Quantitative Studies
• Descriptive researcher is
concerned with
finding out who,
where, when or how
much
• AS IT IS
• Experimental researcher is
concerned with
learning why, how
one variable
produces change in
another
• CAUSE & EFFECT
RELATIONSHIPS
Descriptive and Casual
• Whatever the type, both
– demand good research skills
– insist on the same high standards for design and
execution
Cause
• Referring to a kind of prediction
• predictions can be considered to reflect
cause only when all the relevant
information is considered
• of course, we can never know all the
relevant information
Descriptive Research Designs
– Correlational research
– developmental designs
– observation studies
– survey research
• all of these approaches yield quantitative
data that can be summarized through
statistical analyses.
Correlational Research
• Examines the extent to which differences in
one variable are related to differences in one
or more other variable
• A correlation exists, if when one variable
decrease, the other variable either increases
or decrease in a somewhat predictable
manner
Data Pairs
• Every data point is a pair, one for each of
the characteristic being measured.
• The researcher uses these pairs to calculate
a correlation coefficient.
• Using a scattergram allows a visual
inspection of the relationship between
variables.
Age
Reading Grade Level
Values of correlation coefficient
•
•
•
•
Range +1.00 (perfect positive correlation)
-1.00 (perfect negative correlation)
0.0 (unrelated)
Rare to find perfect correlation, generally
moderate
Inspecting a Scattergram
• Look at the extent the homogeneity of the
variables (only C program with LOC >
5,000) or heterogeneity (C and VB program
from 500 to 10,000 LOC)
• Describe the degree to which the variables
are related ( correlation coefficient)
• Interpret these data and give them meaning
An Example of a Correlational
Study
A Correlational Study of the
CMM and Software
Development Performance
The Software Engineering Institute's (SEI)
Capability Maturity Model (CMM) is widely used
to measure an organization's software
development process maturity. The Department of
Defense (DoD) has adopted this model with the
belief that a more mature software development
process will result in a more successful software
project. Although there is a growing body of
anecdotal evidence that supports this presumed
correlation, we were unable to find any studies
that validate this premise.
The study reported in this article--master's thesis research
at the Air Force Institute of Technology (AFIT)--set out to
find empirical evidence to determine if the premise could
be validated. The goal of our research was to determine the
nature of the correlation, if any, between software process
maturity and software project success. We measured
process maturity using a CMM rating, and success was
measured using cost and schedule indicators.
First, we provide an introduction to the concepts and
definitions we used in our work. Then, we provide details
of our methodology, that describe our approach. Finally,
we provide the details of our analysis, then summarize our
results.
The key assumption is that there is a significant positive
correlation between the SEI CMM rating and the success
of the software development.
Although the concept of "success" in terms of software
development has many definitions, a consistent theme
found in software engineering literature is that success
can be measured as a combination of cost, schedule, and
quality performance
It is important to note that all of the data points had CMM
ratings of 1,2, and 3. It is still highly unusual to find
organizations with higher ratings, so these represent the
expected data values. However, it means that our research
findings are only valid for these three CMM levels.
CMM rating data is at best ordinal in nature. Hence,
statistical analysis techniques such as multiple linear
regression, which require interval or ratio data, cannot be
rigorously applied. However, a combination of descriptive
and nonparametric techniques are adequate to establish the
presence or absence of a statistically significant
correlation of software process maturity and software
development success.
Scatter plots are used to visualize data by plotting two
elements of each data point. Box and whiskers plots
show similar data except that they indicate data
groupings by a box and outliers by "whiskers," rather
than plotting each individual point. For our analysis we
used plots of CPI vs. CMM rating as well as SPI vs.
CMM rating.
In project management, the Cost Performance Index (CPI) and the
Schedule Performance Index (SPI) are the standard indices in use.
Actual Cost of Work Performed (ACWP) is the sum of funds
actually expended in the accomplishment of the planned work tasks.
The Budgeted Cost of Work Performed (BCWP) represents the
earned value of the work performed and is an estimate of the value
of the work completed. Deviations in the actual vs. planned cost can
be expressed in the ratio of BCWP to ACWP. This is called the Cost
Performance Index (CPI).
