Inferential Statistics
Today and next thursday
Check in
• Method Draft due today
• 3rd article assignment is posted
– It is due November 29th
• For Tuesday: Articles for in-class discussion
– These are popular media articles about problems in
research, it should be a fun discussion
– Please come with one question or comment about
each article
– I will bring snacks!
Before we get to statistics…
• Proposal draft
– More about writing an introduction
The structure of an introduction
• 1st paragraph
– A general introduction of the problem with
some references
• 2nd paragraph
– Often begins with theory or empirical studies
• 3rd paragraph
– May continue this…and more paragraphs if
necessary
More introduction
• 4th paragraph…and perhaps more
– Identifies where you will add to the research
– May focus on methods, or limitations or
previous studies
• 5th paragraph
– Summarizes what you have said in brief
– States the research questions or hypotheses
clearly and in moderate detail
Now back to statistics
• Inferential statistics: Today
– Null and alternate hypotheses
– Type I and Type II error
– The “normal curve” the “empirical rule” and
probability
– The Chi-squared test
Stating hypotheses
• Comes before any statistics
• Uses basic language
• But requires careful thinking about the
language you use
• Thinking that stems from the scientific
approach
– We never prove anything
– We only find support for it
Hypothesis testing
• Divides a study into two possible
outcomes
– Study does not only mean experiment
– Can mean survey, observation, etc.
• Support for the “null hypothesis” or…
• Support for the “alternate hypothesis”
• You can only end up with one or the other
The null hypothesis
• Is usually what we don’t want to find
support for
– Note, we do not say it is what we “disprove”
– We can say that we “reject” it
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Perhaps a commonly accepted status quo
A stereotype
What we believe to be untrue
What was true once and is no longer true
The alternate hypothesis
• What we propose is actually the case
• Usually we have some reason to think that
things aren’t just “status quo”
• Its what we hope will emerge from our
study or data
– We say we “find support for it”
• But if it doesn’t emerge in our data
– We “fail to find support for it”
– We “fail to reject” the null hypothesis
The null hypothesis
• College students have high rates of casual
sex
– This could be a stereotype
– A pop culture myth
– Could have some research data to support it
• That is perhaps outdated
– Could be true, but we the researcher think it
isn’t
The alternate hypothesis
• College students do not have high rates of
casual sex
– Maybe we have qualitative interviews that
suggest casual sex is a myth
– Maybe we think that problems with STDs has
changed people’s behavior
Now, back to statistics
• Inferential statistics
– Making guesses about what is happening in
the population based on what we see in our
sample
– How can we do this
Type I and Type II error
• Hang on to your logic hats
• These make most sense when you know
some statistics
• This is just a conceptual introduction
Type I error
• When I believe that my alternate
hypothesis is supported
• But actually the support is a statistical
accident
• And actually I’m wrong.
Type I error
• I do a study
• I propose that people are smarter than
cats (this is my alternate hypothesis)
• My sample data do show that people are
smarter than cats
• But actually this is a statistical accident
• Cats actually are smarter than people
• This is a type I error
Type 2 error
• When, after my study, I believe that my
alternate hypothesis was NOT supported
• But actually the lack of support was a
statistical accident
– Often due to small sample size
• This is a type two error
Type I and type II error
• Science tends to focus on Type I error
• We agree that a chance of type I error 5%
of the time is OK
• Type 2 error is harder to predict exactly
– We usually agree that type 2 is OK 20% of the
time
• A more strict cutoff for Type I error is
probably good since we tend to favor our
own beliefs and think we are right
Type I and Type II error
are both bad
• Do you want to be the person who thinks
you have discovered the cure for HIV but
really you haven’t?
• Do you want to be the person who really
does discover the cure for HIV but
concludes you haven’t?
• Neither option is very appealing
The empirical rule
• Is a series of probability statements about
data
• Is based on how data occur within the
normal distribution
• The empirical rule forms the conceptual
basis for a lot of inferential statistics