Transcript [Product Name] Marketing Plan

Statistics
Loyola Law School – Spring 2008
Doug Stenstrom
email: [email protected]
phone: (213)422-0909
http://www.psychwiki.com/wiki/Statistics_Spring_2008
Purpose of the Course
After completing this course, you will be able to:
• Theory:
Well-versed on statistical concepts and theorizing;
understand underlying methodology behind
statistical reasoning and problem solving
• Application: Analyze data using all the major statistical
techniques using most popular software
• Evaluation: Critically examine and understand statistical
claims; learn to interpret “Results” sections,
statistical criteria, news articles, etc.
• Also… Write a “Results” section
Know the vocabulary/terminology of statistics
Today’s objective
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Overview of the course
Help you map out your semester (e.g., time, tasks, etc.)
Discuss the underlying THEORY behind Statistics
Answer questions you may have about statistical
process
Why Statistical reasoning is important:
• Information bombardment! Is there data?
• If you cannot distinguish good from faulty reasoning,
then you are vulnerable to manipulation
• Applicable to all areas of life, such as health,
business, sports, politics, personal relationships, etc.
– Almost 85% of lung cancers in men and 45% in women are
tobacco-related.
– People tend to be more persuasive when they look others
directly in the eye and speak loudly and quickly.
– A surprising new study shows that eating egg whites can
increase one's lifespan.
– News today – “Justices Hear Arguments in Lethal Injection Case”
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http://www.cnn.com/ELECTION/2008/primaries/results/epolls/index.html#IADEM
Overview of the Research Process
Pre-production
Pre-production
Research
Idea
Research
Design
Pick a topic
Translate topic into Question
Translate into Hypothesis
Preemption search
Production
Production
Collecting
Data
Post-production
Post-production
Analyzing
Data
Approval for study via IRB
Preparation to conduct study
Recruiting subjects
Conducting the study
Coding and entering data
Selecting the methodological approach
Operationalizing variables/materials
Crafting procedures/paradigms
Determining sample
Evaluating the practicality of the research
Publication
Process
Deciding when to start writing paper
How to write psychology manuscripts
How to write in APA format
How to decide where to submit manuscript
Journal review process
Talks, posters, and other ways to disseminate your work
Data preparation and screening
Evaluating sample statistically
Evaluating materials statistically
Evaluating procedures statistically
Analyzing research Hypothesis
Interpreting the results
Most people find statistics to be difficult
to learn because of the way it is taught
• Old way = Bottom-up
This class = Top-down
• Old way = Disconnect between class and real-world
This class = Learn both Theory and Application
• Old way = Overwhelming complexity
This class = Read textbook AFTER class is over
Syllabus
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I would suggest getting the textbook for three reasons…
How to read the textbook…
What will happen in class each day…
What will be covered this semester…
Motivation!
• Statistics can be boring
• I would suggest having your own data…
• The class is structured so that you don’t
need your own data
• The class is also structured so that we can
analyze your data during class
THEORY
(what is statistics?)
10 statements to understand the
theorizing behind statistics
(1) In every study there is error.
• Error is the difference between your study
(sample) and the true value (population)
• Measurement error
• Sampling Error
(2) Since there is error, there is
always some doubt
• Imagine you were conducting a study about
whether males or females are happier…
• Given the error, you may find a difference (sample)
when one does not exist (population);
• Or, you may find no difference (sample)
when in fact one does exist (population).
(3) Since there is some doubt, you are
dealing with PROBABILITIES of being
right/wrong
• Any outcome you receive (sample), you need to
determine the probability or percentage of being
right (population), such as 90% confident, 80%
confident, 55% confident, etc.
(4) You calculate probabilities using
a “probability distribution”
• A probability distribution describes the frequency
or probabilities that an event can take
• Given any probability distribution, you can
calculate the probability of any given score
taking place.
(5) But how do we know the “probability
distribution” of the entire population?
• We DON’T!
(6) Instead, we assume it
approaches a “normal” distribution.
• A normal distribution is a symmetric bell-shaped
curve defined by two things: the mean (average)
and variance (variability).
• The idea behind statistics is that as sample size
increases, distributions will approximate normal.
(6) Instead, we assume it
approaches a “normal” distribution.
• Also, the sampling distribution
of the sample means
approximates normal,
even if the population from
which the sample is taken is
not normal.
• http://www.ruf.rice.edu/~lane/stat_s
im/sampling_dist/index.html
(7) Statisticians have already created
distributions for all possible situations
• For every type of statistical test (e.g., correlation,
regression, t-test, ANOVA, etc) and for every
type of situation (e.g., sample size, group size,
degrees of freedom, etc) statisticians have
created probability distributions to fit that
situation.
(8) And, they have determined
“Rejection Regions” based upon how
much doubt you are willing to live with
• Given the doubt involved in research, how much
doubt are you willing to live with?
(9) “Statistics” is about comparing your
Sample (Test Statistic) to the
Population (Distribution and Rejection Regions)
Three step process:
• Step 1 - Calculate Test Statistic (Your Sample)
• Step 2 – Obtain Sampling Distribution and
Rejection Regions (Population)
• Step 3 – Compare your Sample to the Population.
EXAMPLE
• Step 1 - Calculate Test Statistic (Your Sample)
– For every type of statistical test (e.g., correlation, regression,
t-test, ANOVA, etc), statisticians have created a formula for
that test that measures how much variance is explained by
sample.
– In our “happiness” study, males=4.2 females=4.8
From our study we know means, standard deviation, size.
Plug those numbers into t-test formula.
Lets say the formula tells us that t=3.2
EXAMPLE
• Step 2 - Obtain Distribution and Rejection Regions
– (As indicated by statement #7 and #8) For every type of
statistical test (e.g., correlation, regression, t-test, ANOVA,
etc) and for every type of situation (e.g., sample size, group
size, degrees of freedom, etc) statisticians have created
probability distributions and rejection regions to fit that
situation.
- In our “happiness” study, here is distribution:
EXAMPLE
• Step 3 – Compare your Sample to the Population.
– If your “Test Statistic” falls in rejection region, then we have
LESS than 5% doubt, so we consider the outcome of the
study as valid
– In our example, 3.2 is in the rejection region
(10) Thus, the theorizing behind
conducting statistics is:
anytime you conduct a statistical test,
we calculate the probability that the
outcome is wrong,
and if we calculate a 5% or less chance
of being wrong, we accept the
outcome as valid (called “significant”).
10 statements
(1)
(2)
(3)
(4)
(5)
(6)
(7)
(8)
(9)
In every study there is error.
Since there is error, there is always some doubt.
Since there is doubt, you are dealing with Probabilities of being right/wrong.
You calculate probabilities using a “probability distribution”.
But how do we know the “probability distribution” of the entire population?
Instead, we assume it approaches a “normal” distribution.
Statisticians have already created distributions for all possible situations.
And they have determined “Rejection Regions” based upon 5% doubt.
“Statistics” is about comparing your Sample (Test Statistic) to the
Population (Distribution and Rejection Regions).
(10) Thus, the theorizing behind conducting statistics is: anytime you conduct a
statistical test, we calculate the probability that the outcome is wrong, and if
we calculate a 5% or less chance of being wrong, we accept the outcome
as valid (called “significant”).