Statistical Analysis
Construction Engineering 221
Decision Making Under Uncertainty
Statistics
• “Statistics” has several meanings in the
general public
– The data on performance (the game stats)
– A particular calculation made from the data
(mean, median, deviation, etc.)
– A field of study whose objective is to improve
decision making under conditions of imperfect
information
Statistics
• Statistics is poorly understood by the general
public, misused by government agencies and
academic researchers, and abused by special
interest groups:
– A researcher counts every observation twice in order to
increase sample size in an effort to achieve statistically
significant results
– The often quoted “10% of the population is gay” is
based on a study where 10% of a prison population
was found to have engaged in homosexual behaviors
Statistics
– A radical feminist researcher at a university
published a report stating that the majority of
married women were unhappy and married men
were happy, thereby “proving” that marriage
was an institution of oppression
– A report commissioned under the Reagan
Administration found that men who view
pornography and adult magazines are more
likely to commit rape, so Playboy was banned
from military bases and federal prisons
Statistics
• What’s wrong with these studies?
– Statistical significance is not the same as
practical significance. If you sample large
enough, the test will be significant, but the
result meaningless. Also, counting every
observation twice biases the sample.
– Results from a prison population cannot be
generalized to the general public because
prisoners are not a representative sample
Statistics
– The feminist researcher measured unhappiness by how
often a married person cried. Crying under stress is
much more common among women than men. When
anger or withdrawal is included (male reactions to
stress), the unhappiness with marriage is equal.
Measurement must be free from bias
– In the Meese study, men were randomly sampled, but
age was not controlled for. Most rapes are committed
by young people, and most adult magazines are read by
young people. It is being young that creates the risk.
The relationships were poorly understood
Statistics
• Good statistical studies:
– Are done right the first time (don’t redo the
data until you get the result you want)
– Have representative samples of the population
under study
– Use unbiased measurement of the
characteristics under investigation
– Understand the relationships (use theory to set
up the statistical analysis)
Statistics
• Statistics was first developed for agricultural
applications (animal breeding, plant crossfertilization, etc.)
• Even today, most top statistics departments are in
state ag schools (ISU, Texas A & M, Colorado
State)
• Current important uses are in medical research,
risk management and decision theory, quality
control, market research, advertising, insurance
Statistics
• For our class, statistics will be used as a
method for improved decision making in
situations of incomplete information, or in
other words, a tool for risk management
Statistics
• Two types or uses of statistics
– Descriptive- describe the data or observations
found in the sample
• Pictorial descriptions: histogram, bar or pie chart,
line graph, frequency distribution, classification
• Numerical description: mean, median, mode, range,
variance, standard deviation
Statistics
• What can descriptive statistics tell us? (how
something is different or the same)
Statistics
• In a normal distribution, each ½ standard
deviation captures 19%, 15%, 9%,, 5% of
the variation in observations. (rule of 9’s
and 5’s)
2% 7% 16% 31% 50% 69% 84% 93% 98%
Statistics
– Inferential statistics
• Decision made about a population based on sample
(incomplete) data:
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–
–
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Random samples representative of the population
Hypotheses tests and the null hypothesis
Confidence intervals
Shape of distribution
Statistics
• What could we infer from the Exam 3
scores in this class?
– What population does the Con E 221 class
“represent” (sampling)
– What relationships could we build (time spent
studying for the test, class attendance, pages
read in the text, homework completed on time)
– How would we measure our variables