
3 4 5 5 5 6 7 8 8 9
Mean = (3+4+5+5+5+6+7+8+8+9)/10
= 60 / 10 = 6


It is the best way to show the central tendency of
scores, since in calculating it every score is
involved.
For population use , for population use X
Mean (continue)

Extreme high or low score(s) will
influence it as a good representative of
central tendency.
3 4 5 5 5 6 7 8 8 9
Mean = 6
3 4 5 5 5 6 7 28 8 9
Mean = (3+4+5+5+5+6+7+28+8+9)/10
= 80 / 10 = 8
Measure Central Tendency
3. Median

A point that divides a set of scores into two equal
halves. There are same numbers of scores above
and below it.
3 4 5 5 5|6 7 8 8 9
Median = (5 + 6)/2 = 5.5
5 5 3 6 7|8 9 4 8 5
3 4 5 5 6 7 8 8 9
Median = 6
Median (continue)
It is not influenced by extreme scores.
3 4 5 5 5|6 7 8 8 9
Median = 5.5
3 4 5 5 5 6 7 28 8 9
3 4 5 5 5 | 6 7 8 9 28
Median = 5.5
Selection of Central Tendency



Usually mean is the best representative
If extreme value is included, median is the
best representative
For category information, mode is the only
choice
(Compare score band across classes or schools)
Standard Deviation
Standard Deviation is most commonly
used and the most important measure
of variability.
It uses the mean of the distribution as a
reference point.
It measures variability by considering the
difference between each score and
the mean.
Normal distribution
 normal distribution is standard, there is a
known percentage of scores It is a
symmetrical, bell-shaped distribution.
 Because the shape of
- About 34% of the scores fall between the mean
and 1 SD from the mean.
- About 14% of the scores fall between 1 SD and
2 SD.
- Close to 2% of the scores fall between 2 SD and
3 SD.
Normal Distribution
Conduct a survey
 In your group, use the questionnaire survey you
designed earlier to investigate the following
situation.
 Attitudes towards the use of contemporary music in
worship services in your church in your country
 Design a set of 5 descriptors, e.g. “Must be very
charismatic”; “Must have contemporary musical
instruments”
 Design a Likert scale 1 to 5, 1 – Agree Absolutely, 2Very much agree, to 5-Totally Disagree
 Conduct the survey in class
 Compile your results
 Calculate the Mean, Mode, Median, Average and
Standard Deviation of your results.
Hypothesis testing
Hypothesis testing is an inferential
procedure that uses sample data to
evaluate the credibility of a
hypothesis about a population.
 Four steps are usually included in
the procedure of hypothesis testing
Hypothesis testing
Step 1: Stating the hypothesis
 Null hypothesis (H0) states that the
independent variable (treatment) has no
effect on the dependent variable for the
population.
Example: H0 : final score = 70
 Alternative (scientific) Hypothesis (H1)
predicts that the independent variable
(treatment) will have an effect on the
dependent variable for the population.
Hypothesis testing
Step 2: Setting the criteria for a decision
Set a criteria for making the right decision
when we reject the null hypothesis
Step 3: Collecting sample data
Collecting data is the procedure to design
and conduct a study.
Step 4: Evaluating the null hypothesis
 Reject the null hypothesis
 Fail to reject the null hypothesis
ANOVA: Analysis of Variance
Single factor (one-way) experiment
involves a single independent
variable.
One independent variable can be
called as a factor in statistics.
Levels of the independent variable?
Correlation
Correlation
Correlation
Correlation is a statistical technique that
is used to measure and describe a
relationship between two variables.
Characteristics of a relationship
1. The direction of the relationship
Positive, Negative, Zero
2. The degree of the relationship
(correlation coefficient)
(from -1 to +1)
Summary
 Descriptive statistics
Central tendency: mean, media, mode
Variability: standard deviation
 Inferential statistics: hypothesis testing
Significant and P value
Z test
Independent t test: two independent
groups
t test for related groups
F test: more than 2 groups
Correlation r
Experimental and
Quasi-Experimental
Designs
Quasi-Experimental Design
Source: Gray, D.E. (2009), Doing Research in the
Real World (2nd ed.). London: Sage
 Research has suggested that teenage pregnancy has
significant effects on girls in terms of their later income level,
educational attainment and general welfare – putting them
on a lower rung of the economic ladder. But it is also
acknowledged that teenage pregnancy is more common
among lower income families, a potentially confounding
factor.
 It is not possible to randomly assign teenage girls to become
or not to become pregnant. This problem can be overcome
by using as a non-equivalent group, the sisters of girls who
became pregnant in their teens, but who themselves did not
become pregnant until at least the age of 20. This allowed