CPI = BCWP/ACWP
A CPI of less than 1.00 implies that for every dollar of value
earned, more than one dollar was actually spent--a cost overrun. A
CPI of more than 1.00 implies that for every dollar of value
earned, less than one dollar was spent, and a CPI of 1.00 implies
an "on-target" condition.
Similarly, the projected rate of funds expenditure is the
Budgeted Cost of Work Scheduled (BCWS), which can be
expressed as the planned expenditure of funds over time,
based on the completion of the planned work packages. The
ratio of BCWP to BCWS defines the degree to which a project
is ahead of or behind schedule and is called the Schedule
Performance Index (SPI).
SPI = BCWP/BCWS
An SPI of less than 1.00 implies that for every dollar of work
scheduled, less than one dollar has been earned--a schedule
overrun. An SPI of more than 1.00 implies that for each dollar
of work scheduled, more than one dollar of work has been
earned, and an SPI of 1.00 implies an on-target condition.
At Level 1, the central tendency
is somewhere below the target,
and the distribution exhibits a
high variance.
At Level 2, the central tendency
of the distribution is now on or
very near the target, but the
distribution still exhibits a high
degree of variance.
At Level 3 and above, the central
tendency of the distribution is the
same as the target, and the
variance of the distribution
decreases as the CMM rating
increases
The indices of CPI and SPI are the standard cost
and schedule performance measures for both
government and industry. The closer the CPI and
SPI are to a value of 1.00, the more successful the
project can be considered, at least in terms of cost
and schedule . This establishes our performance
baseline against which we can compare actual
performance data.
Very High Relevance - The project under consideration was
the sole project evaluated in the CMM rating process.
The Kruskal-Wallis Test is a nonparametric analysis of variance, testing the
null hypothesis that samples subjected to different treatments, e.g., CMM
ratings, actually belong to the same population. The rejection of the null
hypothesis suggests that the populations are different. In our analysis, the
rejection of the null hypothesis suggests there is a difference in the median
performance of organizations at different maturity levels.
The Kruskal-Wallis Test can only determine if at least two of the samples are
from different distributions. To determine if there is a statistically significant
difference in more than one pair of samples and which samples differ from
which others, a multiple comparison test is required. The multiple comparison
test compares the absolute values of the differences of the mean ranks between
two samples to determine if there is a significant difference in the two
samples. It is important to note that the overall level of significance used in
multiple comparisons frequently is larger than those ordinarily used in an
inference involving a single comparison. Our multiple comparison test was
performed at a level of significance of 0.2, which implies an 80 percent level
of confidence in the result. This is consistent with recommended values for
this type of nonparametric analysis technique [2].
The aim of our research was to determine the nature of a correlation between the
CMM rating and software development success. Though success is difficult to
measure directly, by using the indicators of cost and schedule performance, we
were able to show correlation between CMM rating and the cost and schedule
performance of a generally representative sample of historical software
development contracts.
We observed improved cost and schedule performance with increasing process
maturity. Specifically, the least mature organizations were likely to have difficulty
adhering to cost and schedule baselines. In contrast, the more mature organizations
were likely to have on-baseline cost and schedule performance. This observed
correlation was evident in the data set as a whole, but was more evident in the
sample which had high to very high rating- to-project relevance. The correlation
was more evident in cost performance than in schedule performance.
This study has validated a correlation between project success and
CMM ratings established in the same time frame as the project
development.Although this result suggests that CMM ratings
might be used as a predictor of future project success, more
research is required before such a predictive relationship can be
established.
Cautions About Interpreting
Correlational Results
• Need to aware of whether you are attempting to
corroborate an association or a casual relationship.
• For example, there is a significant correlation
between the number of storks in Scandinavia and
the human population. However, we do not
believe that killing storks will reduce human
population level, because the relationship is
associative not causal.
• Correlational is just a sign-post
How Validity and Reliability
Affect Correlation Coefficients?
• Is only as accurate as the instrument we are
using to measure. -> The Budgeted Cost of Work
Performed (BCWP) represents the earned value of the
work performed and is an estimate of the value of the
work completed-> this is wrong or inaccurate
• Only can find substantial correlations if both variables are
measured with a reasonable degree of validity and
reliability.
