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Transcript
Statistical
Reasoning
Chapter 1, Lecture 3
“To be an educated person today is to be able to apply
simple statistical principles to everyday reasoning.
One needn’t memorize complicated formulas to think
more clearly and critically about data.”
- David Myers
Statistical Reasoning
Statistical procedures analyze and interpret data
allowing us to see what the unaided eye misses.
Composition of ethnicity in urban locales
Statistical Reasoning in Everyday Life
Doubt big, round, undocumented numbers
as they can be misleading and before long,
become public misinformation.
Apply simple statistical reasoning in
everyday life to think smarter!
Describing Data
A meaningful description of data is important in
research. Misrepresentation may lead to
incorrect conclusions.
Measures of Central Tendency
Mode: The most frequently occurring score
in a distribution.
Mean: The arithmetic average of scores in a
distribution obtained by adding the
scores and then dividing by the number
of scores that were added together.
Median: The middle score in a rank-ordered
distribution.
Measures of Central Tendency
A Skewed Distribution
Measures of Variation
Range: The difference between the highest and
lowest scores in a distribution.
Standard Deviation: A computed measure of
how much scores vary around the mean.
Standard Deviation
Page 36
Normal Curve
A symmetrical, bell-shaped curve that
describes the distribution of many
types of data (normal distribution).
Most scores fall near the mean.
Remember the 68-95-99.7 rule???
Illusion of Control
That chance events are subject to personal control
is an illusion of control fed by:
1. Illusory Correlation: the perception of a
relationship where no relationship actually
exists.
2. Regression Toward the Mean: the tendency
for extremes of unusual scores or events to
regress toward the average.
Making Inferences
A statistical statement of how frequently
an obtained result occurred by
experimental manipulation or by chance.
Making Inferences
When is an Observed Difference Reliable?
1. Representative samples are better than biased
samples.
2. Less-variable observations are more reliable
than more variable ones.
3. More cases are better than fewer cases.
Making Inferences
When is a Difference Significant?
When sample averages are reliable and the
difference between them is relatively large, we say
the difference has statistical significance. It is
probably not due to chance variation.
For psychologists this difference is measured
through alpha level set at 5 percent.
Interesting Statistical Facts
Given any two people in the United States, how many
intermediaries are necessary, on the average, before
the two are in communication, assuming that the
intermediaries may only contact people they know on
a first-name basis?
5 people
Imagine a huge piece of paper about the thickness of
one textbook page. If it were folded in half 50 times,
how thick would it be?
About 50,000,000 miles
Interesting Statistical Facts
Assuming a world population of about 6.5 billion, if
we gathered everyone together and allotted each
person a generous two-by-two feet of ground, how
large an area would we need?
About 933 square miles, considerable less than
Rhode Island’s 1545.
What if we allowed everyone to sit comfortably in
216 cubic feet (6 feet on a side)?
Every human being on earth would fit
comfortably into the Grand Canyon.
Homework
Read p.38-43
Now let’s practice calculating some of
our own statistics from the data gathered
on Handout 1-12…