the researchers to control for the family economic
disadvantage variable. When the data were analysed, it
was found that the previously negative effects associated
with teenage pregnancy were not as pronounced as
expected.
Discuss the following
questions in relation to the
previous case.
1.Why is this a quasi-experimental rather
than an experimental study?
2.Why is it that the greater incidence of
teenage pregnancy among lower income
groups is a confounding factor for this
particular study?
Source: Gray, D.E. (2009), Doing Research in the
Real World (2nd ed.). London: Sage
Answers
Source: Gray, D.E. (2009), Doing Research in the Real World (2nd
ed.). London: Sage
1. This is a quasi-experimental study because
there was no opportunity to randomly assign
subjects to the condition (pregnancy)
2. The objective of the research is to examine the
impact of teenage pregnancy on later income
levels, educational attainment and general
welfare. If teenage pregnancy was evenly
spread across all income groups, the
independent variable of income level would be
controlled for. Unfortunately, as we are told, this
is not the case. Lower income families tend to
have higher incidences of teenage pregnancy –
which could confound the results.
Experimental Group with
Control
Subjects are
randomly
assigned to each
of the
experimental
and control
group
All
independent
variables are
controlled
Review Basic Concepts
Related to Experiment
 Any examples?
 Experiment of using new teaching method
 Characteristics
(At least) two variables, one of them is
manipulated by researcher (manipulated or
independent variable)
Other variables (extraneous variables) were
controlled
Causal relationship: effect of manipulated variable
on other variable (dependent variable)
Basic Steps Conducting Experiment
 Identify the causal research problem(s)
 Operationally define the manipulated variable(s) and the
dependent variable(s) in the experiment
 Select suitable experimental design
 Decide the ways of controlling extraneous variables
 Select participants and collect data
 Perform statistical analysis and interpret the results
Control extraneous variables
 While there are an infinite number of extraneous
variables in any situation, we need normally
worry only about those that might have an
influence on the dependent variable.
 Four general approaches:
1. Hold extraneous variables constant or eliminate
extraneous variables
2. Balance the possible extraneous variables
3. Include extraneous variable as an independent
variable
4. Statistical control
Example
You want to study how a course on ‘Crosscultural communication’ helps your church
members to be more effective in reaching
people of different cultures.
The experimental group would receive the
treatment, i.e. the training on ‘Cross-cultural
Communication’.
The control group will not receive any training.
If the test scores of the experimental group are
higher than the control group, then the training
has been effective.
Factorial Design
Sometimes, it is necessary to investigate
the impact of changes in two or more
variables
Reason 1:
Reason 2:
Hence
• there is more than one hypothesis to confirm or
reject
• explore relationships and interactions between
variables
• a factorial design is used which allows us to look
at all possible combinations of selected values.
Experiment
For example, you want to find out
which combination of factors gives
rise to better attentiveness in your
sanctuary
Dull light, combined with both
heat and cold
Bright/hot conditions
Interactions of brightness with cold
2 x 2 factorial design
LIGHT
Cold
Heat
Hot
Dull
Bright
Dull/cold
Bright/cold
Hot/dull
Hot/bright
Summary
 The structure of experimental research generally
comprises two stages: planning stage and
operational stage
 Experimental designs begins with research
question and hypothesis that the research is
designed to test. Research questions should
express a relationship between variables. A
hypothesis is predictive and capable of being
tested.
 Dependent variables are what experimental
research designs are meant to affect through
the manipulation of one or more independent
variables.
Summary
 In a true experimental design, the researcher has
control over the experiment: who, what, when,
where and how the experiment is conducted.
This includes random sampling.
 Where any of these elements of control is either
weak or missing, the study is known as quasiexperiment.
 In true experiments, it is possible to assign
subjects to conditions, whereas in quasiexperiments, subjects are selected from
previously existing groups.
 Research instruments need to be both valid and
reliable. Validity means that an instrument
measures what it is intended to measure.
Reliability means that an instrument is consistent
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