Developmental Designs
• How something changes over time (as
people grow older)
• Cross-sectional - several different age
groups
• Longitudinal – single group over the course
of time
Observation Studies
• Focus on a particular aspect of behavior
• Each is either counted to determine overall
frequency or rated for accuracy, intensity, maturity
or some other dimension
• Researcher - objective as possible
• The versatility of observation makes it an
indispensable primary source method and
supplement for other methods
• In a design we either observe or we communicate
Observations
• Nonbehavioral observation
– Record analysis – (current financial records, economic
data)
– Physical condition analysis ( financial condition)
– Physical process analysis (time/motion studies of the
process)
• Behavioral observation – focus an particular
aspect and the behavior is quantified – different
than qualitative studies
Strengths of Observation
• Securing information about people or activities
that cannot be derived from experience or surveys
(small children)
• Avoiding respondent filtering and forgetting
(common details are left out and might be just as
important like weather, day of the week)
• Securing environmental context information
• Optimizing the naturalness of the setting
• Reducing obtrusiveness
Limits of Observation
• Difficulty of waiting long periods to capture
phenomena
• Expense of observer costs and equipment
• The reliability of inferences from surface
indicators
• The problems of quantification and
disproportionately large records
• Limitation of present activities and inferences
about cognitive processes
Survey Research
• Get a better idea of present
• Captures a fleeting moment in time
• Conjecture – extrapolate over a longer a
period of time
• When reading survey reports keep in mind
that the researcher samples a population at
one particular time – nothing is permanent
but change
Survey Methods
• Face to Face and Telephone Interviews
• Questionnaires
Interviews
• Make sure your interviewees are representative of
the group
• Find a suitable location
• Take a few minutes to establish rapport
• Get written permission
• Focus on the actual rather than on the abstract or
hypothetical
• Don’t put words in people’s mouths
• Record responses verbatim
• Keep your reactions to yourself
• Remember that you are not necessarily getting the
facts
Constructing a Questionnaire
• Short, simple, unambiguous
• Check for implicit assumption
– How many cigarettes do you some each day? (This implies that it
is the same number each day.)
• Do not give clues about desirable responses
– What strategies have you tried to quit smoking (May never have
tried, but desirable so gives you all kinds that seriously were never
tried.)
• Check for consistency (have 2 questions especially on
socially acceptable answers)
Sampling
• Want generalizations – if the sample is truly
representative of the population
• 2 approaches
– Probability
– nonprobability
Probability Sampling
• The researcher can specify in advance the segment
of the population
• Random selection – pure chance must dictate
choice
• Simple random – every member of the population
has an equal chance
• Stratified random – equally from each of the
layers in the population
• Cluster – a subset of identified cluster is selected
• Systematic sampling – selecting according to a
predetermined sequence
Appropriate Technique
• Generally
homogeneous
• Contains strata that are
approx. equal in size
• Contains strata that
appear in different
proportions
• Contains
heterogeneous clusters
• Simple random
sampling
• Stratified random
sampling
• Proportional stratified
random sampling
• Cluster sampling or
systematic sampling of
clusters
Nonprobability Sampling
• Convenience – no pretense of identifying a
representative subset of the population, just
what’s available
• Quota sampling – bases selection upon the
same proportions found in general public.
• Purposive sampling – choose a combination
of a voting districts, in the past elections,
quite useful in predicting final outcomes
Sufficient Sample Size
•
•
•
•
•
•
The larger the better
Small populations (less than 100) use entire
Around 500, 50% sampled
Around 1500, 20% sampled
Above, 400 sampled
Also more heterogeneous the population,
the larger the sample
Bias in Research Sampling
• Bias is any influence, condition, or set of
conditions that singly or together distort data
• In sampling, example telephone book, selecting
from here, the poorest do not have, the richest are
not listed
• People not listed have a 0% chance of being
selected
• Mailed questionnaire on IRS audits with only a
30% return rate. These people many not be
representative of the original population. (
respondents not wanting to indicate that they have
been audited will throw it away.)