POLS 3650 Lecture : February 5 2014 POLS 3650.docx
3 Apr 2014
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February 5 2014 POLS 3650 Lecture X
Causal Models
Overview
- What is statistical significance?
- Testing hypotheses
oType I and type II error
- Testing univariate hypotheses
- Bivariate analysis
oBivariate hypotheses (verbal)
oGraphic bivariate hypotheses: causal models
oMisspecification of bivariate relationship
What is statistical Significance? [1/2]
- Whenever we use a sample to generalize about a population, we nee to establish
how large the chance is that our findings are the product of randomness
oExample: Imagine a magician who claims he can magically ensure that all
his coin flips turn up tails
Even if he did not have this magic power there was a 50% chance
this would happen
o0.5*0..5= 0.25
•0.5*0.5*0.5= 0.125
•Etc.
- If we establish that this chance is small, we call our findings statistically
significant
oThe findings we find may be purely random
oIf chances of randomness are small than we have statistical significance
We wont say it’s randomness
What is Statistical Significance? [2/2]
- We express statistical significance as the probability (p) that we could reach the
same conclusion under the condition of randomness
- It is not the probability that the findings are the result of randomness
- It is not an indicator of how large or important our findings are
oIt only means that an indicator is an estimate of the probability that we
will find the conclusion we find if nothing was going in our sample
Formulating hypotheses
In the coin flipper example we can give an estimate (calculate)
how likely it would have happened if he wasn’t a magician
Testing Hypotheses [1/3]
- There are two hypotheses:
- An alternative hypothesis (
H1
)= expectation we want to investigate
oThe one we are actually interested in
oThe one we want to calcualte
o(‘The magician has magic powers’)
- Null hypothesis (
H0
)= there is no effect, no difference, no significant findings
oFormulate this basically the logical opposite of our research hypothesis
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